Analysis of the rainfall variability over temporal and spatial patterns: A case study in Adelaide, South Australia

Analysis of the rainfall variability over temporal and spatial patterns: A case study in Adelaide, South Australia | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Case Report Analysis of the rainfall variability over temporal and spatial patterns: A case study in Adelaide, South Australia Hoan To, Faisal Ahammed This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3834670/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Climate change has presented a tremendous impact on the weather patterns on Earth. Many studies conducted to investigate the changing patterns of meteorological data in Australia. This study aimed to investigate the variability of rainfall data over time and terrain in Adelaide, South Australia. The annual daily maximum rainfall (ADMR) data over a 40-year period in four stations was collected to identify the distribution of rainfall data across the time recorded. Moreover, the ADMR data in 2018 and elevation data across 86 stations were used to investigate the changing rainfall patterns over the terrain. Two non-parametric tests including Kruskal–Wallis, and Mann–Whitney were applied to perform the hypothesis analysis. Correlations, regression, and multivariate tests were performed to identify the relationship between variables. It was found that the ADMR data in four stations did not vary over the 40-year period from 1981 in Adelaide. However, there was a strong correlation between the extreme rainfall data in the year 2018 and elevation data in these stations. Results also suggested that it is relatively possible to use the elevation data to predict ADMR across Adelaide in certain years. Policymakers and researchers can use these tests for climate projections and extreme rainfall forecasts. Rainfall Kruskal–Wallis Mann–Whitney correlation regression Adelaide Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. Introduction Climate change has been one of the most major concerns in recent years. Many scientists suggest that extreme weather conditions might occur more frequently as the consequences of climate change [ 1 ]. Among contributing factors, rising global temperatures were found to be the most significant driver for the increase in the likelihood of climate-related phenomena such as wildfires [ 2 ], and severe droughts [ 3 ]. Scientists also provide evidence of these disasters related to the fields of meteorology, climatology, and hydrology in which precipitation presents a vital connection with governing moisture content in the hydrological cycle [ 4 ]. Many studies have shown that global warming may lead to more droughts due to decreased precipitation and increased evaporation in the 21st century [ 3 , 5 ]. For instance, under the climate change impacts, the precipitation level was predicted to decrease by mid-century in Ireland [ 6 ]. Precipitation deficits are also known as an initial condition to triggers droughts to occur; meteorological droughts progress over time to affect soil moisture, runoff, streamflow, and finally socioeconomic aspects [ 4 ]. Meanwhile, the extreme rainfall events that are bound to happen more frequently and intensely might partly be due to climate change and global warming [ 7 ]. A recent review showed that there was a significant increase in the total volume of rainfall in the rainy season during the last seven decades in Brazil [ 7 ]. Apart from that, a similar trend was found in southwest Taiwan where the extreme rainfall intensity and frequency has continuously increased and become unpredictable during the study period 1960–2017 [ 8 ]. In Southeastern Australia, a review of climate variability by Murphy & Timbal [ 9 ] indicated that a decreasing trend of rainfall was seen due to the effects of the El Nino-Southern Oscillation, highlighting the significant impacts of climate change. Few recent studies were carried out to investigate the rainfall trends over time in South Australia. Statistics showed that Adelaide experienced prolonged wet periods in the 1850s and 1920s with the wettest year occurring during 1992 due to a very wet austral spring [ 10 ]. This study found that the wettest Adelaide day was recorded on 6 February 1925 when 145.5 mm of rainfall was recorded, well-known as a Tropical Downpour in Adelaide. Several previous studies have identified rainfall characteristics, variability, and trends in South Australia. For instance, Chambers [ 11 ] found that the coastal regions in the southeast experienced an increase in rainfall over time while a decreasing trend was observed in the inland eastern regions in South Australia in the period 1900s to 2000s. Chowdhury & Beecham [ 12 ] found one station in Adelaide showing an increasing trend of monthly rainfall depth based on its relation to the southern oscillation index (SOI). Having said that, little is known about the recent trends and variability of rainfall in South Australia. Recent studies in Australia showed that they might be likely to stay uncertain. For example, the monthly rainfall in South Australia over the past 100 years was observed not having any consistent tendency or any changes in the seasonal patterns [ 13 ]. Recently, a notable trend of decreasing mean rainfall was seen in southwest and southeast Australia while an increase was observed in northwest Australia since the 1950s [ 14 ]. In addition, the rainfall variability in South Australia might be affected by seasonal climate factors. It was reported that the most robust decrease in rainfall was found in the winter while it was not particularly true for the other seasons, especially in the summer [ 15 ]. Although the question of the relationship between rainfall and spatial patterns remains, several studies in the past have revealed promising results. A study was conducted by Gergis & Ashcroft [ 16 ] in eastern New South Wales (NSW) over the 1788–2008 period to identify the relationship between droughts and wet years and El Nino–Southern Oscillation (ENSO). It was found that the relationship between the El Nino phenomenon and the rainfall in the coastal area is much stronger than that in the inland eastern NSW area, indicating that the rainfall can be significantly influenced by the location and climate conditions in Australia [ 16 ]. Some scientists suggested that there were upward and downward trends in the rainfall data observed in the regions across South Australia. Chowdhury et al. [ 17 ], for example, researched the trends and step changes in different locations in South Australia. Results showed that locations including Adelaide, Arid Lands, Alinytjara Wilinara, and Mount Lofty Ranges regions experienced increasing annual rainfall trends over the period of 100 years whereas decreasing trends were found in the rainfall data in Murray Darling Basin, Eyre Peninsula Southeast regions. Earlier, the study conducted by Chambers [ 11 ] discovered that both mean and median rainfall tended to increase from the north to the south in the state of South Australia for the study period in the 20th century. The summer rainfall dominated the winter rainfall in the northern stations while the opposite was true in the southern stations [ 11 ]. In addition, a recent study based on a spatial model for daily rainfall in South Australia indicated that there was a strong association between rainfall and climatic indicators related to spatial factors [ 18 ]. Although a relationship between rainfall and spatial patterns might exist in several locations across South Australia, a large uncertainty occurs. For instance, Ye & Ahammed [ 19 ] found that the factor of distance from the stations to the sea was proved to have an insignificant influence on the temperature and rainfall in South Australia though these data did vary according to station locations. To identify the relationship between climate data, several statistical hypothesis tests were normally used [ 19 ]. The purpose of hypothesis testing is to see whether an assumption or observation is true to describe the sample and population [ 20 ]. In other words, hypothesis testing determines how likely it is that the difference would be seen between two (or more) groups by chance alone if the null hypothesis were true [ 21 ]. Which, four hypothesis tests are commonly in use, namely t-test, ANOVA, Mann-Whitney, and Kruskal-Wallis [ 19 ]. T-test is a type of statistical test used to compare the means of two groups [ 21 ]. Researchers suggest that the T-test requires the scale data to be normally distributed [ 19 ]; hence, it is a type of parametric test [ 22 ]. Likewise, ANOVA is also a parametric method and is used to determine differences among the means of three or more input groups [ 20 ]. On the other hand, Mann–Whitney and Kruskal–Wallis tests are well-known as non-parametric statistical tests [ 19 ]. Mann-Whitney U test is a test that assesses the differences between two groups on a single with no specific distribution [ 23 ]. The Mann-Whitney U test is rather similar to the t-test for identifying whether two sample groups are from a single population; hence, the Mann-Whitney U test is regarded as the non-parametric version of the t-test [ 24 ]. Kruskal–Wallis test is known as a test of three or more independently sampled groups on a single and the non-parametric version of ANOVA [ 24 – 25 ]. Although it is claimed to be suitable for non-normally distributed data, there is no specific requirement of the distribution of data for analyzing hypothesis by using this test [ 24 ]. There were several applications of these statistical tests in research. Ahammed & Smith [ 26 ], for instance, investigated the association between learning online engagement and academic achievement for students at the University of South Australia by using non-parametric Mann–Whitney and Kruskal–Wallis tests. They found that the distribution of student activities on course sites across several categories namely genders, grades, and origin of students showed almost no difference [ 26 ]. In terms of applications of statistical tests in the environment and climate field, Ye & Ahammed [ 19 ] used Mann-Whiney, Krukal-Wallis, and Correlations tests to determine the relationship between annual daily maximum temperature and annual daily maximum rainfall in South Australia. They suggested that temperatures and rainfall in South Australia varied according to the distance to the sea. The correlation test measures the relation strength of the relationship between variables [ 20 ]. The most important fact is that correlation does not determine causation, meaning that each variable does not cause the other [ 27 ]. Furthermore, some research used linear regression analysis to predict a phenomenon based on contributing factors. He, Shirowzhan & Pettit [ 28 ], for instance, used regression analysis to explore how meteorological factors (temperature, precipitation, wind speed) and natural factors (slope, soil moisture, vegetation, NDVI) influence bushfires in NSW Australia while spatial correlation analysis was applied to support to create a wildfire susceptibility map in Sydney by sixteen wildfire-related factors [ 29 ]. In addition, Bayesian Generalized Least Squares Regression (BGLSR), another method, was applied to construct a regression equation to predict rainfall data at ungauged stations in Australia [ 30 ]. Since the number of applications of using a statistical test for analyzing rainfall data in the City of Adelaide remains confined, this study might be helpful for further research in the study area in the future. This paper is a case study of the City of Adelaide to investigate the association between rainfall data and other factors including time and elevation. The Kruskjal-Wallis and Mann-Whitney tests were performed for hypothesis testing. The first objective of the research is to identify the variability of the extreme rainfall data over the recorded time in the City of Adelaide. In addition, it is aimed to observe how the rainfall data vary over the space by using the terrain data. The annual daily maximum rainfall (ADMR) data in four stations was collected over a 40-year period to identify the relationship between ADMR and time data. Furthermore, the ADMR in the year 2018 and elevation data across 86 stations were collected to determine how the rainfall data vary spatially. By understanding the variability of rainfall data, policymakers and researchers can use the results for climate projections and extreme rainfall predictions in any location across Adelaide. 2. Study area and data 2.1 Study area The study area is the City of Adelaide with its centroid coordinates of -34.94 o South, 138.73 o East. Having an area of 3.260 km², Adelaide is the capital and largest city in the State of South Australia (SA), Australia. It is the fifth-most populous city in Australia with a population of more than 1.3 million people [ 31 ]. Being a coastal city situated in southeast Australia, Adelaide has a Mediterranean climate with hot dry summers and mild winters [ 32 ]. The hottest months fall into January and February with the average daily maximum temperature of 29oC compared to about 15oC in the winter months [ 32 ]. 