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In this article, https://www.tandfonline.com/doi/abs/10.1080/03610910902859574 Peter Austin describes how to calculate the standardized difference between two groups, pg 1229 and pg 1230.

However am dealing with 4 groups.

 drug_g                     Mean_Age StdD_Age sample.siz
1 Surgery+Chemo+Ox6months   58.1     10.9       6146
2 Surgery+Chemo+Ox3months   62.3     11.5        154
3 Surgery+Chemo             59.2     10.8       8215
4 Surgery Only              59.8     11.0       1019

How do I calculate the standardized difference between these four groups ? Thanks.

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  • $\begingroup$ The standardized difference discussed in that paper is only defined for two groups. So you could compute pairwise standardized differences for any subset of two drugs. Other papers may define differences for more than two groups using ANOVA methods but this particular paper only defines the difference for $n=2$ groups. $\endgroup$ – StatsStudent Mar 23 at 17:11
  • $\begingroup$ @StatsStudent, could you give me some reference to papers that talk about ANOVA approach for these things (more than 2 groups). Thanks. $\endgroup$ – Sundown Brownbear Mar 23 at 19:28
  • $\begingroup$ By any chance are you trying to determine if there are significant differences between groups for propensity scores? $\endgroup$ – StatsStudent Mar 23 at 19:43
  • $\begingroup$ @StatsStudent yes eventually that is the plan $\endgroup$ – Sundown Brownbear Mar 23 at 22:08
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You need to ensure the means of each pair of groups you want to compare are similar to each other, which is to say that there is a small standardized mean difference for each pair of groups. To summarize balance across the entire sample for one variable, you can use the maximum standardized mean difference across all pairs.

If you're using R, check out the cobalt package, which allows for easy balance assessment for any number of groups and computes the maximum standardized mean difference for each variable.

Using an ANOVA F-test for each variable across the four groups is one possible approach, but it hasn't been evaluated and relies on the sample size, which makes it undesirable.

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