FK3BR Scale: Development of an Ultra-Short Measure

FK3BR Scale: Development of an Ultra-Short Measure | 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 Research Article FK3BR Scale: Development of an Ultra-Short Measure Emmanuel Marques Silva, Patricia Maria Bortolon This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6279772/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 Financial knowledge has been recognized as an essential element for making informed financial decisions, promoting greater autonomy, security, and financial well-being. To ensure a valid and reliable measurement of this knowledge, we selected nine questions from instruments developed and validated in the Brazilian context and applied Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) to validate an ultra-short scale, resulting in a three-item instrument, which we named KF3BR. To assess convergent validity, we used three basic conditions outlined in the literature: Composite Reliability (CR), Average Variance Extracted (AVE), and the relationship between them. The results indicate that the proposed structure for KF3BR provides satisfactory evidence of quality, reliability, and convergent validity. Macroeconomics Scale Development Financial Knowledge FK3BR Reliability and Validity Figures Figure 1 Figure 2 Figure 3 1. INTRODUCTION Financial literacy is widely recognized as a key factor in economic and financial stability and development (Subova et al., 2021; Potrich et al., 2015a). It is such an important topic for society, being defined by the Organization for Economic Cooperation and Development as a combination of “financial awareness, knowledge, skills, attitudes and behaviors needed to make sound financial decisions and, ultimately, achieve financial well-being” (OECD, 2023). Financial literacy consists of two dimensions: knowledge, which pertains to an individual's understanding of personal finance, and application, referring to behavior and attitudes in managing money. It consists of both knowledge and the application of specific human capital for personal finances (Huston, 2010). The importance of financial knowledge in this process is salutary. It allows individuals to manage their financial affairs, compare financial products and services to make appropriate and well-informed financial decisions, and react to events that may affect their financial well-being (OECD, 2023). Thus, understanding and measuring the level of financial knowledge of individuals, as well as the application of this knowledge in personal financial management, plays an important role so that governments of emerging and developed countries can outline policies related to improving the financial education of young people and adults. In this context, over the last few decades there has been a growing effort to measure individuals' financial knowledge, such as the scales by Lusardi & Mitchell (2008, 2011) and the financial knowledge scales by van Rooij et al. (2011) and Knoll & Houts (2012) and the Digital Financial Knowledge Scale (DFKS) by Vieira et al. (2024). Other scales innovate by implementing concepts from Item Response Theory (IRT) and Factor Analysis in their validation, such as those by Vieira et al. (2020) and Bajaj & Kaur (2024). However, some of these scales comprise a large number of items for measuring the construct, others lack validation procedures and psychometric evaluation of their validity (Vieira et al., 2020),, and others, because they were developed in developed countries, with economic, structural and cultural characteristics distinct from economies in transition, carry a significant risk that concepts and measures tested in these contexts are not cross-culturally valid for other economies (Silva et al., 2025a; Tomar et al., 2021; Abrantes-Braga & Veludo-de-Oliveira, 2019). At another point, in the context of research, there is an increasing need to collect information in a short period of time, which highlights the importance of instruments that can be completed quickly and have good reliability (Mastrascusa et al., 2023). In order to fill this gap, the objective of this article was to structure an ultra-short scale, with only 3 items, capable of measuring the level of financial knowledge of individuals quickly and reliably for an economy in transition, the Brazilian one. We chose Brazil as the field of interest for this study for three main reasons. First, because it is one of the largest global economies, representing a population of over 212.6 million (IBGE, 2024). Second, due to its historical economic instability, with an economic environment in which the population, in general, is vulnerable to any financial emergency (Abrantes-Braga & Veludo-de-Oliveira, 2019). And last but not least, for convenience, considering practical criteria such as accessibility, availability, willingness to participate, and low cost of access for participants (Etikan, 2016). To achieve the objectives of this article, we start from the scale proposed by Vieira et al. (2020), which innovates by proposing a financial knowledge scale based on Item Response Theory (IRT). To validate the reduced scale, we used Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA), statistical techniques that allow reducing the number of observed variables, in a smaller set of latent variables, by examining the covariation between the items (Silva et al., 2025a; Silva et al., 2025b; Schreiber et al., 2006). As a result, we validated the KF3 BR (Financial Knowledge – 3 items, Brazil) , an instrument for measuring individuals' financial knowledge appropriate to the Brazilian context. 2. THEORETICAL FRAMEWORK 2.1. Financial knowledge: concepts and their influence on decision making Financial literacy is an important construct that represents more than an individual's stock of explicit financial knowledge. It consists of both the knowledge and application of human capital specific to personal finance (Huston, 2010). Its concept involves and includes skill and self-efficacy, and requires knowledge and skill, as well as a facility for critical thinking (Warmath & Zimmerman, 2019). Financial literacy refers to the ability to evaluate new and complex financial instruments and make informed judgments, both in choosing these instruments and in their most appropriate use (Potrich et al., 2016a; Schagen & Linnes, 1996). It can be defined as the measurement of how well an individual can understand and use information related to personal finances (Huston, 2010), and has three pillars: financial knowledge, financial behavior and financial attitude (OECD, 2023). Financial knowledge is the main focus of financial education, which is divided into two distinct components: financial knowledge and financial skills (Knoll & Houts, 2012). Financial knowledge is a particular type of human capital that is acquired throughout the life cycle, through learning about subjects that affect the ability to manage income, expenses and savings effectively (Potrich et al., 2015a; Delavande et al., 2008). On the other hand, financial skills concern the way individuals process financial information and make decisions. The second component, financial behavior, is an essential element of financial literacy and, without a doubt, the most important (Atkinson & Messy, 2012). Financial behavior deals with the way in which the individual deals with money. It refers to the actions and decisions that individuals take regarding the management of their financial resources, including spending (consumption), saving, investing and getting into debt, where financial education is shown to be a key variable that influences financial behavior (Ingale & Paluri, 2020). Positive outcomes of being financially literate are driven by behaviors such as spending planning and building financial security (Atkinson & Messy, 2012). The last component, financial attitude, can be understood as the economic and non-economic beliefs held by a given individual about the outcome of a given behavior (Ajzen, 1991), impacting decisions about consuming, saving, investing or getting into debt. Given the above, it is clear that financial literacy and financial knowledge are both human capital, but different constructs. Financial education is an input intended to increase a person's human capital, specifically financial knowledge and/or application, i.e., financial literacy (Huston, 2010). Thus, understanding current levels of financial education and needs for improvement becomes an essential tool for the effective development of financial education strategies and programs (OECD, 2023). Given the growing complexity of financial products and services available to society, having financial knowledge is important not only for individuals and families, becoming an essential skill for participation in society (Bajaj & Kaur, 2024; Potrich & Vieira, 2018). Regarding the influence of financial knowledge on economic decisions, empirical studies indicate that this knowledge plays a fundamental role in financial decision-making. Furthermore, it is highly correlated with several factors, with higher education being one of the main determinants (Thaler, 2013). Individuals with higher levels of education tend to have higher levels of financial literacy and access to financial information (Messy & Monticone, 2016; Potrich et al., 2015; Chen & Volpe, 1998). Studies show that positive financial behaviors are directly related to the level of economic and non-economic resources, and contribute to reducing financial stress and increasing financial satisfaction (Xiao et al., 2006), and that the level of knowledge has a positive influence on self-confidence and financial behaviors (Ramalho & Forte, 2019). Confidence in one's own financial knowledge, in turn, is positively related to credit card use and overall financial satisfaction (Atlas et al., 2019). Furthermore, a higher level of financial knowledge, combined with better money management skills and less impulsiveness in financial behavior, can reduce individuals' financial vulnerability (Singh & Malik, 2022). These findings highlight the relevance of the topic in contemporary research on savings, consumption, investment and debt (Silva et al., 2024, 2023). 