15.4 Hedges’ g from a one-way ANOVA

We can also derive the SMD from the $$F$$-value of a one-way ANOVA with two groups. Such ANOVAs can be detected if you look for the degrees of freedom ($$df$$) underneath of $$F$$. In a one-way ANOVA with two groups, the degrees of freedom should always start with $$1$$ (e.g. $$F_{1,147}=5.31$$). The formula for this transformation looks like this (Cohen 1992; Rosnow and Rosenthal 1996; Rosnow, Rosenthal, and Rubin 2000):

$d = \sqrt{ F(\frac{n_t+n_c}{n_t n_c})(\frac{n_t+n_c}{n_t+n_c-2})}$

To calculate Hedges’ g from $$F$$-values, we can use the esc_f function with the following parameters:

• f: F-value of the ANOVA
• grp1n: Number of participants in group 1
• grp2n: Number of participants in group 2
• totaln: The total number of participants (if the n for each group is not reported)
• es.type: the effect measure we want to calculate. In our case this is "g". But we could also calculate Cohen’s d using "d".

Here’s an example

esc_f(f=5.04,grp1n = 519,grp2n = 528,es.type = "g")
##
## Effect Size Calculation for Meta Analysis
##
##      Conversion: F-value (one-way-Anova) to effect size Hedges' g
##     Effect Size:   0.1387
##  Standard Error:   0.0619
##        Variance:   0.0038
##        Lower CI:   0.0174
##        Upper CI:   0.2600
##          Weight: 261.1022

References

Cohen, Jacob. 1992. “A Power Primer.” Psychological Bulletin 112 (1). American Psychological Association: 155.

Rosnow, Ralph L, and Robert Rosenthal. 1996. “Computing Contrasts, Effect Sizes, and Counternulls on Other People’s Published Data: General Procedures for Research Consumers.” Psychological Methods 1 (4). American Psychological Association: 331.

Rosnow, Ralph L, Robert Rosenthal, and Donald B Rubin. 2000. “Contrasts and Correlations in Effect-Size Estimation.” Psychological Science 11 (6). SAGE Publications Sage CA: Los Angeles, CA: 446–53.