Statistical Measures

Reaction time curves obtained in over-learned prolonged work tasks usually show an increase at the beginning of the test and, after some time, reach a stationary state. According to inhibition theory, if the initial inhibition at the beginning of the task deviates from its stationary value, then it will be some time for the stationary state to be reached. The phenomenon of increasing reaction time curves can be explained by assuming that the inhibition at the beginning of the task is lower, because in a state of non-work, in the period before the task, the inhibition will fluctuate at a lower level than in a state of work during the task. This assumption is known as the perseveration hypothesis. The perseveration hypothesis has recently be tested by van der Ven (1997). The inhibition model is very capable of describing this long-term trend in the RTs. However, the PE model does not allow any long-term trend in the RTs. If one wants to use the PE model as an approximation of the PE model, then one should only make use of the RTs in the stationary part of the RT series. Since the Poisson-Erlang model will be used as an approximation of the Poisson-Inhibition model, it was decided to compute the relevant statistics such as the mean and the variance from the reaction times 7 to 30, considering that part of the reaction time series as stationary. The cut-off was set between the sixth and seventh reaction time in order to obtain stationary series of 24 RTs (24 can be divided by 3 and by 4, see below). The reaction times 31 to 33 were disregarded due to an end spurt effect (see van der Ven, Smit and Jansen, 1989). To be certain that stationarity had been reached in the reaction times 7-30, all subjects were excluded from the sample who still showed exponential regression. The following procedures was followed.

1.

First, the exponential regression parameters were estimated for each individual reaction time curve according to a least square criterium. Due to a lack of sufficient computational precision, in three cases, no minimum could be found. Therefore, these subjects were also excluded from the total sample, leaving 712 subjects. Finally, one subject showed a regular pattern in the RT's 1-10, but an irregular pattern in the RT's 21-30:

10.0	12.0	13.0	12.0	14.0	13.0	13.0	14.0	10.0	12.0
13.0	12.0	11.0	41.0	21.0	31.0	51.0	21.0	11.0	41.0
51.0	11.0	43.0	15.0	12.0	14.0	12.0	15.0	14.0	14.0

This subject was also excluded, leaving 711 subjects for the final dataset.

2.

Next, all subjects were excluded for which the predicted reaction times 8-30 were not equal (up to the first decimal) to the predicted reaction time 7. Reaction times were measured in seconds.

3.

Finally, all subjects were excluded for which $\beta$ was positive and for which the minimum RT of the RTs 1-6 was greater then the minimum RT of the RTs 7-30. In this way the minimum RT was always situated at the beginning of the test (RTs 1-6). These two criteria were used to ascertain increasing curves, with the minimum RT in the beginning of the test.

The total number of cases left was equal to 185.

The observable parts of the two linear equations given above are A, E(T) and Var(T). The minimum of the reaction times 1-6, that is the also the minimum of the reaction times 1-30, will be used as an estimate of A. The difference between the mean of a subsample (to be specified below) of the reaction times 7-30 and the minimum reaction time will be used as an estimate of E(T)-A. This difference will be referred to as the mean difference. The variance of a subsample (to be specified below) of the reaction times 7-30 will be used as an estimate of Var(T).