2.2 Data The Annual Daily Maximum Rainfall (ADMR) data over a 40-year period (1981–2018) in four stations was collected to use as the SPSS input data to investigate the variability of rainfall data over time. Four random stations from different elevation ranges (from 2 m to over 500m) and locations (1 station near the sea, 3 stations on land) were chosen as shown in Fig. 1 . In this research, the ADMR data was collected from the Australian Bureau of Meteorology (BOM) website. The detail of data collection is shown in Table 1 , and Appendix A. Meanwhile, the Annual Daily Maximum Rainfall data in one chosen year and elevation data in 86 stations out of 269 stations across the study area were collected to investigate the changing rainfall patterns over the terrain. In this study, the ADMR_2018 data of the year 2018 was chosen since this year had the most up-to-date data; and it was recorded with a large number of stations. The elevation data was derived from the 3-second SRTM Derived Digital Elevation Model (DEM) Version 1.0. The 3-second DEM was produced for use by the government and the public under Creative Commons attribution. The elevation value in each station was derived by the GIS applications in ArcGIS. The detail of the data is shown in Table 2 , Fig. 2 , and Appendix B. The collected ADMR and elevation data are in the scale measurement. Table 1 The details of the ADMR data and stations over 40-year period Weather station name Adelaide airport Adelaide (Tea tree gully council) Meadows Ashton Co-op Station number 23034 23748 23730 23803 Data ADMR ADMR ADMR ADMR Elevation (m) 2.0 145.0 358.0 553.0 Recorded time 1981–2018 1981–2018 1981–2018 1981–2018 Coordinates -34.94 S, 138.53 E -34.83 S, 138.70 E -35.18 S, 138.76 E -34.94 S, 138.73 E Table 2 The details of ADMR data and elevation data across Adelaide in 2018 Data ADMR_2018 (mm) Elevation (m) Year of interest 2018 - The number of stations 86 86 3. Methodology In this study, several statistical tests were performed in the software SPSS. A flowchart of the methodology is provided in Fig. 3 . Before performing the hypothesis tests to identify the variability of the data, the descriptive and normality tests were prepared. In which, descriptive analytics is the first step of data analysis. It gives information about the summary of historical data, and it shows whether additional data is needed for predictive modelling [ 20 ]. Afterward, the normality test was performed. Testing the normality of data is a prerequisite in the hypothesis testing procedure [ 20 ]. Its result identifies whether the data is non-parametric or parametric, which provides an indication to choose the suitable type of hypothesis test. For testing the distribution patterns of the data, the number of samples in the population determines which tests can be used. Specifically, the Shapiro-Wilk is used to interpret the result for the population having a small number of samples ( 50 samples) [ 33 ]. The next step in analysing data is performing statistical hypothesis tests. A hypothesis test is a statistical test that allows researchers to use sample data to evaluate a hypothesis about a population [ 34 ]. Depending on the distribution pattern and the number of variables, several hypothesis tests such as t-test, ANOVA, Man-Whitney, and Kruskal-Wallis are valid in use as shown in Table 4 . As discussed, while t-test and ANOVA are parametric tests, the Man-Whitney and Kruskal-Wallis tests are used for non-parametric data or the normality unsure [ 19 ]. In addition, the t-test and Mann-Whitney can be used for two samples or two variables, whereas ANOVA and Kruskal-Wallis require the data to have the number of comparison groups of 3 or more [ 20 , 22 , 33 , 34 ]. In this study, two groups of ADMR data corresponding to two different periods of time were used to identify the relationship between rainfall data over time. Meanwhile, the ADMR data was also divided into 3 groups or more based on elevation level to investigate the variability of rainfall data over the terrain. After the hypothesis tests (Mann-Whitney and Kruskal-Wallis), the relationship or association between dependent and independent variables can be identified. If the association between variables is not statistically significant, it is impossible to identify the significant correlations between them. As such, the testing process can be terminated. Otherwise, the correlation test can be performed to ensure that the assumption is correct. The correlation test was developed to detect the presence of a mathematical relation between two or more variables [ 35 ]. If the correlation between them is not statistically significant, the procedure will be stopped; and the decision will be made. On the other hand, if there is a statistically significant correlation between variables, the Regression test will be performed. The result of regression is an equation employing the correlation coefficient to predict one variable from one another [ 36 ]. It is clear that the accuracy of the prediction depends on the magnitude of the correlation coefficient [ 36 ]; hence, Regression is also a platform to reconfirm the significance level of the test. Finally, the multivariate analysis was performed. It is a technique that investigates the relationship between two or more independent variables and a single dependent variable [ 20 ]. The purpose of this test is to confirm the consistency in the results from previous tests. After this test, the final decision will be made. 4. Selection of statistical tests The Statistical Package for the Social Sciences (SPSS), version 28.0 was used to perform the data analysis. Table 3 and Table 4 show the hypothesis tests and their data requirements. The Chi-square, Cramer’s V, and Phi tests need both independent and dependent data in categorical scales [ 19 – 20 ]. The Mann-Whitney, Kruskal-Wallis, t-test, and ANOVA tests require dependent variable in scale measurement and independent variables to be categorical data such as groups [ 20 ]. Correlation and regression, on the other hand, use both variables to be in numeric (scale) data [ 20 ]. Depending on the nature of the investigation, there is a wide range of statistics. However, the result of any statistical test is a P value [ 37 ]. According to Whitley & Ball [ 37 ], the ‘P’ stands for probability, meaning that it measures how likely it is that any observed difference between groups is due to change. As a probability, P can take any value between 0 and 1 [ 37 ]. The closer value to 0, the more unlikely the observed differences is due to chance; meanwhile, a P value close to 1 indicates there is no difference between groups [ 37 ]. In a hypothesis test, the p-value is the smallest level that is to reject the null hypothesis [ 20 ]. While there are three conventional levels of significance that are normally in use such as P ≤ 0.05; P ≤ 0.01; and P ≤ 0.001 [ 36 ]. McCarthy et al. [ 20 ] claimed that it is usually set to 5% or 0.05. Hence, the value of 0.05 was used in this research. If the p-value is smaller than 0.05, the null hypothesis is rejected [ 20 ]. Table 3 Hypothesis tests for different data types Independent variable (data) Dependent variable (data) Hypothesis tests Categorical Categorical Chi-square, Cramer’s V and Phi Categorical Scale t-test, Mann-Whitney, ANOVA, Kruskal-Wallis Scale Scale Correlation, regression Table 4 Dataset requirements for hypothesis tests Type of test No. of comparison groups Hypothesis test Parametric 2 t-test 3 or more ANOVA Non-parametric 2 Mann- Whitney 3 or more Kruskal-Wallis It was shown from the normality test results that the ADMR, ADMR_2018, and Elevation data were not normally distributed. Since the t-test and ANOVA require the parametric data, they were both invalid for hypothesis testing. Therefore, the Mann-Whitney and Kruskal-Wallis tests were chosen for checking hypotheses. Subsequently, the hypothesis dataset was prepared. As mentioned above, the Mann-Whitney was used to identify the relationship between ADMR data over time. The ADMR data from 1979 to 1998 was recoded as 1, and data from 1999 to 2018 was recoded as 2. Meanwhile, based on the elevation levels of stations, there are two Kruskal-Wallis tests prepared to identify the association between rainfall data and elevation groups. In the first Kruskal-Wallis test, the 40-year ADMR data was categorized as 1 = Station 23034/ Elevation: 2m; 2 = Station 23748/ Elevation: 145 m; 3 = Station 23730/Elevation: 358 m; 4 = Station 23803/ Elevation: 553 m. For the second Kruskal-Wallis test, the ADMR_2018 data was categorized as 1 = Elevation: 0-200 m, 2 = Elevation: 200–400 m, 3 = Elevation: 400–685 m. Elevation ranges were chosen and based on increasing values which helps determine how the distribution of rainfall data changes in different ranges of elevation. The detailed group information can be found in Table 5 . Table 5 The groups for hypothesis test Test Dependent variables (Data) Independent variables (Groups) Description Mann–Whitney 40-year ADMR data Group 1 Time: 1979–1998 Group 2 Time: 1999–2018 Kruskal-Wallis 40-year ADMR data Group 1 Station 23034/ Elevation: 2 m Group 2 Station 23748/ Elevation: 145 m Group 3 Station 23730/ Elevation: 358 m Group 4 Station 23803/ Elevation: 553 m Kruskal-Wallis ADMR_2018 data Group 1 Elevation: 0-200 m Group 2 Elevation: 200–400 m Group 3 Elevation: 400–685 m Afterwards, the ADMR_2018 and Elevation data were used to perform the correlation and regression tests. Pearson’s correlation and Spearman’s correlation are known as two types of correlation tests. Spearman’s rank and Pearson’s correlations are based on linear relationships between variables [ 19 ]. Pearson correlation is used if both variables are parametric data while Spearman’s rho is applied if one of two variables is non-parametric data [ 38 ]. Since the normality test showed that the ADMR, ADMR_2018, and Elevation data were non-parametric, the Spearman’s rho result was employed. In this study, two Correlation tests were performed, including the relationship between ADMR and Year data, and ADMR_2018 and Elevation data. The final stage in the research is multivariate analysis. In this analysis, the ADMR_2018 data was split into two groups to perform a multivariate hypothesis test using Kruskal-Wallis. Group 1 was defined as a station number less than 23733; Group 2 was defined as a station number more than 23733. The details of the dataset are shown in Table 6 . Table 6 The dataset for multivariate analysis Test Dependent variables (Data) Independent variables (Groups) Description Split data Description Multivariate analysis for Kruskal-Wallis ADMR data (2018) Group 1 Elevation: 0-200 m Group 1 Station number 23733 Group 3 Elevation: 400–685 m 5. Null, alternative hypotheses The null and alternative hypotheses for the Kruskal–Wallis and Mann–Whitney tests were prepared by the tests themselves in SPSS itself [ 19 ]. In the hypothesis test, the significant value determines whether the hypothesis is rejected or retained. The significant level for hypothesis testing in SPSS is 0.05. It means that if the significant value (p-value) is less than 0.05, the null hypothesis is rejected [ 20 ]. For the Kruskal–Wallis test, the null hypothesis (H o ) was expressed as the distribution of ADMR is the same across categories of time groups; the alternative hypothesis (H A ) was expressed as the distribution of ADMR is not the same across categories of time groups. For the Mann–Whitney test, the null hypothesis (H o ) was expressed as the distribution of ADMR is the same across categories of station groups; the alternative hypothesis (H A ) was expressed as the distribution of ADMR is not the same across categories of station groups. 6. Results and discussions 6.1 The normality test The result of the frequency analysis is shown in Table 7 . As can be seen in the table, there were differences between the mean, median, and mode values. Hence, these three data might be not normally distributed. The normality test result in Table 8 was used to confirm this assumption. Table 7 The result of frequency analysis ADMR ELEVATION ADMR_2018 Valid 160 86 86 Missing 0 0 0 Mean 40.5712 257.7558 32.4233 Median 38 296 32 Mode 26.00a 10.00a 26.00a Std. Deviation 17.27621 179.1371 11.46535 Skewness 1.155 0.033 0.571 Std. Error of Skewness 0.192 0.26 0.26 Kurtosis 1.919 -1.194 -0.099 Std. Error of Kurtosis 0.381 0.514 0.514 Minimum 13.3 6 13.3 Maximum 107.6 675 65.2 Table 8 The result of normality test Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk Statistic df Sig. Statistic df Sig. ADMR (4 stations) .086 160 .006 .925 160 .000 ELEVATION (86 stations) .133 86 .001 .927 86 .000 ADMR_2018 (86 stations) .080 86 .200 * .965 86 .021 The ADMR data is comprised of the data in four stations, and each station has 40-year data values. As a result, the number of ADMR samples in the normality test is 160 values (> 50). Therefore, the Kolmogorov-Smirnova test was used to interpret the result. Meanwhile, the significant value (p-value) in the normality test was 0.05 as the common value [ 20 ]. As such, if the significant value is less than 0.05, the data is non-parametric. As can be seen from Table 8 , the significant value is 0.006, which is smaller than 0.05. Therefore, the ADMR data were not normally distributed. Similarly, the values of the Kolmogorov-Smirnova test were also used to determine the normality result for Elevation and ADMR_2018 data since these two types of data have 86 samples. The significance for Elevation and ADMR_2018 data were 0.001 and 0.2, respectively, and both were smaller than 0.05. Therefore, the Elevation and ADMR_2018 data were also not normally distributed. In addition, the Q-Q plot results showed that the data values in all three graphs were not entirely close to diagonal line, claiming that all these data were non-parametric. 6.2 Mann-Whitney U result The Mann-Whitney test is to check the differences between the ADMR data and year groups. The result of the test is shown in Table 9 . Table 9 The Mann-Whitney U result Hypothesis Test Summary Null Hypothesis Test Sig. a,b Decision 1 The distribution of ADMR is the same across categories of Year groups. Independent-Samples Mann-Whitney U Test .309 Retain the null hypothesis. The null hypothesis is never accepted; the result is either fail to reject or reject it [ 20 ]. In other words, if the p-value is bigger than 0.05, the result fails to reject the null hypothesis [ 20 ]. In this study, the result of the Mann-Whitney test showed that the significant value is 0.309, which is obviously bigger than 0.05. Therefore, the decision for the hypothesis test is to retain the null hypothesis. As such, the distribution of ADMR data is the same across categories of year groups. There is no difference between the ADMR data and Year groups. Therefore, it was claimed that the ADMR data does not vary temporally. In this case, the testing procedure can be terminated. The decision can be made as the ADMR data does not vary over the recorded time. In this study, to ensure that the result of Mann-Whitney test is accurate, a correlation test was conducted to check the consistency of these two tests. The result can be found in Table 14 . 