Reaction time distributions are characteristically positively skewed, with a roughly Gaussian body and a long right tail. The ex-Gaussian distribution captures this shape as the convolution of a Gaussian component (parameterized by μ and σ) and an exponential component (parameterized by τ). This decomposition provides more information than simple mean and standard deviation about the processes generating RT variability.
Parameters and Interpretation
The Gaussian component (μ, σ) is often interpreted as reflecting the central decision process, while the exponential component (τ) reflects the tail of the distribution — slow responses that may arise from attentional lapses, complex processing, or decision difficulty. Experimental manipulations often selectively affect one component: stimulus quality tends to shift μ, while attention-demanding tasks tend to increase τ.
Ex-Gaussian parameters can be estimated by the method of moments (equating sample moments to theoretical moments) or by maximum likelihood estimation. Quantile maximum probability estimation (QMPE) provides robust estimates even with moderate sample sizes. At least 40–50 observations per condition are recommended for stable parameter estimation.
Limitations
While the ex-Gaussian provides an excellent descriptive fit, it is not a process model — the parameters do not directly correspond to cognitive mechanisms in the way that diffusion model parameters do. The ex-Gaussian should be viewed as a useful data analysis tool rather than a theoretical model of decision processes. Nevertheless, its parameters often show orderly relationships with experimental variables that support their psychological interpretation.