Pairwise comparison of means

The -ttest- allows comparison of means between groups; the syntax of which is:

ttest varname [if] [in] , by(groupvar) [options1]

However, this only works if you have at most 2 distinct groups in groupvar. What would you do if you have more than 2 groups and you want to compare the means for each pairwise combination? This problem was presented to me recently. Since I am not aware of a single command that does this, it seems that the solution is to loop between groups.

Below, I used student2.dta (used in Statistics with STATA: Version 12) to illustrate one way of solving the problem. In this example, I want to (1) test whether the mean gpa between students taking different majors are the same, and (2)  save the results I need into a tab-delimited text file. Since there are 7 groups in major — coded as 1,2,…,7 — 21 pairs of means will be tested.

Since comparing the means of gpa for i=1 and j=2 is the same as comparing the means for i=2 and j=1, the -if- command is specified so that these duplicates are excluded. The -makematrix- (Nick Cox) command produces a matrix of the results of the command specified after the “:”. Here, we have specified that it will keep in memory 3 saved results from -ttest-: (1) mean for the 1st group, (2) mean for the 2nd group, and (3) the two-sided p-value. -matrix colnames-, on the other hand, is specified to indicate the names for each column. If this is not indicated, the default column names are the names of the saved results — “r(mu_1),” “r(mu_2),” and “r(p)”. Lastly, -mat2txt- (Michael Blasnik and Ben Jann) writes the matrix into a text file. Note that -mat2txt- needs to be installed. To install, type:

ssc install mat2txt

Now, what if I need to test the means for more than 1 variable, say for both gpa and study?  I can just add another loop for this:

The code above tests for means of gpa and study between each pair of groups in major.

I am sure there is a shorter and better way to do this. Until I find that solution, I will have to bear with what I have come up with.

Note: The code above is “wrapped”. If the line is long, its continuation is indented in the next line. Thanks to Cuong Nguyen for giving me the opportunity to learn something new over the weekend.