6.3 Kruskal-Wallis test This test is to identify whether there is a difference between the ADMR data and the elevation groups. The result is shown in Table 10 . Table 10 Hypothesis testing using Kruskal-Wallis for 40-year ADMR data Hypothesis Test Summary Null Hypothesis Test Sig. a,b Decision 1 The distribution of ADMR is the same across categories of station groups. Independent-Samples Kruskal-Wallis Test .000 Reject the null hypothesis. As mentioned above, if the p-value is smaller than 0.05, the null hypothesis is rejected [ 20 ]. The result of the Kruskal-Wallis test showed that the significant value is 0.000, which is smaller than 0.05. Therefore, the decision is rejecting the null hypothesis. Specifically, the distribution of ADMR data is not the same across categories of four station/ elevation groups. Hence, there is a difference between ADMR data over elevation groups. The pairwise comparisons in Table 11 claimed that there is only one pair of sample groups having a significance value bigger than 0.05. That is the pair group 1–2 where the p-value stands at 1.0, meaning there is no difference between ADMR data in this pair group. However, the other pair groups all have significant values smaller than 0.05. Therefore, there is a relationship between them. Table 11 The pairwise comparisons of station groups for 40-year ADMR data Pairwise Comparisons of station groups Sample 1-Sample 2 Test Statistic Std. Error Std. Test Statistic Sig. Adj. Sig. a 2.00–1.00 4.800 10.360 .463 .643 1.000 2.00–3.00 -40.513 10.360 -3.911 .000 .001 2.00–4.00 -72.288 10.360 -6.978 .000 .000 1.00–3.00 -35.713 10.360 -3.447 .001 .003 1.00–4.00 -67.488 10.360 -6.514 .000 .000 3.00–4.00 -31.775 10.360 -3.067 .002 .013 The results of hypothesis testing using ADMR data in the four stations above indicated that there is a relationship between the ADMR and elevation data, which means that the ADMR data might spatially vary with the elevation data. To check this assumption, another Kruskal-Wallis test was performed by using the ADMR data in one year (ADMR_2018) and the elevation data in stations across the study area. In this research, the year 2018 for the one-year ADMR data was chosen since this year satisfies the availability and quality of data. Regarding the year 2018 data, the latest data can be obtained. In terms of the elevation data, 86 stations out of 269 stations across the City of Adelaide were used, each station provided one data of elevation. Table 12 Hypothesis testing using Kruskal-Wallis for ADMR_2018 data Hypothesis Test Summary Null Hypothesis Test Sig. a,b Decision 1 The distribution of ADMR_2018 is the same across categories of Elevation groups. Independent-Samples Kruskal-Wallis Test .000 Reject the null hypothesis. The result for this Kruskal-Wallis test in Table 12 showed that the significant value is 0.000, which is clearly smaller than 0.05. The decision is to reject the null hypothesis. It means that the distribution of ADMR_2018 data is not the same across categories of three elevation groups. Therefore, there is an association between the ADMR_2018 data and elevation groups. The difference between groups and pairwise comparisons are shown in Table 10 and Table 13 . Table 13 The pairwise comparisons of elevation groups for the ADMR_2018 data Pairwise Comparisons of Elevation groups Sample 1-Sample 2 Test Statistic Std. Error Std. Test Statistic Sig. Adj. Sig. a 1.00–2.00 -23.470 6.158 -3.811 .000 .000 1.00–3.00 -40.407 6.999 -5.774 .000 .000 2.00–3.00 -16.937 7.161 -2.365 .018 .054 6.4 Correlations As mentioned above, the first correlation test was performed to examine the consistency of Mann-Whitney U and correlations tests. Since the ADMR data is non-parametric, Spearman's rho table was used to interpret the result. One common way to determine the strength of relationships between two variables is using the scatter plot [ 20 ]. The more points are close to the fitting line, the more strength association has. Additionally, the value of the correlation coefficient (r) also represents the strength of the association; it ranges from − 1 to 1 [ 20 ]. The closer the correlation coefficient (r) to zero suggests no or weak correlation, whereas the closer the correlation coefficient (r) to either − 1 or 1, the greater the association strength [ 20 ]. If the significant value (p-value) in the Correlations test is smaller than 0.01, it indicates the test is statistically significant. As can be seen from Table 14 , the Correlation coefficient value is -0.046, which is very close to 0. Therefore, it indicates no linear relationship exists between ADMR and Year data. In addition, the significant value is 0.559 which is significantly bigger than 0.01. Hence, the relationship between the two data is realatively weak. In short, it can be observed that the Mann-Whitney U and Correlations tests showed consistency in their results. The decision was made as the ADMR data does not vary according to the time of the data. Table 14 The result of Correlations test for ADMR and Year data Correlations ADMR YEAR Spearman's rho ADMR Correlation Coefficient 1.000 -0.046 Sig. (2-tailed) . .559 N 160 160 YEAR Correlation Coefficient -0.046 1.000 Sig. (2-tailed) .559 . N 160 160 Following the result from the Kruskal-Wallis test above, this second Correlations test is to determine the size and direction of association between the ADMR_2018 and Elevation data. Since the ADMR_2018 and Elevation data are not normally distributed, Spearman’s rho table was used to interpret the results. The result is shown in Table 15 . Table 15 The result of Correlations test for ADMR_2018 and Elevation data Correlations ELEVATION ADMR_2018 Spearman's rho ELEVATION Correlation Coefficient 1.000 .679 ** Sig. (2-tailed) . .000 N 86 86 ADMR_2018 Correlation Coefficient .679 ** 1.000 Sig. (2-tailed) .000 . N 86 86 The Spearman’s is based on linear relationships between variables and its value is measured between − 1 and + 1 [ 20 ]. Looking at Table 15 , the correlation coefficient value is 0.679, which is not too close to 0. Therefore, the correlation between the ADMR_2018 and elevation data is significantly strong. In addition, the significant value (p-value) is 0.000, which is clearly smaller than 0.01. As a result, the test is statistically significant. It is clear to see that these two criteria showed consistency in their result. Therefore, it is reasonable to claim that there is a strong relationship between the ADMR_2018 and Elevation data. In the graph, several scatter points tended to distribute close to each other and close to the fitting line. The R 2 value is relatively significant (0.401), indicating that the correlation between the two variables is relatively strong. The line had the slope > 0; therefore, the relationship is positive. In short, the results from the Correlations and Kruskal-Wallis tests were the same. 6.5 Regression The result from the correlations test showed a strong relationship between the ADMR_2018 and elevation. Based on this validation, the regression was considered to identify how the ADMR data changes corresponding to the Elevation. The equation between two variables can be determined by: Y = a + bX. Where, Y is dependent (target) variable; X is independent (input) variable; b is a slope of the best-fit line (Beta coefficient); and a is the point at which the line crosses the Y-axis (intercept). In this research, the ADMR (mm) is considered as the dependent variable, while the Elevation (m) is considered as independent the variable. Therefore, the equation can be substituted as below. ADMR_2018 = a + b*Elevation The value of a and b can be determined as the result from coefficient below. Table 16 The result of coefficients test Coefficients a Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 21.973 1.693 12.979 .000 ELEVATION .041 .005 .633 7.503 .000 a. Dependent Variable: ADMR_2018 Firstly, the significance value is 0.000 < 0.05, hence, it showed that the test is statistically significant. Furthermore, the result illustrates that the coefficient Beta (that is Pearson’s) is equal to 0.633, which is not close to 0. Hence, it showed the strong positive associations between the ADMR_2018 and Elevation variables. After the test, the a and b values can be obtained as 21.97 and 0.04, respectively. Therefore, the regression equation is formed as ADMR_2018 = 21.97 + 0.04*Elevation. 6.6 Multivariate analysis The result of Multivariate analysis using Kruskal-Wallis is shown in Table 17 . The significant values in the two split groups were 0.000 and 0.001, which are both smaller than 0.05. As a result, the hypothesis is rejected. The result was expressed as the distribution of ADMR_2018 is not the same across categories of Elevation groups. These differences can be observed in Fig. 11 . This result is the same as the Kruskal-Wallis test above. Thus, the Multivariate analysis reconfirmed the validation of the Kruskal-Wallis test. It is reasonable to conclude that the results from the Kruskal-Wallis, Correlations, and Regression tests are credible. Table 17 Multivariate analysis for hypothesis testing using Kruskal-Wallis Test Hypothesis Test Summary MC station number Null Hypothesis Test Sig. a,b Decision 1.00 1 The distribution of ADMR_2018 is the same across categories of Elevation groups. Independent-Samples Kruskal-Wallis Test .000 Reject the null hypothesis. 2.00 1 The distribution of ADMR_2018 is the same across categories of Elevation groups. Independent-Samples Kruskal-Wallis Test .001 Reject the null hypothesis. 7. Conclusions This study is to investigate the variability of rainfall over time and terrain in the City of Adelaide. Several statistical tests were performed, namely Kruskal–Wallis, Mann–Whitney, correlation, and regression tests. It was found that the Annual Daily Maximum Rainfall (ADMR) data showed no significant difference over the recorded time. Meanwhile, the elevation has a significant influence on the ADMR data. The research has shown that the distributions of ADMR across categories of elevation groups were different by using Mann–Whitney and Kruskal-Wallis tests. Plus, there was a strong correlation between ADMR and elevation data. Although there was a relationship, there is no evidence to claim that the elevation causes the variability of rainfall data. However, it is relatively possible to use elevation data to predict ADMR data in Adelaide. It is important to note that the application of the Kruskal–Wallis, Mann–Whitney tests in rainfall data is not common. Hence, more research needs to be done to fully understand the extreme rainfall patterns in the study area. In further research, it is necessary to collect more data in the long time series and different locations to obtain comprehensive results. Policymakers and researchers can use the results for climate projections and extreme rainfall predictions in any location across Adelaide. Declarations Author Contributions: Conceptualization and methodology, H.T and F.A; Writing original draft preparation, H.T; Feedback and advice, F.A. All authors have read and agreed to the published version of the manuscript. Ethical Approval: Not applicable. Funding: Not applicable. Availability of data and materials: This paper used the Climate data online from the Australian Government Bureau of Meteorology (BOM) website. Acknowledgments: The authors would like to acknowledge the generous provision of data by the Australian Government Bureau of Meteorology (BOM). 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J Hydrol 527:62–76. https://doi.org/10.1016/j.jhydrol.2015.04.043 Australian Bureau of Statistics (2018) Annual report 2017-18 , ABS Website, accessed 11 December 2023 Varghese, BM, Barnett, AG, Hansen, AL, Bi, P, Hanson-Easey, S, Heyworth, JS, … Pisaniello,DL 2019, ‘The effects of ambient temperatures on the risk of work-related injuries and illnesses:Evidence from Adelaide, Australia 2003–2013’, Environmental Research , vol. 170, pp. 101–109. https://doi.org/10.1016/j.envres.2018.12.024 Mishra P, Singh U, Pandey C, Mishra P, Pandey G (2019b) ‘Application of student’s t-test, analysis of variance, and covariance’, Annals of Cardiac Anaesthesia , vol. 22, no. 4, p. 407. https://doi.org/10.4103/aca.ACA_94_19 Frederick G, Larry W (2017) Statistics for the behavioral sciences , 10th edition, Cengage Learning, 20 Channel Center Street, Boston, MA 02210, USA Oosterbaan RJ (1994) Drainage Principles and Applications , Second revised edition, Wageningen, The Netherlands Ho R (2017) Understanding Statistics for the Social Sciences with IBM SPSS, 1st edn. Chapman and Hall/CRC Whitley E&, Ball J (2002) ‘Statistics review 3: Hypothesis testing and P values’, Critical Care , vol. 6, no. 3, pp. 222–225. https://doi.org/10.1186/cc1493 Hauke J&, Kossowski T (2011) ‘Comparison of Values of Pearson’s and Spearman’s Correlation Coefficients on the Same Sets of Data’, QUAGEO , vol. 30, no. 2, pp. 87–93. https://doi.org/10.2478/v10117-011-0021-1 Australian Government Bureau of Meteorology (BOM), Climate data online, http://www.bom.gov.au/climate/data/ , accessed 13 June 2023 Additional Declarations No competing interests reported. Supplementary Files Appendix.