Notes and Comment

Researchers have shown increasing interest in characterizing the shape of response time (RT) distributions, rather than addressing only a measure of the distribution’s central tendency, such as the mean. Ratcliff (1979) demonstrated that moment-based estimators, such as skew and kurtosis, are not suitable for characterizing the shape of empirical distributions because they suffer from problems with efficiency (i.e., very large sample sizes are required) and robustness (i.e., higher order moments are too sensitive to outliers). He suggested an alternative strategy, characterizing shape by fitting an explicit density function; the ex-Gaussian density (McGill, 1963) has been widely adopted (e.g., Andrews & Heathcote, 2001; Balota & Spieler, 1999; Heathcote, Popiel, & Mewhort, 1991; Hockley, 1984; Leth-Steenson, Elbaz, & Douglas, 2000; Mewhort, Braun, & Heathcote, 1992; Ratcliff & Murdock, 1976; Smith & Mewhort, 1998; Spieler, Balota, & Faust, 1996; Wixted & Roher, 1993). Here, we propose and evaluate a new robust method of fitting densities. Van Zandt (2000) examined several methods for fitting a density, f, with parameter vector u , to RT data. For a range of densities commonly used in RT analysis, the generally least variable and biased parameter estimates were obtained by maximum likelihood (ML) estimation. The likelihood of u given a data vector RT, L( u |RT) is proportional to the probability of the data given u , p(RT | u ) (likelihood is defined only up to an arbitrary scale factor, Edwards, 1972). For RT data measured with precision 2L (i.e., RTi falls in the range RTi 6 L , i = 1 . . . n), the probability of observing RTi is