A BASIC program for metaanalysis of effect sizes using r, BESD, and d

Metaanalytic statistics combine the results of independent studies for the purpose of integrating their fmdings (Glass, 1976; Rosenthal, 1978, 1979, in press; Rosenthal & Rubin, 1982a, 1982b, 1982c). Metaanalysis has recently been applied to reviews of research in a wide variety of areas (e.g., Cooper, 1979; Mullen & Suls, 1982; Rosenthal, 1978; Smith & Glass, 1977). Mullen (1982) has recently made available a BASIC program that calculates metaanalytic statistics that summarize the significance levels of a body of research (i.e., standard normal deviate for metaanalysis of significance, the probability associated with this standard normal deviate, and fail-safe number for the .05 level of significance). The BASIC program described here, designed as a complement to Mullen (1982), allows the user to perform a metaanalysis that summarizes the effect sizes of a body of research (for computational procedures, cf. Cohen, 1977; Cooper, 1979; Rosenthal, 1978,1979, in press). Input. The program requires the user to enter information about the test statistic used in each data set included in the metaanalysis. Specifically, the program prompts the user to enter: the type of test statistic (t test, F test, chi square, or correlation coefficient), the numerical value of the test statistic, the df associated with this statistic (N in the case of chi square), and the direction of the effect ("+" if in the expected direction, "-" if in the opposite direction). When the user has entered all of the relevant information for each study, the user signals the end of input and the metaanalytic statistics are calculated and displayed. Output. The program outputs eight related effectsize statistics for each study: r, the derived Pearson correlation coefficient; r , the proportion of variance accounted for; zr, the standard normal deviate associated with the derived r; p, the probability associated with this standard normal deviate (cf. Rosenthal, in press); BESD, the binomial effect-size display (i.e., the amount of change in success rate, improvement rate, etc., attributable to the variable of interest; Rosenthal & Rubin, 1982c); d, the standardized difference between the means (Cohen, 1977); Zd, the standard normal deviate associated with the standardized difference between the means (Rosenthal, 1979); and p, the probability associated with this standard normal deviate. When the user signals the end of input, the program outputs eight similar related metaanalytic statistics: r; the mean correlation coefficient; r, the proportion of variance accounted for; 2[, the standard normal deviate associated with the mean correlation coefficient; p, the probability associated with this standard normal deviate; BESD, the binomial effect-size display associated with the mean correlation coefficient; d, the mean standardized difference between the means; zer, the standard normal deviate associated with the mean standardized difference between the means; and p, the probability associated with this standard normal deviate. Limitations. The primary limitation of this program is that it allows the user to include in this metaanalysis of effect sizes only those studies that report a t test, an F test, a chi square, and/or a correlation coefficient. However, given the apparent hegemony of these statistics in many areas of social science research, this limitation may be less than restrictive. The only F-test values that can legitimately be entered into the program are those for which df for the numerator is equal to 1, as in the comparison of two group means. Similarly, the only chi-square values that can legitimately be entered into the program are those for which df is equal to 1 (cf. Rosenthal, in press). The r, r2 , z, p, BESD, and d values estimated by this program are generally accurate to within ±.005 of the values retrieved by hand from standard statistical tables and/or from computational formulas. Application of this program to the demonstration data in Rosenthal (1978, Table 1) essentially reproduces the standardized differences between the means; application of this program to the demonstration data in Rosenthal (in press, Table 4) essentially reproduces the binomial effect-size displays. Language. The program takes up approximately 3,000 bytes of memory and consists of 57 lines. The program is written in Radio Shack Level II BASIC and can be readily translated into other versions of BASIC. Availability. A program listing is available free of charge from Brian Mullen, Department of Psychology, North Central College, Naperville, Illinois 60566.