3. METHODOLOGICAL PROCEDURES 3.1 Choosing items for FK3BR. Given the importance of validated instruments that measure individuals' level of financial knowledge, the first step in validating the FK3BR was to search for scales developed in the Brazilian context in two peer-reviewed scientific repositories, Scopus and Web of Science (WoS). The search results indicated that the authors Potrich and Vieira are central references in the field, with several scales that, although varying in length and number of items, present significant overlap in their contents. Among the instruments identified, the following stand out: the scale by Potrich et al. (2015b) with 37 items, of which 17 are focused on financial knowledge; those by Potrich et al. (2015a, 2016), with 50 items, including 18 on financial knowledge; that by Potrich et al. (2016b), with 37 items, of which 17 are related to financial knowledge; and that by Potrich & Vieira (2018), with 71 items, of which 10 address financial knowledge. More recently, Vieira et al. (2020) proposed leaner versions, with scales containing 7, 9 and 12 items on financial knowledge and Vieira et al. (2024) developed the DFKS, specifically aimed at measuring digital financial knowledge. After evaluating the content of these scales, we chose to use the scale developed and validated by Vieira et al. (2020) as the main input for validating the FK3BR. Table 1 presents the chosen questions of the instrument, the response options and the level of knowledge represented by the item as proposed in the related literature. Table 1 List of items (questions) used to develop the FK3BR scale. Item code Question Answer option Item Difficulty Level CF01 Suppose you saw the same television in two different stores for the initial price of R $ 1,000.00. Store A offers a discount of R $ 150.00, while Store B offers a discount of 10%. Which is the best alternative? Buy at store A (discount of R $ 150.00 )* Buy at store B (10% discount). I don't know Basic CF02 Suppose you borrowed R $ 100.00 from a friend and after one week you paid back R $ 100.00 (one hundred reais). How much interest are you paying? 2% 1% 0%* I don't know Basic CF03 When inflation increases, the cost of living increases. This statement is: True* False I don't know Basic CF04 Suppose you put R $ 100.00 in a savings account that yields 2% per year. You do not make any other deposits or withdraw any money from this account. How much would you have in this account at the end of the first year, including interest? R $ 98.00 R $ 100.00 R $ 102.00* R $ 120.00. I don't know Intermediary CF05 Imagine that the interest rate on your savings account is 6% per year and the inflation rate is 10% per year. After 1 year, how much will you be able to buy with the money in this account? (Assume that no money has been deposited or withdrawn). More than today Exactly the same Less than today* I don't know Intermediary CF06 Typically, which asset experiences the greatest fluctuations over time? Savings Actions* Public securities I don't know Intermediary CF07 An investment with a high rate of return will have a high rate of risk. This statement is: True* False I don't know Intermediary CF08 José takes out a loan of R $ 1,000.00 with an interest rate of 20% per year. If he does not make payments on the loan, at this interest rate, how many years would it take for the amount owed to double in value? Less than 5 years From 5 to 10 years More than 10 years I don't know Advanced CF09 When an investor spreads his investment across different assets, the risk of losing money: Increase Decreases* It's still the same I don't know Advanced Source : Vieira et al. (2020) Note : (*) Correct answer. Each correct answer is worth one point, totaling nine. After defining the scale items, the next step was to submit the research instrument for consideration by the Research Ethics Committee (CEP/UFES), thus meeting the legal requirements for the execution of the other research procedures. After approval by the CEP, the research instrument was structured in an electronic survey system, with the necessary clarifications regarding participation and data confidentiality, and a copy of the Free and Informed Consent Form (FICF) for later sending to the respondents. 3.2 Procedure for data collection and scale validation After structuring the respective measurement instruments, the data collection stage was carried out. This process occurred through the provision of the link or QR Code of the research instrument and the strategy for disseminating and processing the data followed the same criteria adopted by Silva et al. (2025a) and Silva et al. (2025b). Dissemination occurred through different channels, including social media platforms (such as Facebook, Instagram, Linkedin and WhatsApp ), in addition to sending by e-mail , containing a direct link to the research instrument. The sample was selected by convenience, considering practical criteria such as accessibility, availability, willingness to participate and low cost of access to participants (Etikan, 2016). Participation was voluntary and no compensation was offered to respondents. The collection covered three large groups of individuals: (i) undergraduate and graduate students from various educational institutions in the country; (ii) participants in lectures held within the scope of a university extension project; and (iii) participants in university extension projects related to financial education. The survey instrument was sent between November 2024 and January 2025, and 406 participants were collected. It is worth noting that the instrument allowed respondents not to respond to some items, or to choose the option “ I prefer not to respond ”. Therefore, before performing statistical analyses on the collected database, a data processing and refinement process was carried out. First, regarding data processing, the listwise exclusion methodology was used, in which all respondents with at least one missing value were completely removed from the analysis, mitigating the possibility of generating non-positively defined covariance, which constitutes a mathematical problem for EFA (Van Ginkel et al., 2014). This exclusion process resulted in a total of 389 forms completed completely. After excluding these respondents, the data was refined. For this stage, based on the concepts of Item Response Theory (IRT), it is assumed that each person who answers the questions must have some skill. At each skill level, there will be a probability of giving the correct answer to the item by each respondent (Bajaj & Kaur, 2024). In this context, the lower the difficulty of the item, the lower the skill level required, and vice versa. Therefore, a key assumption of IRT is that individuals who answer the more difficult items correctly should answer the easier ones correctly, otherwise it is assumed that there was some interference or random marking. Thus, we chose to exclude from the database respondents who presented results inconsistent with IRT, a process that resulted in a total of 349 forms answered completely and consistently with IRT. Although the available literature offers limited and sometimes conflicting guidance on the ideal minimum sample size (Kyriazos, 2018), it is recommended that studies should be designed to achieve significance levels of at least 0.05 ( p-value ), with power levels of 80% (Cohen, 1988). Furthermore, Hair et al. (2009) recommend that the relationship between sample size, effect and statistical power follows a rule of thumb: for a significance level of 0.01, 200 respondents per group are required; for 0.05, the recommended number is at least 130; and for 0.10, a sample of 100 participants is sufficient. Based on these criteria, it is noted that the sample used in this study (349 participants) meets the methodological recommendations to achieve significance levels of at least 0.01. Finally, descriptive data analysis was performed using a Microsoft Excel ® spreadsheet. Regarding model analysis and scale validation, the software used Jasp ® to perform the Kaiser Meyer-Olkmin (KMO) and Bartlett 's sphericity tests . To confirm the dimensionality, reliability and validity of the scale, Exploratory Factor Analysis (EFA) techniques were used and Confirmatory Factor Analysis (CFA), both performed using the Jasp software ®. 4. RESULTS The procedures and acceptability criteria of the indicators for validating the FK3BR scale were structured in line with the methodologies used in the works of Costa et al. (2025), Silva et al. (2025a), Silva et al. (2025b), Jain et al. (2022), Ritika & Kishor (2020) e Khan et al. (2015). These studies provided robust guidelines for assessing the quality, validity and reliability of the measures of the investigated scale, ensuring adherence to the best methodological practices provided in the literature. We present the results in three large blocks. First, the results of the descriptive analysis of the sample. Next, the criteria used to perform the Exploratory Factor Analysis (EFA) and its results are presented, and finally, the criteria used to perform the Confirmatory Factor Analysis (CFA), followed by the presentation of the results. 4.1 Descriptive Analysis of the Sample The present study had the responses of 349 participants, 57% female and 43% male. In terms of age group, the majority of participants (28.6%) were between 41 and 50 or 21 and 30 years old, followed by individuals aged between 31 and 40 years old (19.5%), between 51 and 60 years old (9.5%), under 21 years old (7.7%) and equal to or under 61 years old (6.0%). Regarding marital status, 41.3% were married, 40.7% were single, 9.1% were in a stable union, 8.6% were separated or divorced and 0.3% were widowed. A total of 51.9% of the participants had no children, while 19.5% had one child, 20.9% had two children, 5.4% had three children and 2.3% had four or more children. Regarding qualifications, the majority of respondents have completed secondary education (31.5%), followed by individuals with an undergraduate degree (24.4%), postgraduate degree at a specialization level (22.4%), master's degree (15.8%), doctorate (5.2%) and completed primary education (0.9%). Regarding income (expressed in terms of minimum wages), most respondents (33.0%) reported receiving more than 5 minimum wages. Next came people with incomes between 1 and 2 minimum wages (14.9%) and between 2 and 3 minimum wages (13.5%). In addition, 11.2% reported earning less than 1 minimum wage or between 3 and 4 minimum wages, 8.9% reported earning between 4 and 5 minimum wages, 5.2% reported having no income at all, and 2.3% were unable to provide information or preferred not to respond. Table 2 illustrates the results. Table 2 Descriptive analysis of the sample Demographic characteristics Description Frequency (%) Sex Feminine 199 57.0 Masculine 150 43.0 Age Up to 20 years 27 7.7 From 21 to 30 years old 100 28.6 From 31 to 40 years old 68 19.5 From 41 to 50 years old 100 28.6 From 51 to 60 years old 33 9.5 Equal to or greater than 61 years old 21 6.0 Marital status Single 142 40.7 Married 144 41.3 Stable union or living with a partner 32 9.2 Separated / Divorced / Broken 30 8.6 Widower 1 0.3 Number of children No children 181 51.9 A son 68 19.5 Two children 73 20.9 Three children 19 5.4 Four or more children 8 2.3 Education Up to Elementary School 3 0.9 High School 110 31.5 Higher education 85 24.4 Postgraduate (specialization) 78 22.4 Master's degree 55 15.8 PhD 18 5.2 Income No income 18 5.2 Up to 1 minimum wage (up to R $ 1,412.00 inclusive) 39 11.2 More than 1 to 2 minimum wages (from R $ 1,412.01 to R $ 2,824.00) 52 14.9 More than 2 to 3 minimum wages (from R $ 2,824.01 to R $ 4,236.00) 47 13.5 More than 3 to 4 minimum wages (from R $ 4,236.01 to R $ 5,648.00) 39 11.2 More than 4 to 5 minimum wages (from R $ 5,648.01 to R $ 7,060.00) 31 8.9 More than 5 minimum wages (from R $ 7,060.01) 115 33.0 I don't know how to say / I