# How do I perform a homogeneity test of proportions or percentages in the R-DAS?

The R-DAS does not have the Comparison of Means analysis available. The Frequencies/Crosstabulation program has an option of Summary Statistics to perform a test of independence (or no association) between two categorical variables using the Rao-Scott F statistics. These statistics take the complex design effect into account. The test of independence of a two-way contingency table is equivalent to the test of homogeneity of row (or column) percents (StataCorp 2011, page: 141-142). The null hypothesis for the later test is that row (or column) percents are equal for every category of the column (or row) variable.

For example, if your variable of interest is *levels of alcohol consumption* in the Column field, you can use the row percentage option and the resulting table output to approximately determine homogeneity (or the lack of homogeneity) of row (ethnic) groups among the levels of alcohol consumption. In other words, this test determines whether the distributions of each of the ethnic groups (among the alcohol levels) are equal.

The Rao-Scott F statistics are calculated from the contingency table for Row by Column variables. The test is significant at x% level of significance if the p-value of the Rao-Scott F statistic is less than x%. And, overall, the test concludes that there is association (or dependence) between Row and Column variables. The first screenshot shows RACE4 x ALCREC (recoded) table output for Total percent with the Summary Statistics box checked. From this table display of cell percent (i.e., total percent), confidence intervals and weighted cell frequencies, it is difficult to compare the prevalence of alcohol in different racial groups. In order to interpret the table output with regard to the test of homogeneity, we have to look at the table display in a better way. The second screenshot shows the contingency table output for Row percent. A larger percent (i.e., 63.7%) of whites have consumed alcohol within the last 30 days than blacks, other, or Hispanics. Since we only changed the way the percentages are displayed, the Rao-Scott F statistic is identical for both screenshots.

Reference:

StataCorp. 2011. Stata Survey Data Reference Manual, Release 12. Statistical Software. College Station, TX: StataCorp LP.