Closed-form estimates of ex-Gaussian response time models in two-digit number comparison

In the context of two-digit number comparison, the unit-decade compatibility effect (UDCE) refers to a slowdown that occurs during trials that are unit-decade incompatible – that is, trials where the order relationship of the tens digits is reversed from that of the ones digits. This slowdown demonstrates an inability to ignore the irrelevant ones digits when comparing two-digit numbers. The purpose of this thesis was to investigate the potential cognitive mechanisms behind the UDCE by using ex-Gaussian modeling. The ex-Gaussian model decomposes a distribution of observed response times into two components: a normal component with mean μ and an exponential component with mean τ. If the effect appears in the tail component τ, this implies that the UDCE involves analytic processes (e.g., thinking, decision making). If the effect appears in the normal component μ, this implies that the UDCE involves nonanalytic processes (e.g., stimulus driven automatic processes). We used a method of moments technique to develop closed-form equations for estimating μ and τ directly from the summary statistics of observed response times. Then, we applied these closed-form equations to an existing dataset. Subsequent Bayesian hypothesis testing demonstrates that the UDCE occurs in the μ parameter, but not in the τ parameter. Therefore, the UDCE reflects only nonanalytic processing.