prefer not to say 8 2.3 As shown in Table 2 , the sample presented a diverse profile in terms of gender, age, marital status, number of children, education and income. Regarding the analysis of the level of correct answers per item, the value “zero” was assigned to incorrect answers and the value “one” to correct answers, and the percentage of correct answers and the difficulty of the item were analyzed. The results can be seen in Table 3 . Table 3 Frequency distribution of responses Percentage of correct answers Item Difficulty Total respondent points Number of respondents (%) (%) accumulated Item Level % correct 0 6 1.7 1.7 CF01 Basic 98.0 1 1 0.3 2.0 CF02 Basic 98.0 2 0 0 2.0 CF03 Basic 98.3 3 4 1.1 3.1 CF04 Intermediary 84.0 4 6 1.7 4.8 CF05 Intermediary 79.1 5 8 2.3 7.1 CF06 Intermediary 88.5 6 29 8.3 15.4 CF07 Intermediary 91.7 7 48 13.8 29.2 CF08 Advanced 60.2 8 95 27.2 56.4 CF09 Advanced 80.2 9 152 43.6 100.0 As illustrated, the sample demonstrated a high level of financial knowledge, since 95.1% of respondents answered more than half of the questions correctly (5 correct answers), and the majority (70.8%) answered 8 or 9 questions correctly. Regarding item difficulty, for questions that make up the basic level items, the average correct answer rate was very close to 100% (98.1%), while for the intermediate level it is 85.8% and for the advanced level, 70.2%. Given the high percentage of correct answers for items CF01, CF02 and CF03 and the inconsistencies generated in subsequent analyses, in line with the objective of this work (scale with 3 items), it was decided to exclude them. 4.2 Exploratory Factor Analysis The proposed scale (FK3BR) is an ultra-short version, with 3 items, developed based on the results of the study by Vieira et al. (2020). As a procedure for validating the scale, it was decided to preliminarily perform Exploratory Factor Analysis (EFA), before proceeding to Confirmatory Factor Analysis (CFA). This procedure aimed to verify which items share the same common variance, in addition to enabling the identification of problematic items, which have low factor loadings or which carry more than one factor (Silva et al., 2025b). To check whether the data matrix could be factored, the KMO and Bartlett's sphericity tests were carried out, two of the most commonly used evaluation methods in the literature (Damásio, 2012). The KMO test, which varies between 0 and 1, has the following evaluation parameters: KMO values below 0.50 are considered unacceptable or insufficient; between 0.50 and 0.59, low; between 0.60 and 0.69, moderate; between 0.70 and 0.79, good; between 0.80 and 0.89, very good; and above 0.90, optimal or excellent (Damásio, 2012; Hutcheson & Sofroniou, 1999; Kaiser, 1974). After the aforementioned tests, Exploratory Factor Analysis (EFA) was carried out, based on a correlation matrix using Weighted Least Squares (WLS) as the method for extracting factors. The decision on the number of factors to be retained was made using the Parallel Analysis technique with random permutation of the observed data (Timmerman & Lorenzo-Seva, 2011). In order to facilitate the interpretation of the extracted factors, Promax oblique rotation was applied. This type of rotation allows the extracted factors to correlate with each other and is therefore more suitable for assessing human and social aspects than so-called orthogonal methods (Damásio, 2012; Schmitt & Sass, 2011). 4.2.1 Results of Exploratory Factor Analysis The first step before the EFA was to analyze the level of correlation between the items. The result indicated a high correlation (between 0.92 and 1.00) between items CF01, CF02 and CF03, generating inconsistencies in subsequent analyses. Thus, in line with the objective of this study (scale with 3 items), it was decided to exclude them. This procedure made it possible to proceed with the EFA. Next, the KMO test was performed. The test result (0.802) suggested a very good overall adequacy of the data for factor analysis. Regarding individual values, all items presented values above 0.80, and were therefore also considered very good. The analysis of the dimensionality of the scale and the retention of factors, carried out using the “ Eigenvalue greater than 1” technique, indicated the retention of a single factor. Similarly, the parallel analysis considering a correlation matrix using the WLS method for factor extraction, it also suggested the existence of only one factor, as illustrated in Fig. 1 . Finally, the analysis of the relationship between the variables and the factor loadings of the items can be seen in Fig. 2 . As can be seen in Fig. 2 , the results indicate that most items (except items CF04 and CF 08) presented factor loading values greater than 0.50. Although slightly below the desirable level, we chose to maintain them, moving on to the next stage, Confirmatory Factor Analysis (CFA). 4.3 Análise Fatorial Confirmatória Confirmatory Factor Analysis (CFA) was performed to assess the plausibility of the FK3BR scale structure proposed in this study. The analysis was implemented using the Robust estimation method Diagonally Weighted Least Squares (RDWLS), suitable for categorical data and robust against violations of normality(Li, 2016; Brown, 2015; DiStefano & Morgan, 2014). The adequacy of the model was assessed using the following adjustment indices: Comparative Fit Index (CFI); Tucker-Lewis Index (TLI); Standardized Root Mean Residual (SRMR) and Root Mean Square Error of Approximation (RMSEA). According to the parameters recommended by the literature, CFI and TLI values should be greater than 0.90 and, preferably, above 0.95; and SRMR and RMSEA values should be less than 0.08 or, preferably, less than 0.06, with a confidence interval (upper limit) less than 0.10 (Brown, 2015; Schreiber et al., 2006). Additionally, the quality of the model was analyzed through convergent validity, which aims to verify whether the items that measure the same latent factor actually share a high common variance and reflect the same theoretical construction (Silva et al., 2025). To achieve convergent validity, three basic conditions must be met: (i) the item has a factor loading greater than 0.50 (preferably greater than 0.70), demonstrating a strong association with the latent variable to which it belongs; ( ii ) the composite reliability (CR) values must be greater than the average variance extracted (AVE); and ( iii ) the AVE must be greater than 0.50 (Jain et al., 2022; Hair et al., 2009). 4.3.1 Results of Confirmatory Factor Analysis The dimensional structure for the FL3BR scale measurement model presented satisfactory preliminary results for all indicators. However, as the objective of this work was to create an instrument with only 3 items, the scale reduction process was carried out. After re-specification of the model, all adjustment indexes presented satisfactory values, as illustrated in Table 3 . Table 3 Fit indices of the FK3BR model CFI TLI SRMR RMSEA (90% IC) Results 1,000 1,000 0,000 0,000 (0,000–0,000) Note : CFI = Comparative Fit Index; TLI = Tucker-Lewis Index; SRMR = Standardized Root Mean Square Residual; RMSEA = Root Mean Square Error of Approximation As can be seen, the CFI and TLI values reached values above the acceptable parameters (> 0.95), the SRMR index obtained an acceptable value (< 0.06), and the RMSEA index also obtained acceptable indices, presenting a value lower than 0.06, with a confidence interval (upper limit) lower than 0.10, supporting the model. Figure 4 complements the analysis, presenting the structure, factor loadings, measurement errors and average variance extracted (AVE) for the FK3BR scale. The convergent validity analysis was verified through three conditions listed by Jain et al. (2022). Analyzing the first criterion for evaluating convergent validity, the analysis of individual factor loadings indicated that all items in the model presented values greater than 0.50, as recommended in the literature (Jain et al., 2022; Hair et al., 2009), which highlights the existence of a strong association between the items and the latent variable to which they belong. The analysis of the composite reliability values, according to the criterion to be verified, indicated that the latent variable (financial knowledge dimension) obtained a CR value (0.843) higher than the average variance extracted (0.641), indicating that the items belonging to the factor present good internal consistency, as indicated by Hair et al. (2009). Finally, the analysis of the value referring to the average variance extracted (AVE), the third criterion to be verified, indicated that the proposed model presented an AVE greater than 0.50. Therefore, given the results found, it is noted that the structure proposed for the FK3BR presented satisfactory evidence of quality, reliability and convergent validity, supporting the model. 5. FINAL CONSIDERATIONS The objective of the study was to develop an ultra-short scale, with only 3 items, to measure the level of financial knowledge of individuals. After a literature review, a preliminary instrument was structured with 9 items structured for the Brazilian context, which were subjected to an Exploratory Factor Analysis and later, Confirmatory. The results of the AFE using a correlation matrix using Weighted Least Squares (WLS), as a factor extraction method, made it possible to reduce the number of questions to 6, eliminating items with low factor loading and which proved to be problematic. These items served as the basis for performing the Confirmatory Factor Analysis. Confirmatory Factor Analysis (CFA) was performed to assess the reliability and validity of the scale, which presented satisfactory results for all indicators used in the analysis. The CFI, TLI, SRMR and RMSEA indices reached values ​​considered acceptable by the literature, reinforcing the adequacy of the model. Regarding convergent validity, assessed based on three criteria established in the literature, the CR values indicated that all items in the model had factor loadings above 0.50, that the CR values were higher than the average variance extracted (AVE) and that the AVE also exceeded the limit of 0.50, evidencing a good fit of the model. Given these results, the structure proposed for the FK3BR, developed for the Brazilian context, demonstrated robust evidence of convergent reliability and validity, proving to be an effective instrument for quickly and accurately measuring individuals' financial knowledge. REFERENCES Abrantes-Braga, F. D. M. A., & Veludo-de-Oliveira, T. (2019). 