# Is there a way to compare multiple means using the MEANS analytic option in SDA?

Yes. There are ways to compare multiple means (k-1 comparisons) using the Comparison of Means Program in SDA. Note that if a dependent variable is coded as 0/1, then the mean of the dependent variable is essentially the proportion.

In the Means Program, there are different dropdown options when selecting from the *main statistic to display box*. The default setting is to display the Means of the dependent variable against the required Row variable categories. Row variable categories define domains for subpopulation analysis. The selection of *differences from Row category* option allows you to choose a base category in the *If differences from a row or column, indicate base category* box. When you run the analysis for this selection, the result produced in each of the other row cells is the difference between that cell's mean and the base Row category cell mean. The above selection along with the selection of the *z/t-statistic and p-value* options produce the (k-1) comparisons of means or proportions and associated statistics from a single comparison of means run. This is a comparison of domain means for an outcome variable where domains are defined by a Row-only variable categories.

NOTES:

- In comparison of means testing, there are k(k-1)/2 differences of means or proportions being compared from k domains (or subpopulations or subgroups). In a single table run, the Means program enables us to simultaneously test the differences of (k-1) pair of means from a base category mean of a k category classification variable. So you will have k(k-1)/2 distinct comparison tests after choosing a different base category from separate (k-1) Means program runs. For a Row variable with k=4 levels (say, A, B, C and D), you will obtain 6 tests of difference of means (i.e., B-A, C-A, D-A for base reference A, C-B, D-B for base reference B and D-C for base reference C) from 3 (=4-1) separate MEANS program run when A, B, and C are used as base categories respectively.
- The computing in the R-DAS analysis system is equivalent to the Frequencies/Crosstabulation program module in SDA. It is not possible to perform a (k-1) means or proportions comparison using the R-DAS or SDA Frequencies/Crosstabulation program, while it is possible to perform a test of homogeneity of row (or column) percents for a two-way table. There is a separate FAQ on How do I perform a homogeneity of proportions or percentages using the Frequencies/Crosstab program in R-DAS?

Additional information on using the "Main statistic to display" option in the MEANS program can be found here: http://www.icpsr.umich.edu/SDAHELP/helpan.htm#mstats