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3834670","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Case Report","associatedPublications":[],"authors":[{"id":266382513,"identity":"02a1548c-22ef-4aea-9c6a-899160bff93c","order_by":0,"name":"Hoan To","email":"data:image/png;base64,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","orcid":"","institution":"Sustainable Infrastructure and Resource Management (SIRM), UniSA STEM, University of South Australia, Mawson Lakes, SA 5095","correspondingAuthor":true,"prefix":"","firstName":"Hoan","middleName":"","lastName":"To","suffix":""},{"id":266382514,"identity":"0f74208f-47bc-4acc-ad86-c25289394f00","order_by":1,"name":"Faisal Ahammed","email":"","orcid":"","institution":"Sustainable Infrastructure and Resource 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area\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/d0acf40e88c2335faf16b703.png"},{"id":49542240,"identity":"6a591a8d-4f2a-4b42-9b5b-3c39579f9ecf","added_by":"auto","created_at":"2024-01-12 17:32:42","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":252347,"visible":true,"origin":"","legend":"\u003cp\u003eThe terrain data and location of 86 stations across the study area.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/b6b5dd199c3041ff0a72cec8.png"},{"id":49542231,"identity":"2bdf9b01-fa75-42bf-8b26-f223ba67a0d8","added_by":"auto","created_at":"2024-01-12 17:32:41","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":144009,"visible":true,"origin":"","legend":"\u003cp\u003eFlow chart of methodology\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/f91979b658967d6ffc8058bd.png"},{"id":49543203,"identity":"6b812208-2747-4df7-8496-5e9668acf62c","added_by":"auto","created_at":"2024-01-12 17:40:41","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":23393,"visible":true,"origin":"","legend":"\u003cp\u003eThe normal Q-Q Plot of ADMR data in four stations within 40 years\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/906f84db0419f6a6b95eb8f9.png"},{"id":49543201,"identity":"af6b043f-956f-4457-b078-4f37fa6041b8","added_by":"auto","created_at":"2024-01-12 17:40:41","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":24650,"visible":true,"origin":"","legend":"\u003cp\u003eThe normal Q-Q plot of Elevation data for 86 stations in 2018\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/e44eaa80195ffcafc483001a.png"},{"id":49542241,"identity":"6a379455-2062-407b-9857-492f2ac35d75","added_by":"auto","created_at":"2024-01-12 17:32:42","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":23066,"visible":true,"origin":"","legend":"\u003cp\u003eThe normal Q-Q plot ADMR data for 86 stations in 2018\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/f103f51b3d07ee27849ce273.png"},{"id":49543200,"identity":"4305b880-f251-4707-89d7-82dd98e32daa","added_by":"auto","created_at":"2024-01-12 17:40:41","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":27140,"visible":true,"origin":"","legend":"\u003cp\u003eThe Mann-Whitney U result\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/81dcbf605ae6b4103be81053.png"},{"id":49542233,"identity":"3aa48cbf-1310-4c41-9bfb-4cc036ac959c","added_by":"auto","created_at":"2024-01-12 17:32:41","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":46613,"visible":true,"origin":"","legend":"\u003cp\u003eKruskal-Wallis test results for 40-year ADMR data\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/356ec22e11bf1269f456ee57.png"},{"id":49542237,"identity":"f1822bc4-7200-4a35-8e6c-8c5682c487bf","added_by":"auto","created_at":"2024-01-12 17:32:41","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":41454,"visible":true,"origin":"","legend":"\u003cp\u003eKruskal-Wallis test results for ADMR_2018 data\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/bea16e294fcd88ff6eb125c4.png"},{"id":49544493,"identity":"c3989afa-88a7-4af1-a81d-749009e41039","added_by":"auto","created_at":"2024-01-12 17:48:41","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":35969,"visible":true,"origin":"","legend":"\u003cp\u003eThe scatter graph for ADMR_2018 and elevation data\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/311a6faeef15dce58a02b16c.png"},{"id":49542239,"identity":"5eb2c096-fe72-4735-a5c8-033c244c71e4","added_by":"auto","created_at":"2024-01-12 17:32:42","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":88090,"visible":true,"origin":"","legend":"\u003cp\u003eMultivariate analysis results for ADMR_2018 data\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/e0a974c8d90705d02c452ffc.png"},{"id":50180620,"identity":"980ae1bd-e949-4620-a279-ca82c959b06d","added_by":"auto","created_at":"2024-01-25 18:07:23","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1283961,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/ff83c315-d45f-4dff-8c8e-44608e51737e.pdf"},{"id":49543199,"identity":"456d0210-aeb6-4247-9345-aa9177ba69c6","added_by":"auto","created_at":"2024-01-12 17:40:41","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":33680,"visible":true,"origin":"","legend":"","description":"","filename":"Appendix.docx","url":"https://assets-eu.researchsquare.com/files/rs-3834670/v1/06c6aa73aeb1c2e99bea101b.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Analysis of the rainfall variability over temporal and spatial patterns: A case study in Adelaide, South Australia","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eClimate change has been one of the most major concerns in recent years. Many scientists suggest that extreme weather conditions might occur more frequently as the consequences of climate change [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Among contributing factors, rising global temperatures were found to be the most significant driver for the increase in the likelihood of climate-related phenomena such as wildfires [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], and severe droughts [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Scientists also provide evidence of these disasters related to the fields of meteorology, climatology, and hydrology in which precipitation presents a vital connection with governing moisture content in the hydrological cycle [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Many studies have shown that global warming may lead to more droughts due to decreased precipitation and increased evaporation in the 21st century [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. For instance, under the climate change impacts, the precipitation level was predicted to decrease by mid-century in Ireland [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Precipitation deficits are also known as an initial condition to triggers droughts to occur; meteorological droughts progress over time to affect soil moisture, runoff, streamflow, and finally socioeconomic aspects [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Meanwhile, the extreme rainfall events that are bound to happen more frequently and intensely might partly be due to climate change and global warming [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. A recent review showed that there was a significant increase in the total volume of rainfall in the rainy season during the last seven decades in Brazil [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Apart from that, a similar trend was found in southwest Taiwan where the extreme rainfall intensity and frequency has continuously increased and become unpredictable during the study period 1960\u0026ndash;2017 [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. In Southeastern Australia, a review of climate variability by Murphy \u0026amp; Timbal [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] indicated that a decreasing trend of rainfall was seen due to the effects of the El Nino-Southern Oscillation, highlighting the significant impacts of climate change.\u003c/p\u003e \u003cp\u003eFew recent studies were carried out to investigate the rainfall trends over time in South Australia. Statistics showed that Adelaide experienced prolonged wet periods in the 1850s and 1920s with the wettest year occurring during 1992 due to a very wet austral spring [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. This study found that the wettest Adelaide day was recorded on 6 February 1925 when 145.5 mm of rainfall was recorded, well-known as a Tropical Downpour in Adelaide. Several previous studies have identified rainfall characteristics, variability, and trends in South Australia. For instance, Chambers [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] found that the coastal regions in the southeast experienced an increase in rainfall over time while a decreasing trend was observed in the inland eastern regions in South Australia in the period 1900s to 2000s. Chowdhury \u0026amp; Beecham [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] found one station in Adelaide showing an increasing trend of monthly rainfall depth based on its relation to the southern oscillation index (SOI). Having said that, little is known about the recent trends and variability of rainfall in South Australia. Recent studies in Australia showed that they might be likely to stay uncertain. For example, the monthly rainfall in South Australia over the past 100 years was observed not having any consistent tendency or any changes in the seasonal patterns [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Recently, a notable trend of decreasing mean rainfall was seen in southwest and southeast Australia while an increase was observed in northwest Australia since the 1950s [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. In addition, the rainfall variability in South Australia might be affected by seasonal climate factors. It was reported that the most robust decrease in rainfall was found in the winter while it was not particularly true for the other seasons, especially in the summer [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAlthough the question of the relationship between rainfall and spatial patterns remains, several studies in the past have revealed promising results. A study was conducted by Gergis \u0026amp; Ashcroft [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] in eastern New South Wales (NSW) over the 1788\u0026ndash;2008 period to identify the relationship between droughts and wet years and El Nino\u0026ndash;Southern Oscillation (ENSO). It was found that the relationship between the El Nino phenomenon and the rainfall in the coastal area is much stronger than that in the inland eastern NSW area, indicating that the rainfall can be significantly influenced by the location and climate conditions in Australia [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Some scientists suggested that there were upward and downward trends in the rainfall data observed in the regions across South Australia. Chowdhury et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], for example, researched the trends and step changes in different locations in South Australia. Results showed that locations including Adelaide, Arid Lands, Alinytjara Wilinara, and Mount Lofty Ranges regions experienced increasing annual rainfall trends over the period of 100 years whereas decreasing trends were found in the rainfall data in Murray Darling Basin, Eyre Peninsula Southeast regions. Earlier, the study conducted by Chambers [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] discovered that both mean and median rainfall tended to increase from the north to the south in the state of South Australia for the study period in the 20th century. The summer rainfall dominated the winter rainfall in the northern stations while the opposite was true in the southern stations [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. In addition, a recent study based on a spatial model for daily rainfall in South Australia indicated that there was a strong association between rainfall and climatic indicators related to spatial factors [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Although a relationship between rainfall and spatial patterns might exist in several locations across South Australia, a large uncertainty occurs. For instance, Ye \u0026amp; Ahammed [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] found that the factor of distance from the stations to the sea was proved to have an insignificant influence on the temperature and rainfall in South Australia though these data did vary according to station locations.