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Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavior Research Methods , 48 (3), 936–949. https://doi.org/10.3758/s13428-015-0619-7 Lusardi, A., & Mitchell, O. S. (2008). Planning and Financial Literacy: How Do Women Fare? American Economic Review , 98 (2), 413–417. https://doi.org/10.1257/aer.98.2.413 Lusardi, A., & Mitchell, O. S. (2011). Financial literacy and retirement planning in the United States. Journal of Pension Economics and Finance , 10 (4), 509–525. Scopus. https://doi.org/10.1017/S147474721100045X Mastrascusa, R., de Oliveira Fenili Antunes, M. L., de Albuquerque, N. S., Virissimo, S. L., Foletto Moura, M., Vieira Marques Motta, B., de Lara Machado, W., Moret-Tatay, C., & Quarti Irigaray, T. (2023). Evaluating the complete (44-item), short (20-item) and ultra-short (10-item) versions of the Big Five Inventory (BFI) in the Brazilian population. Scientific Reports , 13 (1), Artigo 1. https://doi.org/10.1038/s41598-023-34504-1 Messy, F., & Monticone, C. (2016). Financial Education Policies in Asia and the Pacific. OECD Working Papers on Finance, Insurance and Private Pensions ,. https://doi.org/10.1787/5jm5b32v5vvc-en . OECD. (2023). OECD/INFE 2023 International Survey of Adult Financial Literacy . OECD. https://www.oecd.org/en/publications/oecd-infe-2023-international-survey-of-adult-financial-literacy_56003a32-en.html OECD - Organisation for Economic Co-Operation and Development. (2013). Financial literacy and inclusion: Results of OECD/INFE survey across countries and by gender. OECD Centre, Paris, France. Potrich, A. C. G., & Vieira, K. M. (2018). Demystifying financial literacy: A behavioral perspective analysis. Management Research Review , 41 (9), 1047–1068. https://doi.org/10.1108/MRR-08-2017-0263 Potrich, A. C. G., Vieira, K. M., Coronel, D. A., & Bender Filho, R. (2015). Financial literacy in Southern Brazil: Modeling and invariance between genders. Journal of Behavioral and Experimental Finance , 6 , 1–12. https://doi.org/10.1016/j.jbef.2015.03.002 Potrich, A. C. G., Vieira, K. M., & Kirch, G. (2015). Determinantes da Alfabetização Financeira: Análise da Influência de Variáveis Socioeconômicas e Demográficas. Revista Contabilidade & Finanças , 26 , 362–377. https://doi.org/10.1590/1808-057x201501040 Potrich, A. C. G., Vieira, K. M., & Kirch, G. (2016). Você é alfabetizado financeiramente? Descubra no Termômetro de Alfabetização Financeira. BASE - Revista de Administração e Contabilidade da Unisinos , 13 (2), Artigo 2. Potrich, A. C. G., Vieira, K. M., & Mendes-Da-Silva, W. (2016). Development of a financial literacy model for university students. Management Research Review , 39 (3), 356–376. https://doi.org/10.1108/MRR-06-2014-0143 Ramalho, T., & Forte, D. (2019). Financial literacy in Brazil—Do knowledge and self-confidence relate with behavior? Rausp Management Journal , 54 (1), 77–95. https://doi.org/10.1108/RAUSP-04-2018-0008 Ritika, & Kishor, N. (2020). Development and validation of behavioral biases scale: A SEM approach. Review of Behavioral Finance , 14 (2), 237–259. https://doi.org/10.1108/RBF-05-2020-0087 Schagen, S., & Linnes, A. (1996). Financial Literacy in Adult Life . NFER - National Foundatition for Education Research. Schmitt, T. A., & Sass, D. A. (2011). Rotation criteria and hypothesis testing for exploratory factor analysis: Implications for factor pattern loadings and interfactor correlations. Educational and Psychological Measurement , 71 (1), 95–113. https://doi.org/10.1177/0013164410387348 Schreiber, J. B., Nora, A., Stage, F. K., Barlow, E. A., & King, J. (2006). Reporting Structural Equation Modeling and Confirmatory Factor Analysis Results: A Review. The Journal of Educational Research , 99 (6), 323–337. Silva, E. M., Costa, D. F., & Bortolon, P. M. (2024). Behavioral biases and personal indebtedness: A systematic literature review . Research Square. https://doi.org/10.21203/rs.3.rs-4510972/v1 Silva, E. M., Costa, D. F., & Bortolon, P. M. (2025). Mental Accounting: An approach to developing and validating a measurement scale . Febrero 2025, (Version 1) available at Research Square . https://www.researchsquare.com/article/rs-6000691/v1 Silva, E. M., Moreira, R. de L., & Bortolon, P. M. (2023). Mental Accounting and decision making: A systematic literature review. Journal of Behavioral and Experimental Economics , 107 , 102092. https://doi.org/10.1016/j.socec.2023.102092 Silva, E. M., Moreira, R. de L., & Bortolon, P. M. (2025). Brazilians’attitude towards personal debt: An approach to developing and validating a measurement scale. Research Square , Febrero 2025, PREPRINT (Version 1) available at Research Square . https://doi.org/10.21203/rs.3.rs-6043283/v1 Singh, K. N., & Malik, S. (2022). An empirical analysis on household financial vulnerability in India: Exploring the role of financial knowledge, impulsivity and money management skills. Managerial Finance , 48 (9/10), 1391–1412. https://doi.org/10.1108/MF-08-2021-0386 Subova, N., Mura, L., & Buleca, J. (2021). Determinants of household financial vulnerability: Evidence from selected EU countries. E + M Ekonomie a Management , 24 , 186–207. https://doi.org/10.15240/tul/001/2021-3-011 Tabachnick, B. G., & Fidell, L. S. (2019). Using Multivariate Statistics (7 a ). Pearson. Thaler, R. H. (2013, outubro 5). Financial Literacy, Beyond the Classroom. The New York Times . https://www.nytimes.com/2013/10/06/business/financial-literacy-beyond-the-classroom.html Timmerman, M. E., & Lorenzo-Seva, U. (2011). Dimensionality assessment of ordered polytomous items with parallel analysis. Psychological Methods , 16 (2), 209–220. https://doi.org/10.1037/a0023353 Tomar, S., Kumar, S., & Sureka, R. (2021). Financial Planning for Retirement: Bibliometric Analysis and Future Research Directions. Journal of Financial Counseling and Planning , 32 (2), 344–362. https://doi.org/10.1891/JFCP-19-00062 Van Ginkel, J. R., Kroonenberg, P. M., & Kiers, H. A. L. (2014). Missing data in principal component analysis of questionnaire data: A comparison of methods. Journal of Statistical Computation and Simulation , 84 (11), 2298–2315. https://doi.org/10.1080/00949655.2013.788654 van Rooij, M. C. J., Lusardi, A., & Alessie, R. J. M. (2011). Financial literacy and retirement planning in the Netherlands. Journal of Economic Psychology , 32 (4), 593–608. https://doi.org/10.1016/j.joep.2011.02.004 Vieira, K. M., Matheis, T. K., Lehnhart, E. dos R., & Tavares, F. O. (2024). Digital Financial Knowledge Scale (DFKS): Insights from a Developing Economy. International Journal of Financial Studies , 12 (4), Artigo 4. https://doi.org/10.3390/ijfs12040120 Vieira, K. M., Potrich, A. C. G., & Bressan, A. A. (2020a). A proposal of a financial knowledge scale based on item response theory. Journal of Behavioral and Experimental Finance , 28 , 100405. https://doi.org/10.1016/j.jbef.2020.100405 Vieira, K. M., Potrich, A. C. G., & Bressan, A. A. (2020b). A proposal of a financial knowledge scale based on item response theory. Journal of Behavioral and Experimental Finance , 28 , 100405. https://doi.org/10.1016/j.jbef.2020.100405 Warmath, D., & Zimmerman, D. (2019). Financial Literacy as More than Knowledge: The Development of a Formative Scale through the Lens of Bloom’s Domains of Knowledge. Journal of Consumer Affairs , 53 (4), 1602–1629. https://doi.org/10.1111/joca.12286 Xiao, J. J., Sorhaindo, B., & Garman, E. T. (2006). Financial behaviours of consumers in credit counselling. International Journal of Consumer Studies , 30 (2), 108–121. https://doi.org/10.1111/j.1470-6431.2005.00455.x Additional Declarations The authors declare no competing interests. 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INTRODUCTION","content":"\u003cp\u003eFinancial literacy is widely recognized as a key factor in economic and financial stability and development (Subova et al., 2021; Potrich et al., 2015a). It is such an important topic for society, being defined by the Organization for Economic Cooperation and Development as a combination of \u0026ldquo;financial awareness, knowledge, skills, attitudes and behaviors needed to make sound financial decisions and, ultimately, achieve financial well-being\u0026rdquo; (OECD, 2023).\u003c/p\u003e \u003cp\u003eFinancial literacy consists of two dimensions: knowledge, which pertains to an individual's understanding of personal finance, and application, referring to behavior and attitudes in managing money. It consists of both knowledge and the application of specific human capital for personal finances (Huston, 2010).\u003c/p\u003e \u003cp\u003eThe importance of financial knowledge in this process is salutary. It allows individuals to manage their financial affairs, compare financial products and services to make appropriate and well-informed financial decisions, and react to events that may affect their financial well-being (OECD, 2023). Thus, understanding and measuring the level of financial knowledge of individuals, as well as the application of this knowledge in personal financial management, plays an important role so that governments of emerging and developed countries can outline policies related to improving the financial education of young people and adults.\u003c/p\u003e \u003cp\u003eIn this context, over the last few decades there has been a growing effort to measure individuals' financial knowledge, such as the scales by Lusardi \u0026amp; Mitchell (2008, 2011) and the financial knowledge scales by van Rooij et al. (2011) and Knoll \u0026amp; Houts (2012) and the Digital Financial Knowledge Scale (DFKS) by Vieira et al. (2024). Other scales innovate by implementing concepts from Item Response Theory (IRT) and Factor Analysis in their validation, such as those by Vieira et al. (2020) and Bajaj \u0026amp; Kaur (2024).\u003c/p\u003e \u003cp\u003eHowever, some of these scales comprise a large number of items for measuring the construct, others lack validation procedures and psychometric evaluation of their validity (Vieira et al., 2020),, and others, because they were developed in developed countries, with economic, structural and cultural characteristics distinct from economies in transition, carry a significant risk that concepts and measures tested in these contexts are not cross-culturally valid for other economies (Silva et al., 2025a; Tomar et al., 2021; Abrantes-Braga \u0026amp; Veludo-de-Oliveira, 2019).\u003c/p\u003e \u003cp\u003eAt another point, in the context of research, there is an increasing need to collect information in a short period of time, which highlights the importance of instruments that can be completed quickly and have good reliability (Mastrascusa et al., 2023). In order to fill this gap, the objective of this article was to structure an ultra-short scale, with only 3 items, capable of measuring the level of financial knowledge of individuals quickly and reliably for an economy in transition, the Brazilian one.\u003c/p\u003e \u003cp\u003eWe chose Brazil as the field of interest for this study for three main reasons. First, because it is one of the largest global economies, representing a population of over 212.6\u0026nbsp;million (IBGE, 2024). Second, due to its historical economic instability, with an economic environment in which the population, in general, is vulnerable to any financial emergency (Abrantes-Braga \u0026amp; Veludo-de-Oliveira, 2019). And last but not least, for convenience, considering practical criteria such as accessibility, availability, willingness to participate, and low cost of access for participants (Etikan, 2016).