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


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.