I am looking to calculate hedge's g effect sizes for a psychological intervention.
A similar paper talks about obtaining "effect sizes by subtracting the posttest mean of the comparison group from the posttest mean of the group treatment and dividing the result by the pooled standard deviation of the two groups."
The equation I can find for pooled standard deviation only reference two groups at one time-point. i.e. √( (Na-1)Sa^2 + (Nb-1)Sb^2 / (Na+Nb-2) )
What equation do I use where the N and SDs of groups (a and b) change between pre-test and post-test?
Many thanks.
Hello John,
First, the formula you give (with the exception of some missing parentheses or braces for the numerator of the expression) is correct; it will give the pooled groups SD.
Since it appears that the statistic of interest is the pre-to-post change across groups, you could:
1. Compute a pre-post ES for each group (and the associated CI, if you like). Generally, you'd use pre-scores to derive the SD (as the change is interpreted relative to baseline values). Then compare the two group ES values.
2. Compute pre-post mean difference for each group, and divide that by the weighted average of each group's SD of difference scores (using the method you outlined in your query). Note that the SD for a difference score is most easily computed by: (a) forming the difference scores, (b) computing the SD of those difference scores directly; and (c) forming the pooled value using the formula.
This gives the ES of pre-post differences between groups.
Note that method #1 and method #2 might lead you to somewhat different conclusions, since the variance of difference scores varies depending on how strongly pre- and post- scores correlate.
Good luck with your work.
Dear John Butler,
It is important to know that the Standard Deviation (SD) is the square root of a variance. Hence, if you want to determine the pooled SD, you have to calculate the pooled variance and then find the square root of the variance to get the pooled SD. Therefore, you need to determine the pooled variance first as shown in the following link.
https://www.planetofbits.com/uncategorized/pooled-variance/
Hope this will help you. Good luck in your studies.
Regards,
S. Senthilnathan.
David Morse
Thank you very much for your answer. I would like to use Method 2. The one bit I still have a query over is part b). What is the equation to use to calculate the SD of mean difference scores directly?
The data I have pulled from each of the studies looks like this (e.g):
Intervention Group Pre-treatment: M=63.92; SD=10.67; N=63
Intervention Group Post-treatment: M=59.43; SD=7.23; N=63
Control Group Pre-treatment: M=64.57; SD=9.79; N=65
Control Group Post-treatment: M=62.69; SD=4.84; N=65
Many thanks for any further assistance.
Hello again John,
To compute the variance or SD of difference scores, you either have to have the difference scores themselves, or know the correlation between pre & post values for the cases. That's because Vdiff = Vpre + Vpost - 2rpre,post*SDpre*SDpost
(where V = variance, r = correlation, SD = standard deviation).
If all you have access to are the summary statistics (as indicated in your second post), you won't be able to get a precise estimate of variation of pre-post scores.
Good luck with your work.
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