\u003c/p\u003e \u003cp\u003eTo achieve the objectives of this article, we start from the scale proposed by Vieira et al. (2020), which innovates by proposing a financial knowledge scale based on Item Response Theory (IRT). To validate the reduced scale, we used Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA), statistical techniques that allow reducing the number of observed variables, in a smaller set of latent variables, by examining the covariation between the items (Silva et al., 2025a; Silva et al., 2025b; Schreiber et al., 2006). As a result, we validated the \u003cb\u003eKF3 BR (Financial Knowledge \u0026ndash; 3 items, Brazil)\u003c/b\u003e, an instrument for measuring individuals' financial knowledge appropriate to the Brazilian context.\u003c/p\u003e"},{"header":"2. THEORETICAL FRAMEWORK","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Financial knowledge: concepts and their influence on decision making\u003c/h2\u003e \u003cp\u003eFinancial literacy is an important construct that represents more than an individual's stock of explicit financial knowledge. It consists of both the knowledge and application of human capital specific to personal finance (Huston, 2010). Its concept involves and includes skill and self-efficacy, and requires knowledge and skill, as well as a facility for critical thinking (Warmath \u0026amp; Zimmerman, 2019).\u003c/p\u003e \u003cp\u003eFinancial literacy refers to the ability to evaluate new and complex financial instruments and make informed judgments, both in choosing these instruments and in their most appropriate use (Potrich et al., 2016a; Schagen \u0026amp; Linnes, 1996). It can be defined as the measurement of how well an individual can understand and use information related to personal finances (Huston, 2010), and has three pillars: financial knowledge, financial behavior and financial attitude (OECD, 2023).\u003c/p\u003e \u003cp\u003eFinancial knowledge is the main focus of financial education, which is divided into two distinct components: financial knowledge and financial skills (Knoll \u0026amp; Houts, 2012). Financial knowledge is a particular type of human capital that is acquired throughout the life cycle, through learning about subjects that affect the ability to manage income, expenses and savings effectively (Potrich et al., 2015a; Delavande et al., 2008). On the other hand, financial skills concern the way individuals process financial information and make decisions.\u003c/p\u003e \u003cp\u003eThe second component, financial behavior, is an essential element of financial literacy and, without a doubt, the most important (Atkinson \u0026amp; Messy, 2012). Financial behavior deals with the way in which the individual deals with money. It refers to the actions and decisions that individuals take regarding the management of their financial resources, including spending (consumption), saving, investing and getting into debt, where financial education is shown to be a key variable that influences financial behavior (Ingale \u0026amp; Paluri, 2020). Positive outcomes of being financially literate are driven by behaviors such as spending planning and building financial security (Atkinson \u0026amp; Messy, 2012).\u003c/p\u003e \u003cp\u003eThe last component, financial attitude, can be understood as the economic and non-economic beliefs held by a given individual about the outcome of a given behavior (Ajzen, 1991), impacting decisions about consuming, saving, investing or getting into debt.\u003c/p\u003e \u003cp\u003eGiven the above, it is clear that financial literacy and financial knowledge are both human capital, but different constructs. Financial education is an input intended to increase a person's human capital, specifically financial knowledge and/or application, i.e., financial literacy (Huston, 2010). Thus, understanding current levels of financial education and needs for improvement becomes an essential tool for the effective development of financial education strategies and programs (OECD, 2023).\u003c/p\u003e \u003cp\u003eGiven the growing complexity of financial products and services available to society, having financial knowledge is important not only for individuals and families, becoming an essential skill for participation in society (Bajaj \u0026amp; Kaur, 2024; Potrich \u0026amp; Vieira, 2018).\u003c/p\u003e \u003cp\u003eRegarding the influence of financial knowledge on economic decisions, empirical studies indicate that this knowledge plays a fundamental role in financial decision-making. Furthermore, it is highly correlated with several factors, with higher education being one of the main determinants (Thaler, 2013). Individuals with higher levels of education tend to have higher levels of financial literacy and access to financial information (Messy \u0026amp; Monticone, 2016; Potrich et al., 2015; Chen \u0026amp; Volpe, 1998).\u003c/p\u003e \u003cp\u003eStudies show that positive financial behaviors are directly related to the level of economic and non-economic resources, and contribute to reducing financial stress and increasing financial satisfaction (Xiao et al., 2006), and that the level of knowledge has a positive influence on self-confidence and financial behaviors (Ramalho \u0026amp; Forte, 2019).\u003c/p\u003e \u003cp\u003eConfidence in one's own financial knowledge, in turn, is positively related to credit card use and overall financial satisfaction (Atlas et al., 2019). Furthermore, a higher level of financial knowledge, combined with better money management skills and less impulsiveness in financial behavior, can reduce individuals' financial vulnerability (Singh \u0026amp; Malik, 2022). These findings highlight the relevance of the topic in contemporary research on savings, consumption, investment and debt (Silva et al., 2024, 2023).\u003c/p\u003e \u003c/div\u003e"},{"header":"3. METHODOLOGICAL PROCEDURES","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Choosing items for FK3BR.\u003c/h2\u003e \u003cp\u003eGiven the importance of validated instruments that measure individuals' level of financial knowledge, the first step in validating the FK3BR was to search for scales developed in the Brazilian context in two peer-reviewed scientific repositories, \u003cem\u003eScopus\u003c/em\u003e and \u003cem\u003eWeb of Science\u003c/em\u003e (WoS). The search results indicated that the authors Potrich and Vieira are central references in the field, with several scales that, although varying in length and number of items, present significant overlap in their contents.\u003c/p\u003e \u003cp\u003eAmong the instruments identified, the following stand out: the scale by Potrich et al. (2015b) with 37 items, of which 17 are focused on financial knowledge; those by Potrich et al. (2015a, 2016), with 50 items, including 18 on financial knowledge; that by Potrich et al. (2016b), with 37 items, of which 17 are related to financial knowledge; and that by Potrich \u0026amp; Vieira (2018), with 71 items, of which 10 address financial knowledge. More recently, Vieira et al. (2020) proposed leaner versions, with scales containing 7, 9 and 12 items on financial knowledge and Vieira et al. (2024) developed the DFKS, specifically aimed at measuring digital financial knowledge.\u003c/p\u003e \u003cp\u003eAfter evaluating the content of these scales, we chose to use the scale developed and validated by Vieira et al. (2020) as the main input for validating the FK3BR. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the chosen questions of the instrument, the response options and the level of knowledge represented by the item as proposed in the related literature.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eList of items (questions) used to develop the FK3BR scale.\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\u003eItem code\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eQuestion\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAnswer option\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eItem Difficulty Level\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCF01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSuppose you saw the same television in two different stores for the initial price of R\u003cspan\u003e$\u003c/span\u003e 1,000.00. Store A offers a discount of R\u003cspan\u003e$\u003c/span\u003e 150.00, while Store B offers a discount of 10%. Which is the best alternative?\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBuy at store A (discount of R\u003cspan\u003e$\u003c/span\u003e 150.00 )*\u003c/p\u003e \u003cp\u003eBuy at store B (10% discount).\u003c/p\u003e \u003cp\u003eI don't know\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBasic\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCF02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSuppose you borrowed R\u003cspan\u003e$\u003c/span\u003e100.00 from a friend and after one week you paid back R\u003cspan\u003e$\u003c/span\u003e100.00 (one hundred reais). How much interest are you paying?\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2%\u003c/p\u003e \u003cp\u003e1%\u003c/p\u003e \u003cp\u003e0%*\u003c/p\u003e \u003cp\u003eI don't know\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBasic\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCF03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWhen inflation increases, the cost of living increases. This statement is:\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTrue*\u003c/p\u003e \u003cp\u003eFalse\u003c/p\u003e \u003cp\u003eI don't know\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBasic\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCF04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSuppose you put R\u003cspan\u003e$\u003c/span\u003e100.00 in a savings account that yields 2% per year. You do not make any other deposits or withdraw any money from this account.\u003c/p\u003e \u003cp\u003eHow much would you have in this account at the end of the first year, including interest?\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003cspan\u003e$\u003c/span\u003e 98.00\u003c/p\u003e \u003cp\u003eR\u003cspan\u003e$\u003c/span\u003e 100.00\u003c/p\u003e \u003cp\u003eR\u003cspan\u003e$\u003c/span\u003e 102.00*\u003c/p\u003e \u003cp\u003eR\u003cspan\u003e$\u003c/span\u003e 120.00.\u003c/p\u003e \u003cp\u003eI don't know\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIntermediary\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCF05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eImagine that the interest rate on your savings account is 6% per year and the inflation rate is 10% per year.\u003c/p\u003e \u003cp\u003eAfter 1 year, how much will you be able to buy with the money in this account? (Assume that no money has been deposited or withdrawn).\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMore than today\u003c/p\u003e \u003cp\u003eExactly the same Less than today*\u003c/p\u003e \u003cp\u003eI don't know\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIntermediary\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCF06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTypically, which asset experiences the greatest fluctuations over time?