\u003c/p\u003e \u003cp\u003eTo identify the relationship between climate data, several statistical hypothesis tests were normally used [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The purpose of hypothesis testing is to see whether an assumption or observation is true to describe the sample and population [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. In other words, hypothesis testing determines how likely it is that the difference would be seen between two (or more) groups by chance alone if the null hypothesis were true [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Which, four hypothesis tests are commonly in use, namely t-test, ANOVA, Mann-Whitney, and Kruskal-Wallis [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. T-test is a type of statistical test used to compare the means of two groups [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Researchers suggest that the T-test requires the scale data to be normally distributed [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]; hence, it is a type of parametric test [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Likewise, ANOVA is also a parametric method and is used to determine differences among the means of three or more input groups [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. On the other hand, Mann\u0026ndash;Whitney and Kruskal\u0026ndash;Wallis tests are well-known as non-parametric statistical tests [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Mann-Whitney U test is a test that assesses the differences between two groups on a single with no specific distribution [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. The Mann-Whitney U test is rather similar to the t-test for identifying whether two sample groups are from a single population; hence, the Mann-Whitney U test is regarded as the non-parametric version of the t-test [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Kruskal\u0026ndash;Wallis test is known as a test of three or more independently sampled groups on a single and the non-parametric version of ANOVA [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Although it is claimed to be suitable for non-normally distributed data, there is no specific requirement of the distribution of data for analyzing hypothesis by using this test [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThere were several applications of these statistical tests in research. Ahammed \u0026amp; Smith [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], for instance, investigated the association between learning online engagement and academic achievement for students at the University of South Australia by using non-parametric Mann\u0026ndash;Whitney and Kruskal\u0026ndash;Wallis tests. They found that the distribution of student activities on course sites across several categories namely genders, grades, and origin of students showed almost no difference [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. In terms of applications of statistical tests in the environment and climate field, Ye \u0026amp; Ahammed [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] used Mann-Whiney, Krukal-Wallis, and Correlations tests to determine the relationship between annual daily maximum temperature and annual daily maximum rainfall in South Australia. They suggested that temperatures and rainfall in South Australia varied according to the distance to the sea. The correlation test measures the relation strength of the relationship between variables [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. The most important fact is that correlation does not determine causation, meaning that each variable does not cause the other [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Furthermore, some research used linear regression analysis to predict a phenomenon based on contributing factors. He, Shirowzhan \u0026amp; Pettit [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], for instance, used regression analysis to explore how meteorological factors (temperature, precipitation, wind speed) and natural factors (slope, soil moisture, vegetation, NDVI) influence bushfires in NSW Australia while spatial correlation analysis was applied to support to create a wildfire susceptibility map in Sydney by sixteen wildfire-related factors [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. In addition, Bayesian Generalized Least Squares Regression (BGLSR), another method, was applied to construct a regression equation to predict rainfall data at ungauged stations in Australia [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Since the number of applications of using a statistical test for analyzing rainfall data in the City of Adelaide remains confined, this study might be helpful for further research in the study area in the future.\u003c/p\u003e \u003cp\u003eThis paper is a case study of the City of Adelaide to investigate the association between rainfall data and other factors including time and elevation. The Kruskjal-Wallis and Mann-Whitney tests were performed for hypothesis testing. The first objective of the research is to identify the variability of the extreme rainfall data over the recorded time in the City of Adelaide. In addition, it is aimed to observe how the rainfall data vary over the space by using the terrain data. The annual daily maximum rainfall (ADMR) data in four stations was collected over a 40-year period to identify the relationship between ADMR and time data. Furthermore, the ADMR in the year 2018 and elevation data across 86 stations were collected to determine how the rainfall data vary spatially. By understanding the variability of rainfall data, policymakers and researchers can use the results for climate projections and extreme rainfall predictions in any location across Adelaide.\u003c/p\u003e"},{"header":"2. Study area and data","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1 Study area\u003c/h2\u003e\n \u003cp\u003eThe study area is the City of Adelaide with its centroid coordinates of -34.94\u003csup\u003eo\u003c/sup\u003e South, 138.73\u003csup\u003eo\u003c/sup\u003e East. Having an area of 3.260 km\u0026sup2;, Adelaide is the capital and largest city in the State of South Australia (SA), Australia. It is the fifth-most populous city in Australia with a population of more than 1.3 million people [\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e]. Being a coastal city situated in southeast Australia, Adelaide has a Mediterranean climate with hot dry summers and mild winters [\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e]. The hottest months fall into January and February with the average daily maximum temperature of 29oC compared to about 15oC in the winter months [\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2 Data\u003c/h2\u003e\n \u003cp\u003eThe Annual Daily Maximum Rainfall (ADMR) data over a 40-year period (1981\u0026ndash;2018) in four stations was collected to use as the SPSS input data to investigate the variability of rainfall data over time. Four random stations from different elevation ranges (from 2 m to over 500m) and locations (1 station near the sea, 3 stations on land) were chosen as shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. In this research, the ADMR data was collected from the Australian Bureau of Meteorology (BOM) website. The detail of data collection is shown in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, and Appendix A.\u003c/p\u003e\n \u003cp\u003eMeanwhile, the Annual Daily Maximum Rainfall data in one chosen year and elevation data in 86 stations out of 269 stations across the study area were collected to investigate the changing rainfall patterns over the terrain. In this study, the ADMR_2018 data of the year 2018 was chosen since this year had the most up-to-date data; and it was recorded with a large number of stations. The elevation data was derived from the 3-second SRTM Derived Digital Elevation Model (DEM) Version 1.0. The 3-second DEM was produced for use by the government and the public under Creative Commons attribution. The elevation value in each station was derived by the GIS applications in ArcGIS. The detail of the data is shown in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, and Appendix B. The collected ADMR and elevation data are in the scale measurement.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe details of the ADMR data and stations over 40-year period\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWeather station name\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAdelaide airport\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAdelaide (Tea tree gully council)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMeadows\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAshton Co-op\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eStation number\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23034\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23748\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23730\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23803\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eData\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eADMR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eADMR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eADMR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eADMR\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eElevation (m)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e145.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e358.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e553.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eRecorded time\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1981\u0026ndash;2018\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1981\u0026ndash;2018\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1981\u0026ndash;2018\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1981\u0026ndash;2018\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eCoordinates\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-34.94 S, 138.53 E\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-34.83 S, 138.70 E\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-35.18 S, 138.76 E\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-34.94 S, 138.73 E\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe details of ADMR data and elevation data across Adelaide in 2018\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eData\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eADMR_2018 (mm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eElevation (m)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYear of interest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2018\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe number of stations\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"3. Methodology","content":"\u003cp\u003eIn this study, several statistical tests were performed in the software SPSS. A flowchart of the methodology is provided in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Before performing the hypothesis tests to identify the variability of the data, the descriptive and normality tests were prepared. In which, descriptive analytics is the first step of data analysis. It gives information about the summary of historical data, and it shows whether additional data is needed for predictive modelling [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Afterward, the normality test was performed. Testing the normality of data is a prerequisite in the hypothesis testing procedure [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Its result identifies whether the data is non-parametric or parametric, which provides an indication to choose the suitable type of hypothesis test. For testing the distribution patterns of the data, the number of samples in the population determines which tests can be used. Specifically, the Shapiro-Wilk is used to interpret the result for the population having a small number of samples (\u0026lt;\u0026thinsp;50 samples), while the Kolmogorov\u0026ndash;Smirnov test is used for large sample size (\u0026gt;\u0026thinsp;50 samples) [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe next step in analysing data is performing statistical hypothesis tests. A hypothesis test is a statistical test that allows researchers to use sample data to evaluate a hypothesis about a population [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. Depending on the distribution pattern and the number of variables, several hypothesis tests such as t-test, ANOVA, Man-Whitney, and Kruskal-Wallis are valid in use as shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. As discussed, while t-test and ANOVA are parametric tests, the Man-Whitney and Kruskal-Wallis tests are used for non-parametric data or the normality unsure [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. In addition, the t-test and Mann-Whitney can be used for two samples or two variables, whereas ANOVA and Kruskal-Wallis require the data to have the number of comparison groups of 3 or more [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. In this study, two groups of ADMR data corresponding to two different periods of time were used to identify the relationship between rainfall data over time. Meanwhile, the ADMR data was also divided into 3 groups or more based on elevation level to investigate the variability of rainfall data over the terrain.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAfter the hypothesis tests (Mann-Whitney and Kruskal-Wallis), the relationship or association between dependent and independent variables can be identified. If the association between variables is not statistically significant, it is impossible to identify the significant correlations between them. As such, the testing process can be terminated. Otherwise, the correlation test can be performed to ensure that the assumption is correct. The correlation test was developed to detect the presence of a mathematical relation between two or more variables [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. If the correlation between them is not statistically significant, the procedure will be stopped; and the decision will be made. On the other hand, if there is a statistically significant correlation between variables, the Regression test will be performed. The result of regression is an equation employing the correlation coefficient to predict one variable from one another [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. It is clear that the accuracy of the prediction depends on the magnitude of the correlation coefficient [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]; hence, Regression is also a platform to reconfirm the significance level of the test. Finally, the multivariate analysis was performed. It is a technique that investigates the relationship between two or more independent variables and a single dependent variable [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. The purpose of this test is to confirm the consistency in the results from previous tests. After this test, the final decision will be made.\u003c/p\u003e"},{"header":"4. Selection of statistical tests","content":"\u003cp\u003eThe Statistical Package for the Social Sciences (SPSS), version 28.0 was used to perform the data analysis. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e show the hypothesis tests and their data requirements. The Chi-square, Cramer\u0026rsquo;s V, and Phi tests need both independent and dependent data in categorical scales [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. The Mann-Whitney, Kruskal-Wallis, t-test, and ANOVA tests require dependent variable in scale measurement and independent variables to be categorical data such as groups [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Correlation and regression, on the other hand, use both variables to be in numeric (scale) data [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eDepending on the nature of the investigation, there is a wide range of statistics. However, the result of any statistical test is a P value [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. According to Whitley \u0026amp; Ball [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], the \u0026lsquo;P\u0026rsquo; stands for probability, meaning that it measures how likely it is that any observed difference between groups is due to change. As a probability, P can take any value between 0 and 1 [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. The closer value to 0, the more unlikely the observed differences is due to chance; meanwhile, a P value close to 1 indicates there is no difference between groups [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. In a hypothesis test, the p-value is the smallest level that is to reject the null hypothesis [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. While there are three conventional levels of significance that are normally in use such as P\u0026thinsp;\u0026le;\u0026thinsp;0.05; P\u0026thinsp;\u0026le;\u0026thinsp;0.01; and P\u0026thinsp;\u0026le;\u0026thinsp;0.001 [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. McCarthy et al. [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] claimed that it is usually set to 5% or 0.05. Hence, the value of 0.05 was used in this research. If the p-value is smaller than 0.05, the null hypothesis is rejected [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eHypothesis tests for different data types\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndependent variable (data)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDependent variable (data)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHypothesis tests\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCategorical\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCategorical\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eChi-square, Cramer\u0026rsquo;s V and Phi\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCategorical\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003et-test, Mann-Whitney, ANOVA, Kruskal-Wallis\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eScale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCorrelation, regression\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDataset requirements for hypothesis tests\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eType of test\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo. of comparison groups\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHypothesis test\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eParametric\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003et-test\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3 or more\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eANOVA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eNon-parametric\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMann- Whitney\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3 or more\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eKruskal-Wallis\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIt was shown from the normality test results that the ADMR, ADMR_2018, and Elevation data were not normally distributed. Since the t-test and ANOVA require the parametric data, they were both invalid for hypothesis testing. Therefore, the Mann-Whitney and Kruskal-Wallis tests were chosen for checking hypotheses.\u003c/p\u003e \u003cp\u003eSubsequently, the hypothesis dataset was prepared. As mentioned above, the Mann-Whitney was used to identify the relationship between ADMR data over time. The ADMR data from 1979 to 1998 was recoded as 1, and data from 1999 to 2018 was recoded as 2. Meanwhile, based on the elevation levels of stations, there are two Kruskal-Wallis tests prepared to identify the association between rainfall data and elevation groups. In the first Kruskal-Wallis test, the 40-year ADMR data was categorized as 1\u0026thinsp;=\u0026thinsp;Station 23034/ Elevation: 2m; 2\u0026thinsp;=\u0026thinsp;Station 23748/ Elevation: 145 m; 3\u0026thinsp;=\u0026thinsp;Station 23730/Elevation: 358 m; 4\u0026thinsp;=\u0026thinsp;Station 23803/ Elevation: 553 m. For the second Kruskal-Wallis test, the ADMR_2018 data was categorized as 1\u0026thinsp;=\u0026thinsp;Elevation: 0-200 m, 2\u0026thinsp;=\u0026thinsp;Elevation: 200\u0026ndash;400 m, 3\u0026thinsp;=\u0026thinsp;Elevation: 400\u0026ndash;685 m. Elevation ranges were chosen and based on increasing values which helps determine how the distribution of rainfall data changes in different ranges of elevation. The detailed group information can be found in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe groups for hypothesis test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDependent variables\u003c/p\u003e \u003cp\u003e(Data)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIndependent variables (Groups)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMann\u0026ndash;Whitney\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e40-year ADMR data\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTime: 1979\u0026ndash;1998\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTime: 1999\u0026ndash;2018\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eKruskal-Wallis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e40-year ADMR data\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStation 23034/ Elevation: 2 m\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStation 23748/ Elevation: 145 m\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStation 23730/ Elevation: 358 m\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStation 23803/ Elevation: 553 m\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eKruskal-Wallis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eADMR_2018 data\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eElevation: 0-200 m\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eElevation: 200\u0026ndash;400 m\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eElevation: 400\u0026ndash;685 m\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAfterwards, the ADMR_2018 and Elevation data were used to perform the correlation and regression tests. Pearson\u0026rsquo;s correlation and Spearman\u0026rsquo;s correlation are known as two types of correlation tests. Spearman\u0026rsquo;s rank and Pearson\u0026rsquo;s correlations are based on linear relationships between variables [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Pearson correlation is used if both variables are parametric data while Spearman\u0026rsquo;s rho is applied if one of two variables is non-parametric data [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Since the normality test showed that the ADMR, ADMR_2018, and Elevation data were non-parametric, the Spearman\u0026rsquo;s rho result was employed. In this study, two Correlation tests were performed, including the relationship between ADMR and Year data, and ADMR_2018 and Elevation data.\u003c/p\u003e \u003cp\u003eThe final stage in the research is multivariate analysis. In this analysis, the ADMR_2018 data was split into two groups to perform a multivariate hypothesis test using Kruskal-Wallis. Group 1 was defined as a station number less than 23733; Group 2 was defined as a station number more than 23733. The details of the dataset are shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe dataset for multivariate analysis\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDependent variables (Data)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIndependent variables (Groups)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSplit data\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eMultivariate analysis for Kruskal-Wallis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eADMR data (2018)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eElevation: 0-200 m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGroup 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eStation number\u0026thinsp;\u0026lt;\u0026thinsp;23733\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eElevation: 200\u0026ndash;400 m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eGroup 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eStation number\u0026thinsp;\u0026gt;\u0026thinsp;23733\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eElevation: 400\u0026ndash;685 m\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"5. Null, alternative hypotheses","content":"\u003cp\u003eThe null and alternative hypotheses for the Kruskal\u0026ndash;Wallis and Mann\u0026ndash;Whitney tests were prepared by the tests themselves in SPSS itself [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. In the hypothesis test, the significant value determines whether the hypothesis is rejected or retained. The significant level for hypothesis testing in SPSS is 0.05. It means that if the significant value (p-value) is less than 0.05, the null hypothesis is rejected [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFor the Kruskal\u0026ndash;Wallis test, the null hypothesis (H\u003csub\u003eo\u003c/sub\u003e) was expressed as the distribution of ADMR is the same across categories of time groups; the alternative hypothesis (H\u003csub\u003eA\u003c/sub\u003e) was expressed as the distribution of ADMR is not the same across categories of time groups.\u003c/p\u003e \u003cp\u003eFor the Mann\u0026ndash;Whitney test, the null hypothesis (H\u003csub\u003eo\u003c/sub\u003e) was expressed as the distribution of ADMR is the same across categories of station groups; the alternative hypothesis (H\u003csub\u003eA\u003c/sub\u003e) was expressed as the distribution of ADMR is not the same across categories of station groups.\u003c/p\u003e"},{"header":"6. Results and discussions","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e6.1 The normality test\u003c/h2\u003e\n \u003cp\u003eThe result of the frequency analysis is shown in Table \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e. As can be seen in the table, there were differences between the mean, median, and mode values. Hence, these three data might be not normally distributed. The normality test result in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e was used to confirm this assumption.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab7\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe result of frequency analysis\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eADMR\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eELEVATION\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eADMR_2018\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eValid\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMissing\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMean\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e40.5712\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e257.7558\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e32.4233\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMedian\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e296\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e32\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMode\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e26.00a\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.00a\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e26.00a\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eStd. Deviation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.27621\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e179.1371\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.46535\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eSkewness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.155\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.033\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.571\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eStd. Error of Skewness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.192\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eKurtosis\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.919\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-1.194\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.099\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eStd. Error of Kurtosis\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.381\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.514\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.514\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMinimum\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMaximum\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e107.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e675\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e65.