Studies were coded to facilitate meta-analytic investigation of whether people who have characteristics common to people with depression attend to negative information differently than positive or neutral information, with respect to how people who are not depressed attend to affectively valenced information. Effect sizes are therefore calculated to express the following quantities for each group of interest, for each study: the difference in reaction times for positive and negative stimuli, the difference in reaction times for negative and neutral stimuli, and the difference in reaction times for positive and neutral stimuli. In each case effect sizes may be expressed as the simple difference between the means of the conditions (henceforth D), and as a standardized difference between means for the different conditions, so as to control for variations in sample size as well as the sampling distribution. This technique allows estimation of negative information processing biases within groups, and comparison of the relative magnitudes of information processing biases between groups.
A traditional method for standardizing a difference between means in which two independent samples are used involves dividing the difference by the pooled standard deviation of the samples yielding Glass's d (Glass, McGaw, & Smith, 1981). Because Glass's d is based on an assumption of independent observations, and the values upon which effect sizes are being calculated are dependent (i.e., within-subjects factors), standardized effect sizes calculated in this manner would, most likely, be underestimated. A more representative effect size (henceforth referred to as d) would be standardized based on the standard deviation of the difference of the means, rather than the pooled standard deviation of each mean. As raw data is unattainable for most published studies, this difference cannot generally be empirically computed. The difference may, instead, be approximated as the sum of the variances for each measure minus twice the covariance, so as to account for the dependence of the measures. While the covariance is generally calculated as the correlation of reaction times for each condition times the product of the standard deviations for each condition, none of the published studies explicitly provided these correlations. Since raw data from two affective lexical decision studies using depressed and nondepressed individuals (Matthews & Southall, 1991; Stip & Le Cours, 1992), one study using only nondepressed individuals (Conway & Bekerian, 1987), as well as personal data were available, correlations between subjects' average reaction times to positive, negative, and neutral words were calculated for depressed and nondepressed individuals. The correlations for each condition were transformed to standard scores using Fisher's R to Z transform and averaged, weighting by sample size. The average Z score was then transformed back to a correlation to yield an average correlation. Conditional error variances for effect sizes for studies for which the raw data were unavailable are thus calculated as s12+s22-2*r12*s1*s2 where s1and s2 represent the standard deviations of reaction times to different groups of words, and r12 represents the correlation between the mean reaction times for those groups of words. Since empirical correlations between reaction times to positive, negative, and neutral words were not available for any study in which a negative mood induction procedure was performed, the average of the estimated effect sizes for depressed and nondepressed individuals are used for this condition.
Table 1, p. 16, provides the estimated zero-order correlations between reaction times to negative, positive, and neutral stimuli for each of the conditions. As noted above, these correlations were used to estimate conditional error variances for all studies for which empirical estimates of the conditional error variance were unavailable.
| Group | Positive-Neutral | Negative-Neutral | Negative-Positive |
| Depressed | .804 | .946 | .815 |
| Nondepressed | .644 | .804 | .677 |
| Induced depressed | .724 | .875 | .746 |
To estimate the average performance on the affective lexical decision task by members of each group, it is useful to aggregate the obtained effect sizes from individual studies in a given condition, thereby creating ``average'' effect sizes for each condition. These average effect sizes will henceforth be referred to as D. for the unstandardized means and d. for standardized means. In each case, weighted average effect sizes will be calculated, using the inverse of the sampling difference variance for weights, as suggested by Hedges and Oaklin (1985). This technique gives higher weights to studies with larger sample sizes and lower difference variances; features which presumably serve to make the effect size obtained from the study more robust.