\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSavings\u003c/p\u003e \u003cp\u003eActions*\u003c/p\u003e \u003cp\u003ePublic securities\u003c/p\u003e \u003cp\u003eI don't know\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIntermediary\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCF07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAn investment with a high rate of return will have a high rate of risk. This statement is:\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTrue*\u003c/p\u003e \u003cp\u003eFalse\u003c/p\u003e \u003cp\u003eI don't know\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIntermediary\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCF08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eJos\u0026eacute; takes out a loan of R\u003cspan\u003e$\u003c/span\u003e1,000.00 with an interest rate of 20% per year.\u003c/p\u003e \u003cp\u003eIf he does not make payments on the loan, at this interest rate, how many years would it take for the amount owed to double in value?\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLess than 5 years\u003c/p\u003e \u003cp\u003eFrom 5 to 10 years\u003c/p\u003e \u003cp\u003eMore than 10 years\u003c/p\u003e \u003cp\u003eI don't know\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAdvanced\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCF09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWhen an investor spreads his investment across different assets, the risk of losing money:\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIncrease\u003c/p\u003e \u003cp\u003eDecreases*\u003c/p\u003e \u003cp\u003eIt's still the same\u003c/p\u003e \u003cp\u003eI don't know\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAdvanced\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cb\u003eSource\u003c/b\u003e: Vieira et al. (2020)\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cb\u003eNote\u003c/b\u003e: (*) Correct answer. Each correct answer is worth one point, totaling nine.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAfter defining the scale items, the next step was to submit the research instrument for consideration by the Research Ethics Committee (CEP/UFES), thus meeting the legal requirements for the execution of the other research procedures. After approval by the CEP, the research instrument was structured in an electronic survey system, with the necessary clarifications regarding participation and data confidentiality, and a copy of the Free and Informed Consent Form (FICF) for later sending to the respondents.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Procedure for data collection and scale validation\u003c/h2\u003e \u003cp\u003eAfter structuring the respective measurement instruments, the data collection stage was carried out. This process occurred through the provision of the \u003cem\u003elink\u003c/em\u003e or QR \u003cem\u003eCode\u003c/em\u003e of the research instrument and the strategy for disseminating and processing the data followed the same criteria adopted by Silva et al. (2025a) and Silva et al. (2025b). Dissemination occurred through different channels, including social media platforms (such as \u003cem\u003eFacebook, Instagram, Linkedin\u003c/em\u003e and \u003cem\u003eWhatsApp\u003c/em\u003e), in addition to sending by \u003cem\u003ee-mail\u003c/em\u003e, containing a direct link to the research instrument.\u003c/p\u003e \u003cp\u003eThe sample was selected by convenience, considering practical criteria such as accessibility, availability, willingness to participate and low cost of access to participants (Etikan, 2016). Participation was voluntary and no compensation was offered to respondents. The collection covered three large groups of individuals: (i) undergraduate and graduate students from various educational institutions in the country; (ii) participants in lectures held within the scope of a university extension project; and (iii) participants in university extension projects related to financial education.\u003c/p\u003e \u003cp\u003eThe survey instrument was sent between November 2024 and January 2025, and 406 participants were collected. It is worth noting that the instrument allowed respondents not to respond to some items, or to choose the option \u0026ldquo;\u003cem\u003eI prefer not to respond\u003c/em\u003e\u0026rdquo;. Therefore, before performing statistical analyses on the collected database, a data processing and refinement process was carried out.\u003c/p\u003e \u003cp\u003eFirst, regarding data processing, the listwise exclusion methodology was used, in which all respondents with at least one missing value were completely removed from the analysis, mitigating the possibility of generating non-positively defined covariance, which constitutes a mathematical problem for EFA (Van Ginkel et al., 2014). This exclusion process resulted in a total of 389 forms completed completely.\u003c/p\u003e \u003cp\u003eAfter excluding these respondents, the data was refined. For this stage, based on the concepts of Item Response Theory (IRT), it is assumed that each person who answers the questions must have some skill. At each skill level, there will be a probability of giving the correct answer to the item by each respondent (Bajaj \u0026amp; Kaur, 2024). In this context, the lower the difficulty of the item, the lower the skill level required, and vice versa.\u003c/p\u003e \u003cp\u003eTherefore, a key assumption of IRT is that individuals who answer the more difficult items correctly should answer the easier ones correctly, otherwise it is assumed that there was some interference or random marking. Thus, we chose to exclude from the database respondents who presented results inconsistent with IRT, a process that resulted in a total of 349 forms answered completely and consistently with IRT.\u003c/p\u003e \u003cp\u003eAlthough the available literature offers limited and sometimes conflicting guidance on the ideal minimum sample size (Kyriazos, 2018), it is recommended that studies should be designed to achieve significance levels of at least 0.05 (\u003cem\u003ep-value\u003c/em\u003e), with power levels of 80% (Cohen, 1988). Furthermore, Hair et al. (2009) recommend that the relationship between sample size, effect and statistical power follows a rule of thumb: for a significance level of 0.01, 200 respondents per group are required; for 0.05, the recommended number is at least 130; and for 0.10, a sample of 100 participants is sufficient. Based on these criteria, it is noted that the sample used in this study (349 participants) meets the methodological recommendations to achieve significance levels of at least 0.01.\u003c/p\u003e \u003cp\u003eFinally, descriptive data analysis was performed using a \u003cem\u003eMicrosoft Excel\u003c/em\u003e\u0026reg; spreadsheet. Regarding model analysis and scale validation, the \u003cem\u003esoftware used Jasp\u003c/em\u003e\u0026reg; to perform the \u003cem\u003eKaiser Meyer-Olkmin\u003c/em\u003e (KMO) and \u003cem\u003eBartlett 's sphericity tests\u003c/em\u003e. To confirm the dimensionality, reliability and validity of the scale, Exploratory Factor Analysis (EFA) techniques were used and Confirmatory Factor Analysis (CFA), both performed using the \u003cem\u003eJasp software \u0026reg;.\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e"},{"header":"4. RESULTS","content":"\u003cp\u003eThe procedures and acceptability criteria of the indicators for validating the FK3BR scale were structured in line with the methodologies used in the works of Costa et al. (2025), Silva et al. (2025a), Silva et al. (2025b), Jain et al. (2022), Ritika \u0026amp; Kishor (2020) e Khan et al. (2015). These studies provided robust guidelines for assessing the quality, validity and reliability of the measures of the investigated scale, ensuring adherence to the best methodological practices provided in the literature.\u003c/p\u003e\n\u003cp\u003eWe present the results in three large blocks. First, the results of the descriptive analysis of the sample. Next, the criteria used to perform the Exploratory Factor Analysis (EFA) and its results are presented, and finally, the criteria used to perform the Confirmatory Factor Analysis (CFA), followed by the presentation of the results.\u003c/p\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e4.1 Descriptive Analysis of the Sample\u003c/h2\u003e\n \u003cp\u003eThe present study had the responses of 349 participants, 57% female and 43% male. In terms of age group, the majority of participants (28.6%) were between 41 and 50 or 21 and 30 years old, followed by individuals aged between 31 and 40 years old (19.5%), between 51 and 60 years old (9.5%), under 21 years old (7.7%) and equal to or under 61 years old (6.0%).\u003c/p\u003e\n \u003cp\u003eRegarding marital status, 41.3% were married, 40.7% were single, 9.1% were in a stable union, 8.6% were separated or divorced and 0.3% were widowed. A total of 51.9% of the participants had no children, while 19.5% had one child, 20.9% had two children, 5.4% had three children and 2.3% had four or more children.\u003c/p\u003e\n \u003cp\u003eRegarding qualifications, the majority of respondents have completed secondary education (31.5%), followed by individuals with an undergraduate degree (24.4%), postgraduate degree at a specialization level (22.4%), master\u0026apos;s degree (15.8%), doctorate (5.2%) and completed primary education (0.9%).\u003c/p\u003e\n \u003cp\u003eRegarding income (expressed in terms of minimum wages), most respondents (33.0%) reported receiving more than 5 minimum wages. Next came people with incomes between 1 and 2 minimum wages (14.9%) and between 2 and 3 minimum wages (13.5%). In addition, 11.2% reported earning less than 1 minimum wage or between 3 and 4 minimum wages, 8.9% reported earning between 4 and 5 minimum wages, 5.2% reported having no income at all, and 2.3% were unable to provide information or preferred not to respond. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the results.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\u0026nbsp;\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\u003eDescriptive analysis of the sample\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDemographic characteristics\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDescription\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFrequency\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\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\" rowspan=\"2\"\u003e\n \u003cp\u003eSex\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFeminine\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e199\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e57.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMasculine\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e150\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e43.