**A.H.G.S. van der Ven and F.M. Gremmen**

In prolonged work tasks subjects are required to engage in simple,
repetitive activities, such as letter cancelation, detecting
differences in simple shapes, adding three digits, and so on.
Prolonged work task are especially used in so-called concentration tests.
Performance is recorded as a series of reaction times.
Previous researchers have suggested using measures of variation,
such as the standard deviation of the reaction
times, to appraise concentration ability. However,
the correlation between the mean and the standard deviation of the
reaction times across subjects is usually very high. For example,
in the case of the Bourdon Vos test, this correlation was equal to 0.804.
This result was obtained
from a sample (N=715), which was used to standardize the test.
It is clear that, if one uses the standard deviation
as a measure for concentration, one has to account for the high
correlation of the standard deviation with the mean. Otherwise
one is not able to make any
statements about the specific nature of the standard deviation
in comparison to the mean. In this paper a particular hypothesis
regarding this correlation is proposed and tested. The hypothesis is
formulated in terms of the Poisson-Erlang model, which
is used as a limiting case of the Poisson-Inhibition model.
The model is tested using structural equation modeling.
The results could also be explained in terms of the Erlang model, which
can be considered as a limiting case of the Poisson-Erlang model.
The Poisson-Erlang model was tested against the Erlang model as a rival
model
by comparing the mean (across subjects) of the predicted third central
moments to the mean of the observed third central moments.
The results show corroborating evidence for the Poisson-Erlang model.

- Introduction
- Reaction Time Variation as a measure for Concentration
- The Poisson-Inhibition Model and the Poisson-Erlang Model
- The Correlation between Mean and Standard Deviation
- Structural Equation Modeling Using the PE Model
- The Erlang model as a rival model for the PE model
- Discussion
- References
- About this document ...