Consequences of base time for redundant signals experiments

Townsend, J. T., & Honey, C. J. (2007). Consequences of base time for redundant signals experiments. Journal of Mathematical Psychology, 51(4), 242-265.

Abstract:
We report analytical and computational investigations into the effects of base time on the diagnosticity of two popular theoretical tools in the redundant signals literature: (1) the race model inequality and (2) the capacity coefficient. We show analytically and without distributional assumptions that the presence of base time decreases the sensitivity of both of these measures to model violations. We further use simulations to investigate the statistical power model selection tools based on the race model inequality, both with and without base time. Base time decreases statistical power, and biases the race model test toward conservatism. The magnitude of this biasing effect increases as we increase the proportion of total reaction time variance contributed by base time. We marshal empirical evidence to suggest that the proportion of reaction time variance contributed by base time is relatively small, and that the effects of base time on the diagnosticity of our model-selection tools are therefore likely to be minor. However, uncertainty remains concerning the magnitude and even the definition of base time. Experimentalists should continue to be alert to situations in which base time may contribute a large proportion of the total reaction time variance.


Note:
This paper discussed the consequence of base time in the redundant-signal design (RSD). The reaction time in the redundant-signal condition (RS) is faster than that in the single-target (SS) condition, showing a RS facilitation effect. Jeffery Miller (1982) developed a race model inequality to test the effect.

Assumption:
(1) In separate channels, the evidence is accumulated toward completion. Different channels are processed in parallel.
(2) The rate of processing in each channel is invariant across SS and RS condition (so-called context invariance).
(3) Obeyed the minimum-time stopping rule.
(4) Each channel is processed independently.
1-3 à race model 1-4 a race model with independent channel

The base time is also called the residual time or non-decisional time (see Ratcliff’s diffusion model). The base time includes two components: the time for basic sensory system to transfer information to higher processing centers and the time to execute a motor response.

* The presence of base time serves to decrease the maximum sensitivity of the race model inequality to the detection of the race model inequality.
* The presence of base time should lead the capacity coefficient to underestimate the capacity.

To exclude the base time component in the RT data, the estimation will be more precise.