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eAge\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eUp to 20 years\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFrom 21 to 30 years old\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e28.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFrom 31 to 40 years old\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e19.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFrom 41 to 50 years old\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e28.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFrom 51 to 60 years old\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEqual to or greater than 61 years old\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"5\"\u003e\n \u003cp\u003eMarital status\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSingle\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e142\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e40.7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMarried\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e144\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e41.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eStable union or living with a partner\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSeparated / Divorced / Broken\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWidower\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"5\"\u003e\n \u003cp\u003eNumber of children\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo children\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e181\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e51.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA son\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e19.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTwo children\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e20.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThree children\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFour or more children\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eEducation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eUp to Elementary School\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigh School\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e110\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e31.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigher education\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e24.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePostgraduate (specialization)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e22.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaster\u0026apos;s degree\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e15.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePhD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"8\"\u003e\n \u003cp\u003eIncome\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo income\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eUp to 1 minimum wage (up to R\u003cspan\u003e$\u003c/span\u003e 1,412.00 inclusive)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e11.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMore than 1 to 2 minimum wages (from R\u003cspan\u003e$\u003c/span\u003e 1,412.01 to R\u003cspan\u003e$\u003c/span\u003e 2,824.00)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMore than 2 to 3 minimum wages (from R\u003cspan\u003e$\u003c/span\u003e2,824.01 to R\u003cspan\u003e$\u003c/span\u003e4,236.00)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e13.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMore than 3 to 4 minimum wages (from R\u003cspan\u003e$\u003c/span\u003e 4,236.01 to R\u003cspan\u003e$\u003c/span\u003e 5,648.00)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e11.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMore than 4 to 5 minimum wages (from R\u003cspan\u003e$\u003c/span\u003e5,648.01 to R\u003cspan\u003e$\u003c/span\u003e7,060.00)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMore than 5 minimum wages (from R\u003cspan\u003e$\u003c/span\u003e 7,060.01)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e115\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e33.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eI don\u0026apos;t know how to say / I prefer not to say\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.3\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\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003eAs shown in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, the sample presented a diverse profile in terms of gender, age, marital status, number of children, education and income. Regarding the analysis of the level of correct answers per item, the value \u0026ldquo;zero\u0026rdquo; was assigned to incorrect answers and the value \u0026ldquo;one\u0026rdquo; to correct answers, and the percentage of correct answers and the difficulty of the item were analyzed. The results can be seen in Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eFrequency distribution of responses\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003ePercentage of correct answers\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003eItem Difficulty\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTotal respondent points\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNumber of respondents\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e(%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e(%) accumulated\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eItem\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLevel\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e% correct\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\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCF01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBasic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.0\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=\"char\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCF02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBasic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\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=\"char\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCF03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBasic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e98.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCF04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIntermediary\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e84.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCF05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIntermediary\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e79.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCF06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIntermediary\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e88.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e15.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCF07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIntermediary\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e91.7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e29.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCF08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAdvanced\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e60.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e27.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e56.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCF09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAdvanced\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e80.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e43.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eAs illustrated, the sample demonstrated a high level of financial knowledge, since 95.1% of respondents answered more than half of the questions correctly (5 correct answers), and the majority (70.8%) answered 8 or 9 questions correctly. Regarding item difficulty, for questions that make up the basic level items, the average correct answer rate was very close to 100% (98.1%), while for the intermediate level it is 85.8% and for the advanced level, 70.2%.\u003c/p\u003e\n \u003cp\u003eGiven the high percentage of correct answers for items CF01, CF02 and CF03 and the inconsistencies generated in subsequent analyses, in line with the objective of this work (scale with 3 items), it was decided to exclude them.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e4.2 Exploratory Factor Analysis\u003c/h2\u003e\n \u003cp\u003eThe proposed scale (FK3BR) is an ultra-short version, with 3 items, developed based on the results of the study by Vieira et al. (2020). As a procedure for validating the scale, it was decided to preliminarily perform Exploratory Factor Analysis (EFA), before proceeding to Confirmatory Factor Analysis (CFA). This procedure aimed to verify which items share the same common variance, in addition to enabling the identification of problematic items, which have low factor loadings or which carry more than one factor (Silva et al., 2025b).\u003c/p\u003e\n \u003cp\u003eTo check whether the data matrix could be factored, the KMO and Bartlett\u0026apos;s sphericity tests were carried out, two of the most commonly used evaluation methods in the literature (Dam\u0026aacute;sio, 2012). The KMO test, which varies between 0 and 1, has the following evaluation parameters: KMO values below 0.50 are considered unacceptable or insufficient; between 0.50 and 0.59, low; between 0.60 and 0.69, moderate; between 0.70 and 0.79, good; between 0.80 and 0.89, very good; and above 0.90, optimal or excellent (Dam\u0026aacute;sio, 2012; Hutcheson \u0026amp; Sofroniou, 1999; Kaiser, 1974).\u003c/p\u003e\n \u003cp\u003eAfter the aforementioned tests, Exploratory Factor Analysis (EFA) was carried out, based on a correlation matrix using Weighted Least Squares (WLS) as the method for extracting factors. The decision on the number of factors to be retained was made using the Parallel Analysis technique with random permutation of the observed data (Timmerman \u0026amp; Lorenzo-Seva, 2011). In order to facilitate the interpretation of the extracted factors, \u003cem\u003ePromax\u003c/em\u003e oblique rotation was applied. This type of rotation allows the extracted factors to correlate with each other and is therefore more suitable for assessing human and social aspects than so-called orthogonal methods (Dam\u0026aacute;sio, 2012; Schmitt \u0026amp; Sass, 2011).\u003c/p\u003e\n \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\n \u003ch2\u003e4.2.1 Results of Exploratory Factor Analysis\u003c/h2\u003e\n \u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eThe first step before the EFA was to analyze the level of correlation between the items. The result indicated a high correlation (between 0.92 and 1.00) between items CF01, CF02 and CF03, generating inconsistencies in subsequent analyses. Thus, in line with the objective of this study (scale with 3 items), it was decided to exclude them. This procedure made it possible to proceed with the EFA.