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\u0026nbsp;\u003ctable id=\"Tab8\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe result of normality test\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"7\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"7\"\u003e\n \u003cp\u003eTests of Normality\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003eKolmogorov-Smirnov\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003eShapiro-Wilk\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStatistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003edf\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStatistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003edf\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eADMR (4 stations)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.086\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.006\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.925\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eELEVATION (86 stations)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.133\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.927\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eADMR_2018 (86 stations)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.080\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.200\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.965\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.021\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eThe ADMR data is comprised of the data in four stations, and each station has 40-year data values. As a result, the number of ADMR samples in the normality test is 160 values (\u0026gt;\u0026thinsp;50). Therefore, the Kolmogorov-Smirnova test was used to interpret the result. Meanwhile, the significant value (p-value) in the normality test was 0.05 as the common value [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. As such, if the significant value is less than 0.05, the data is non-parametric. As can be seen from Table \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e, the significant value is 0.006, which is smaller than 0.05. Therefore, the ADMR data were not normally distributed. Similarly, the values of the Kolmogorov-Smirnova test were also used to determine the normality result for Elevation and ADMR_2018 data since these two types of data have 86 samples. The significance for Elevation and ADMR_2018 data were 0.001 and 0.2, respectively, and both were smaller than 0.05. Therefore, the Elevation and ADMR_2018 data were also not normally distributed.\u003c/p\u003e\n \u003cp\u003eIn addition, the Q-Q plot results showed that the data values in all three graphs were not entirely close to diagonal line, claiming that all these data were non-parametric.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e6.2 Mann-Whitney U result\u003c/h2\u003e\n \u003cp\u003eThe Mann-Whitney test is to check the differences between the ADMR data and year groups. The result of the test is shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab9\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe Mann-Whitney U result\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"5\"\u003e\n \u003cp\u003eHypothesis Test Summary\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNull Hypothesis\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig.\u003csup\u003ea,b\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDecision\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe distribution of ADMR is the same across categories of Year groups.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIndependent-Samples Mann-Whitney U Test\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.309\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRetain the null hypothesis.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eThe null hypothesis is never accepted; the result is either fail to reject or reject it [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. In other words, if the p-value is bigger than 0.05, the result fails to reject the null hypothesis [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. In this study, the result of the Mann-Whitney test showed that the significant value is 0.309, which is obviously bigger than 0.05. Therefore, the decision for the hypothesis test is to retain the null hypothesis. As such, the distribution of ADMR data is the same across categories of year groups. There is no difference between the ADMR data and Year groups. Therefore, it was claimed that the ADMR data does not vary temporally. In this case, the testing procedure can be terminated. The decision can be made as the ADMR data does not vary over the recorded time.\u003c/p\u003e\n \u003cp\u003eIn this study, to ensure that the result of Mann-Whitney test is accurate, a correlation test was conducted to check the consistency of these two tests. The result can be found in Table \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003e6.3 Kruskal-Wallis test\u003c/h2\u003e\n \u003cp\u003eThis test is to identify whether there is a difference between the ADMR data and the elevation groups. The result is shown in Table \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab10\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eHypothesis testing using Kruskal-Wallis for 40-year ADMR data\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"5\"\u003e\n \u003cp\u003eHypothesis Test Summary\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNull Hypothesis\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig.\u003csup\u003ea,b\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDecision\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe distribution of ADMR is the same across categories of station groups.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIndependent-Samples Kruskal-Wallis Test\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eReject the null hypothesis.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eAs mentioned above, if the p-value is smaller than 0.05, the null hypothesis is rejected [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. The result of the Kruskal-Wallis test showed that the significant value is 0.000, which is smaller than 0.05. Therefore, the decision is rejecting the null hypothesis. Specifically, the distribution of ADMR data is not the same across categories of four station/ elevation groups. Hence, there is a difference between ADMR data over elevation groups.\u003c/p\u003e\n \u003cp\u003eThe pairwise comparisons in Table \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e claimed that there is only one pair of sample groups having a significance value bigger than 0.05. That is the pair group 1\u0026ndash;2 where the p-value stands at 1.0, meaning there is no difference between ADMR data in this pair group. However, the other pair groups all have significant values smaller than 0.05. Therefore, there is a relationship between them.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab11\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 11\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe pairwise comparisons of station groups for 40-year ADMR data\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003ePairwise Comparisons of station groups\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSample 1-Sample 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest Statistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStd. Error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStd. Test Statistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAdj. Sig.\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00\u0026ndash;1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.800\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.360\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.463\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.643\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00\u0026ndash;3.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-40.513\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.360\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-3.911\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00\u0026ndash;4.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-72.288\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.360\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-6.978\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.00\u0026ndash;3.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-35.713\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.360\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-3.447\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.003\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.00\u0026ndash;4.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-67.488\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.360\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-6.514\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.00\u0026ndash;4.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-31.775\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.360\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-3.067\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.002\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.013\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eThe results of hypothesis testing using ADMR data in the four stations above indicated that there is a relationship between the ADMR and elevation data, which means that the ADMR data might spatially vary with the elevation data. To check this assumption, another Kruskal-Wallis test was performed by using the ADMR data in one year (ADMR_2018) and the elevation data in stations across the study area.\u003c/p\u003e\n \u003cp\u003eIn this research, the year 2018 for the one-year ADMR data was chosen since this year satisfies the availability and quality of data. Regarding the year 2018 data, the latest data can be obtained. In terms of the elevation data, 86 stations out of 269 stations across the City of Adelaide were used, each station provided one data of elevation.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab12\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 12\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eHypothesis testing using Kruskal-Wallis for ADMR_2018 data\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"5\"\u003e\n \u003cp\u003eHypothesis Test Summary\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNull Hypothesis\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig.\u003csup\u003ea,b\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDecision\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe distribution of ADMR_2018 is the same across categories of Elevation groups.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIndependent-Samples Kruskal-Wallis Test\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eReject the null hypothesis.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eThe result for this Kruskal-Wallis test in Table \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e showed that the significant value is 0.000, which is clearly smaller than 0.05. The decision is to reject the null hypothesis. It means that the distribution of ADMR_2018 data is not the same across categories of three elevation groups. Therefore, there is an association between the ADMR_2018 data and elevation groups. The difference between groups and pairwise comparisons are shown in Table \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e and Table \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab13\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 13\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe pairwise comparisons of elevation groups for the ADMR_2018 data\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003ePairwise Comparisons of Elevation groups\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSample 1-Sample 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest Statistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStd. Error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStd. Test Statistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAdj. Sig.\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.00\u0026ndash;2.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-23.470\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.158\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-3.811\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.00\u0026ndash;3.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-40.407\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.999\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-5.774\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00\u0026ndash;3.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-16.937\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.161\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-2.365\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.018\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.054\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003e6.4 Correlations\u003c/h2\u003e\n \u003cp\u003eAs mentioned above, the first correlation test was performed to examine the consistency of Mann-Whitney U and correlations tests. Since the ADMR data is non-parametric, Spearman\u0026apos;s rho table was used to interpret the result. One common way to determine the strength of relationships between two variables is using the scatter plot [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. The more points are close to the fitting line, the more strength association has. Additionally, the value of the correlation coefficient (r) also represents the strength of the association; it ranges from \u0026minus;\u0026thinsp;1 to 1 [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. The closer the correlation coefficient (r) to zero suggests no or weak correlation, whereas the closer the correlation coefficient (r) to either \u0026minus;\u0026thinsp;1 or 1, the greater the association strength [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. If the significant value (p-value) in the Correlations test is smaller than 0.01, it indicates the test is statistically significant.\u003c/p\u003e\n \u003cp\u003eAs can be seen from Table \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e, the Correlation coefficient value is -0.046, which is very close to 0. Therefore, it indicates no linear relationship exists between ADMR and Year data. In addition, the significant value is 0.559 which is significantly bigger than 0.01. Hence, the relationship between the two data is realatively weak. In short, it can be observed that the Mann-Whitney U and Correlations tests showed consistency in their results. The decision was made as the ADMR data does not vary according to the time of the data.