15.7 Hedges’ g from an independent t-test

The SMD can also be derived from an independent t-test value with the following formula (Thalheimer and Cook 2002):

\[d = \frac {t(n_1+n_2)}{\sqrt{(n_1+n_2-2)(n_1n_2)}}\]

We can calculate Hedges’ g from a t-test using the esc_t function with the following paramters:

  • t: The t-value of the t-test. Either t or its p-value must be given.
  • p: The p-value of the t-test. Either t or its p-value must be given.
  • grp1n: The sample size of group 1.
  • grp2n: The sample size of group 2.
  • totaln: Total sample size, if grp1n and grp2n are not given.
  • 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_t(t = 3.3, grp1n = 100, grp2n = 150,es.type="g")
## Effect Size Calculation for Meta Analysis
##      Conversion: t-value to effect size Hedges' g
##     Effect Size:   0.4247
##  Standard Error:   0.1305
##        Variance:   0.0170
##        Lower CI:   0.1690
##        Upper CI:   0.6805
##          Weight:  58.7211


Thalheimer, Will, and Samantha Cook. 2002. “How to Calculate Effect Sizes from Published Research: A Simplified Methodology.” Work-Learning Research 1.