\u003c/p\u003e\n \u003cp\u003eNext, the KMO test was performed. The test result (0.802) suggested a very good overall adequacy of the data for factor analysis. Regarding individual values, all items presented values above 0.80, and were therefore also considered very good.\u003c/p\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003eThe analysis of the dimensionality of the scale and the retention of factors, carried out using the \u0026ldquo;\u003cem\u003eEigenvalue\u003c/em\u003e greater than 1\u0026rdquo; technique, indicated the retention of a single factor. Similarly, the parallel analysis considering a correlation matrix using the \u003cem\u003eWLS\u003c/em\u003e method for factor extraction, it also suggested the existence of only one factor, as illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eFinally, the analysis of the relationship between the variables and the factor loadings of the items can be seen in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eAs can be seen in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, the results indicate that most items (except items CF04 and CF 08) presented factor loading values greater than 0.50. Although slightly below the desirable level, we chose to maintain them, moving on to the next stage, Confirmatory Factor Analysis (CFA).\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003e4.3 An\u0026aacute;lise Fatorial Confirmat\u0026oacute;ria\u003c/h2\u003e\n \u003cp\u003eConfirmatory Factor Analysis (CFA) was performed to assess the plausibility of the FK3BR scale structure proposed in this study. The analysis was implemented using the Robust estimation method \u003cem\u003eDiagonally Weighted Least Squares\u003c/em\u003e (RDWLS), suitable for categorical data and robust against violations of normality(Li, 2016; Brown, 2015; DiStefano \u0026amp; Morgan, 2014).\u003c/p\u003e\n \u003cp\u003eThe adequacy of the model was assessed using the following adjustment indices: \u003cem\u003eComparative Fit Index\u003c/em\u003e (CFI); \u003cem\u003eTucker-Lewis Index\u003c/em\u003e (TLI); \u003cem\u003eStandardized Root Mean Residual\u003c/em\u003e (SRMR) and \u003cem\u003eRoot Mean Square Error of Approximation\u003c/em\u003e (RMSEA). According to the parameters recommended by the literature, CFI and TLI values should be greater than 0.90 and, preferably, above 0.95; and SRMR and RMSEA values should be less than 0.08 or, preferably, less than 0.06, with a confidence interval (upper limit) less than 0.10 (Brown, 2015; Schreiber et al., 2006).\u003c/p\u003e\n \u003cp\u003eAdditionally, the quality of the model was analyzed through convergent validity, which aims to verify whether the items that measure the same latent factor actually share a high common variance and reflect the same theoretical construction (Silva et al., 2025). To achieve convergent validity, three basic conditions must be met: (i) the item has a factor loading greater than 0.50 (preferably greater than 0.70), demonstrating a strong association with the latent variable to which it belongs; ( ii ) the composite reliability (CR) values must be greater than the average variance extracted (AVE); and ( iii ) the AVE must be greater than 0.50 (Jain et al., 2022; Hair et al., 2009).\u003c/p\u003e\n \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\n \u003ch2\u003e4.3.1 Results of Confirmatory Factor Analysis\u003c/h2\u003e\n \u003cp\u003eThe dimensional structure for the FL3BR scale measurement model presented satisfactory preliminary results for all indicators. However, as the objective of this work was to create an instrument with only 3 items, the scale reduction process was carried out. After re-specification of the model, all adjustment indexes presented satisfactory values, as illustrated in Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u0026nbsp;\u003c/p\u003e\n \u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eFit indices of the FK3BR model\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCFI\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTLI\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSRMR\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRMSEA (90% IC)\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\u003eResults\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\u003e1,000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0,000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0,000 (0,000\u0026ndash;0,000)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003ctfoot\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"5\"\u003e\u003cem\u003eNote\u003c/em\u003e: \u003cem\u003eCFI\u0026thinsp;=\u0026thinsp;Comparative Fit Index; TLI\u0026thinsp;=\u0026thinsp;Tucker-Lewis Index; SRMR\u0026thinsp;=\u0026thinsp;Standardized Root Mean Square Residual; RMSEA\u0026thinsp;=\u0026thinsp;Root Mean Square Error of Approximation\u003c/em\u003e\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tfoot\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003eAs can be seen, the CFI and TLI values reached values above the acceptable parameters (\u0026gt;\u0026thinsp;0.95), the SRMR index obtained an acceptable value (\u0026lt;\u0026thinsp;0.06), and the RMSEA index also obtained acceptable indices, presenting a value lower than 0.06, with a confidence interval (upper limit) lower than 0.10, supporting the model. Figure \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e complements the analysis, presenting the structure, factor loadings, measurement errors and average variance extracted (AVE) for the FK3BR scale.\u003c/p\u003e\n \u003cp\u003eThe convergent validity analysis was verified through three conditions listed by Jain et al. (2022). Analyzing the first criterion for evaluating convergent validity, the analysis of individual factor loadings indicated that all items in the model presented values greater than 0.50, as recommended in the literature (Jain et al., 2022; Hair et al., 2009), which highlights the existence of a strong association between the items and the latent variable to which they belong.\u003c/p\u003e\n \u003cp\u003eThe analysis of the composite reliability values, according to the criterion to be verified, indicated that the latent variable (financial knowledge dimension) obtained a CR value (0.843) higher than the average variance extracted (0.641), indicating that the items belonging to the factor present good internal consistency, as indicated by Hair et al. (2009).\u003c/p\u003e\n \u003cp\u003eFinally, the analysis of the value referring to the average variance extracted (AVE), the third criterion to be verified, indicated that the proposed model presented an AVE greater than 0.50. Therefore, given the results found, it is noted that the structure proposed for the FK3BR presented satisfactory evidence of quality, reliability and convergent validity, supporting the model.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"5. FINAL CONSIDERATIONS","content":"\u003cp\u003eThe objective of the study was to develop an ultra-short scale, with only 3 items, to measure the level of financial knowledge of individuals. After a literature review, a preliminary instrument was structured with 9 items structured for the Brazilian context, which were subjected to an Exploratory Factor Analysis and later, Confirmatory.\u003c/p\u003e \u003cp\u003eThe results of the AFE using a correlation matrix using \u003cem\u003eWeighted Least Squares\u003c/em\u003e (WLS), as a factor extraction method, made it possible to reduce the number of questions to 6, eliminating items with low factor loading and which proved to be problematic. These items served as the basis for performing the Confirmatory Factor Analysis.\u003c/p\u003e \u003cp\u003eConfirmatory Factor Analysis (CFA) was performed to assess the reliability and validity of the scale, which presented satisfactory results for all indicators used in the analysis. The CFI, TLI, SRMR and RMSEA indices reached values ​​considered acceptable by the literature, reinforcing the adequacy of the model.\u003c/p\u003e \u003cp\u003eRegarding convergent validity, assessed based on three criteria established in the literature, the CR values indicated that all items in the model had factor loadings above 0.50, that the CR values were higher than the average variance extracted (AVE) and that the AVE also exceeded the limit of 0.50, evidencing a good fit of the model.\u003c/p\u003e \u003cp\u003eGiven these results, the structure proposed for the FK3BR, developed for the Brazilian context, demonstrated robust evidence of convergent reliability and validity, proving to be an effective instrument for quickly and accurately measuring individuals' financial knowledge.\u003c/p\u003e "},{"header":"REFERENCES","content":"\u003col\u003e\n \u003cli\u003eAbrantes-Braga, F. D. M. A., \u0026amp; Veludo-de-Oliveira, T. (2019). 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Financial behaviours of consumers in credit counselling. \u003cem\u003eInternational Journal of Consumer Studies\u003c/em\u003e, \u003cem\u003e30\u003c/em\u003e(2), 108\u0026ndash;121. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/j.1470-6431.2005.00455.x\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"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},"keywords":"Scale Development, Financial Knowledge, FK3BR, Reliability and Validity","lastPublishedDoi":"10.21203/rs.3.rs-6279772/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6279772/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFinancial knowledge has been recognized as an essential element for making informed financial decisions, promoting greater autonomy, security, and financial well-being. To ensure a valid and reliable measurement of this knowledge, we selected nine questions from instruments developed and validated in the Brazilian context and applied Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) to validate an ultra-short scale, resulting in a three-item instrument, which we named KF3BR. To assess convergent validity, we used three basic conditions outlined in the literature: Composite Reliability (CR), Average Variance Extracted (AVE), and the relationship between them. The results indicate that the proposed structure for KF3BR provides satisfactory evidence of quality, reliability, and convergent validity.\u003c/p\u003e","manuscriptTitle":"FK3BR Scale: Development of an Ultra-Short Measure","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-28 17:42:11","doi":"10.21203/rs.3.rs-6279772/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":"1c6de584-44fe-42a7-9253-c0b26029f64e","owner":[],"postedDate":"March 28th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":46043344,"name":"Macroeconomics"}],"tags":[],"updatedAt":"2025-03-28T17:42:11+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-28 17:42:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6279772","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6279772","identity":"rs-6279772","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}