A clarification of self-terminating versus exhaustive variances in serial and parallel models

Townsend, J. T. (2001). A clarification of self-terminating versus exhaustive variances in serial and parallel models. Perception & Psychophysics, 63(6), 1101-1106.

Abstract:
Comments on the original article by N. Donnelly et al (see record 1999-05611-008) which employs response times variances (in the form of standard deviations) in addition to mean response times. Variances can contribute greatly to model testing. However, there is a danger of perpetuating the kinds of logical and methodological errors that have long attended research employing mean response times alone. This commentary clarifies the theoretical and methodological issues, points out some new results concerning variability in search processes, and indicates how to resolve the global and specific challenges associated with identifying psychological mechanisms.

Note:
This paper discussed whether the measure of variance of RT can be used as an indicator to classify the processing architecture (parallel/ serial) and stopping rule (self-terminating/ exhaustive).

Stemberg (1966) proposed a serial exhaustive search in memory in which the RT increases as the number of to0be0remembered items increases. A rule-of-thumb criterion for serially mean RT slope of greater than 10 ms has been seriously problematic (Wolfe, 1998).

Donnelly, Found, and Muller(1999) used the standard deviation of RT to discriminate serial versus parallel processing. A serial self-terminating may predict a faster increasing variance of RT for target present trails than that for target absent trials. A limited parallel model may predict equally increasing of TRT variance in both conditions. However, Townsend did not agree with this argument.

He gives some examples showing that the var (ST) may be equal to var(EXH), and the var (RT could be keep constant, And Even in a unlimited capacity parallel model, the car(RT) decreases as a function of the load (set-size, n).

Though, the var(RT) could be a useful tool to diagnose the processing architecture, stopping rule, and capacity.

The mathematical computation is little difficult for me, especially for the equation 3 and 4. I should take a close look on these equations.