Reaction Time Variation as a measure for Concentration

Previous researchers have suggested using the variation of the reaction times as a measure of concentration. For example, Binet (1900) and Godefroy (1915) both suggested using the mean deviation of the reaction times as a measure of concentration. One might ask why the mean deviation was proposed instead of the standard deviation. The mean deviation is easy to compute. Electronic calculators were not yet invented. Moreover, the mean deviation was easy to understand for the psychologists of that time who were usually not yet very familiar with probability theory and statistics. The standard deviation, apart from being mathematically very convenient, only makes sense in the case of applications of probability distributions such as the normal distribution, the gamma distribution or other distributions for continuous variables. Note, that reaction time is a continuous variable. In this paper the standard deviation will be used instead of the mean deviation. The importance of fluctuations in the reaction times has also been stressed by Spearman (1927, p. 327). He considered oscillation (read: variation) to be the third universal factor, in addition to the general factor: g, and perseveration. More recently, Vos (1992) has published standardization norms for the mean and the standard deviation of the reaction times. Although measures of variation may be intuitively appealing, they still lack any explicit theoretical foundation. Moreover, there may exist a correlation across subjects between measures of central tendency, such as the mean, and measures of variation, such as the mean deviation or standard deviation. If such correlation exists then one should first inquire the nature of that correlation, in order to know what additional information may be contained in the variation of the reaction times. This is precisely the main subject of this paper. First, the Poisson-Inhibition model is discussed in more detail, as well as, the Poisson-Erlang model, which is a limiting case of the Poisson-Inhibition model. Next, the phenomenon itself is demonstrated by computing the correlation between mean and standard deviation across subjects in a Dutch concentration test, which is known as the Bourdon-Vos Test. Subsequently, the application of the method of structural equation modeling is discussed as a tool to test a specific hypothesis concerning the nature of the correlation between the mean and standard deviation across subjects. This hypothesis originated from the Poisson-Erlang model, which is used as an approximation of the Poisson inhibition model. The statistical results, using structural equation modeling, also apply under the Erlang model, which can be considered as a rival model for the Poisson-Erlang model. Therefore, the Poisson-Erlang model was also tested by comparing the model with the Erlang model in a more direct way.