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab14\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 14\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe result of Correlations test for ADMR and Year data\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"5\"\u003e\n \u003cp\u003eCorrelations\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eADMR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYEAR\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eSpearman\u0026apos;s rho\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eADMR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCorrelation Coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.046\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig. (2-tailed)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.559\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eYEAR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCorrelation Coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.046\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig. (2-tailed)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.559\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eFollowing the result from the Kruskal-Wallis test above, this second Correlations test is to determine the size and direction of association between the ADMR_2018 and Elevation data. Since the ADMR_2018 and Elevation data are not normally distributed, Spearman\u0026rsquo;s rho table was used to interpret the results. The result is shown in Table \u003cspan class=\"InternalRef\"\u003e15\u003c/span\u003e.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab15\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 15\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe result of Correlations test for ADMR_2018 and Elevation data\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"5\"\u003e\n \u003cp\u003eCorrelations\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eELEVATION\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eADMR_2018\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eSpearman\u0026apos;s rho\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eELEVATION\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCorrelation Coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.679\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig. (2-tailed)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eADMR_2018\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCorrelation Coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.679\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig. (2-tailed)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e86\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eThe Spearman\u0026rsquo;s is based on linear relationships between variables and its value is measured between \u0026minus;\u0026thinsp;1 and +\u0026thinsp;1 [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. Looking at Table \u003cspan class=\"InternalRef\"\u003e15\u003c/span\u003e, the correlation coefficient value is 0.679, which is not too close to 0. Therefore, the correlation between the ADMR_2018 and elevation data is significantly strong. In addition, the significant value (p-value) is 0.000, which is clearly smaller than 0.01. As a result, the test is statistically significant. It is clear to see that these two criteria showed consistency in their result. Therefore, it is reasonable to claim that there is a strong relationship between the ADMR_2018 and Elevation data.\u003c/p\u003e\n \u003cp\u003eIn the graph, several scatter points tended to distribute close to each other and close to the fitting line. The R\u003csup\u003e2\u003c/sup\u003e value is relatively significant (0.401), indicating that the correlation between the two variables is relatively strong. The line had the slope\u0026thinsp;\u0026gt;\u0026thinsp;0; therefore, the relationship is positive. In short, the results from the Correlations and Kruskal-Wallis tests were the same.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e6.5 Regression\u003c/h2\u003e\n \u003cp\u003eThe result from the correlations test showed a strong relationship between the ADMR_2018 and elevation. Based on this validation, the regression was considered to identify how the ADMR data changes corresponding to the Elevation. The equation between two variables can be determined by: Y\u0026thinsp;=\u0026thinsp;a\u0026thinsp;+\u0026thinsp;bX.\u003c/p\u003e\n \u003cp\u003eWhere, Y is dependent (target) variable; X is independent (input) variable; b is a slope of the best-fit line (Beta coefficient); and a is the point at which the line crosses the Y-axis (intercept). In this research, the ADMR (mm) is considered as the dependent variable, while the Elevation (m) is considered as independent the variable. Therefore, the equation can be substituted as below.\u003c/p\u003e\n \u003cp\u003eADMR_2018\u0026thinsp;=\u0026thinsp;a\u0026thinsp;+\u0026thinsp;b*Elevation\u003c/p\u003e\n \u003cp\u003eThe value of a and b can be determined as the result from coefficient below.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab16\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 16\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe result of coefficients test\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"7\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"7\"\u003e\n \u003cp\u003eCoefficients\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\" rowspan=\"2\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eUnstandardized Coefficients\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStandardized Coefficients\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003et\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eSig.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStd. Error\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBeta\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(Constant)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21.973\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.693\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.979\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eELEVATION\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.041\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.005\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.633\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.503\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"7\"\u003e\n \u003cp\u003ea. Dependent Variable: ADMR_2018\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eFirstly, the significance value is 0.000\u0026thinsp;\u0026lt;\u0026thinsp;0.05, hence, it showed that the test is statistically significant. Furthermore, the result illustrates that the coefficient Beta (that is Pearson\u0026rsquo;s) is equal to 0.633, which is not close to 0. Hence, it showed the strong positive associations between the ADMR_2018 and Elevation variables. After the test, the a and b values can be obtained as 21.97 and 0.04, respectively.\u003c/p\u003e\n \u003cp\u003eTherefore, the regression equation is formed as ADMR_2018\u0026thinsp;=\u0026thinsp;21.97\u0026thinsp;+\u0026thinsp;0.04*Elevation.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n \u003ch2\u003e6.6 Multivariate analysis\u003c/h2\u003e\n \u003cp\u003eThe result of Multivariate analysis using Kruskal-Wallis is shown in Table \u003cspan class=\"InternalRef\"\u003e17\u003c/span\u003e. The significant values in the two split groups were 0.000 and 0.001, which are both smaller than 0.05. As a result, the hypothesis is rejected. The result was expressed as the distribution of ADMR_2018 is not the same across categories of Elevation groups. These differences can be observed in Fig. \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e. This result is the same as the Kruskal-Wallis test above. Thus, the Multivariate analysis reconfirmed the validation of the Kruskal-Wallis test. It is reasonable to conclude that the results from the Kruskal-Wallis, Correlations, and Regression tests are credible.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab17\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 17\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eMultivariate analysis for hypothesis testing using Kruskal-Wallis Test\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"6\"\u003e\n \u003cp\u003eHypothesis Test Summary\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eMC station number\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNull Hypothesis\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSig.\u003csup\u003ea,b\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDecision\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe distribution of ADMR_2018 is the same across categories of Elevation groups.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIndependent-Samples Kruskal-Wallis Test\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eReject the null hypothesis.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe distribution of ADMR_2018 is the same across categories of Elevation groups.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIndependent-Samples Kruskal-Wallis Test\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eReject the null hypothesis.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"7. Conclusions","content":"\u003cp\u003eThis study is to investigate the variability of rainfall over time and terrain in the City of Adelaide. Several statistical tests were performed, namely Kruskal\u0026ndash;Wallis, Mann\u0026ndash;Whitney, correlation, and regression tests. It was found that the Annual Daily Maximum Rainfall (ADMR) data showed no significant difference over the recorded time. Meanwhile, the elevation has a significant influence on the ADMR data. The research has shown that the distributions of ADMR across categories of elevation groups were different by using Mann\u0026ndash;Whitney and Kruskal-Wallis tests. Plus, there was a strong correlation between ADMR and elevation data. Although there was a relationship, there is no evidence to claim that the elevation causes the variability of rainfall data. However, it is relatively possible to use elevation data to predict ADMR data in Adelaide.\u003c/p\u003e \u003cp\u003eIt is important to note that the application of the Kruskal\u0026ndash;Wallis, Mann\u0026ndash;Whitney tests in rainfall data is not common. Hence, more research needs to be done to fully understand the extreme rainfall patterns in the study area. In further research, it is necessary to collect more data in the long time series and different locations to obtain comprehensive results. Policymakers and researchers can use the results for climate projections and extreme rainfall predictions in any location across Adelaide.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor Contributions:\u0026nbsp;\u003c/strong\u003eConceptualization and methodology, H.T and F.A; Writing original draft preparation, H.T; Feedback and advice, F.A. All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Approval:\u003c/strong\u003e Not applicable.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e Not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials:\u003c/strong\u003e This paper used the Climate data online from the Australian Government Bureau of Meteorology (BOM) website.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments:\u003c/strong\u003e The authors would like to acknowledge the generous provision of data by the Australian Government Bureau of Meteorology (BOM).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of Interest:\u003c/strong\u003e The authors declare no conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAkompab D, Bi P, Williams S, Grant J, Walker I, \u0026amp; Augoustinos M (2012) Awareness of and Attitudes towards Heat Waves within the Context of Climate Change among a Cohort of Residents in Adelaide, Australia. 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Many studies conducted to investigate the changing patterns of meteorological data in Australia. This study aimed to investigate the variability of rainfall data over time and terrain in Adelaide, South Australia. The annual daily maximum rainfall (ADMR) data over a 40-year period in four stations was collected to identify the distribution of rainfall data across the time recorded. Moreover, the ADMR data in 2018 and elevation data across 86 stations were used to investigate the changing rainfall patterns over the terrain. Two non-parametric tests including Kruskal\u0026ndash;Wallis, and Mann\u0026ndash;Whitney were applied to perform the hypothesis analysis. Correlations, regression, and multivariate tests were performed to identify the relationship between variables. It was found that the ADMR data in four stations did not vary over the 40-year period from 1981 in Adelaide. However, there was a strong correlation between the extreme rainfall data in the year 2018 and elevation data in these stations. Results also suggested that it is relatively possible to use the elevation data to predict ADMR across Adelaide in certain years. Policymakers and researchers can use these tests for climate projections and extreme rainfall forecasts.\u003c/p\u003e","manuscriptTitle":"Analysis of the rainfall variability over temporal and spatial patterns: A case study in Adelaide, South Australia","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-12 17:32:37","doi":"10.21203/rs.3.rs-3834670/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4e86d96d-d41c-4f5f-b280-dfb8143e9b3c","owner":[],"postedDate":"January 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-01-25T17:59:16+00:00","versionOfRecord":[],"versionCreatedAt":"2024-01-12 17:32:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3834670","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3834670","identity":"rs-3834670","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}