Theoretical models of reaction times arising from simple-choice tasks

Abstract

In this work we present a group of theoretical models for reaction times arising from simple-choice task tests. In particular, we argue for the inclusion of a shifted version of the Gamma distribution as a theoretical model based on a mathematical result on first hitting times. We contrast the goodness-of-fit of those models with the Ex-Gaussian distribution, using data from recently published experiments. The evidence of the results obtained highlights the convenience of proposing theoretical models for reaction times instead of models acting exclusively as quantitative distribution measurements.

Keywords: Cognitive process; Quantitative distribution measurements; Reaction times; Simple-choice task tests; Theoretical models.

Fig. 1

An illustration of a cognitive processing underlying an RT task. The cognitive process, ${\{X_t\}}_{t\in {\mathbb{R}}_{+}}$, consists of a first time step, $\theta$, in which the individual is primarily receiving the stimulus and no response can be produced during this time-lapse. Then, the decision stage commences by processing the information of task’s difficulty plus random fluctuations. A response is finally produced when ${\{X_t\}}_{t\in {\mathbb{R}}_{+}}$ reaches the barrier at 0

Fig. 2

Histograms for the observed RTs in the case of sour-angular (DS1) and sweet-round (DS2) mapping’s distributions, in Velasco et al. (2016)’s study

Fig. 3

The resulting QQ-plots for the sour-angular (DS1) mapping’s distribution in Velasco et al. (2016)’s study. From top to bottom and left to right, the corresponding R-squared values were $\approx 0,837$, $\approx 0,883$, $\approx 0,835$ and $\approx 0,825$, respectively

Fig. 4

The resulting QQ-plots for the sweet-round (DS2) mapping’s distribution in Velasco et al. (2016)’s study. From top to bottom and left to right, the corresponding R-squared values were $\approx 0,959$, $\approx 0,995$, $\approx 0,948$ and $\approx 0,944$, respectively

Fig. 5

Histograms for the observed RTs in the case of ADHD (DS3) and non-ADHD (DS4) participants in the SC task, in Osmon et al. (2018)’s study

Fig. 6

The resulting QQ-plots for the case of ADHD (DS3) participants in the SC task in Osmon et al. (2018)’s study. From top to bottom and left to right, the corresponding R-squared values were $\approx 0,967$, $\approx 0,997$, $\approx 0,963$ and $\approx 0,958$, respectively

Fig. 7

The resulting QQ-plots for the case of non-ADHD (DS4) participants in the SC task in Osmon et al. (2018)’s study. From top to bottom and left to right, the corresponding R-squared values were $\approx 0,991$, $\approx 0,999$, $\approx 0,986$ and $\approx 0,965$, respectively