Working with frequency tables?

[Welch Suggs]

This is more of a statistics problem than a State-specific problem, but I’m trying to use Stata to solve it. I have Likert-style survey data from a total population and a subpopulation. Unfortunately I do not have actual observations; instead I have frequency counts of responses.

frequency of	5	4	3	2	1
x1	432	107	10	0	4
x2	408	120	10	9	7
x3	444	99	8	0	3
x4	425	107	11	4	4
x5	276	194	43	34	7

and subpopulation

frequency of	5	4	3	2	1
x1	28	9	1	0	1
x2	26	10	0	0	3
x3	28	10	0	0	1
x4	26	9	2	1	1
x5	18	15	2	2	2

My goal is to find variables with statistically significant differences between the subpopulation and the overall population, i.e. where I can reject the null hypothesis that the subpopulation is a random draw from the total population. The data are not normally distributed, but obviously are ordinal. Does anyone have any advice on how to work with these? I can calculate means and standard deviations, but I’m trying to figure out if there’s a way to break the frequency counts into individual observations so I could run a Wilcoxon signed rank sum test or similar on x1(population) = x1(subpopulation) or some such. Thanks in advance!

[William Lisowski]

Other will respond, I hope, with advice on methodology. I just want to make the point that, in theory, you should not need to expand your "value&count" observations into "count" observations each with "value" observed. "Frequency weights" are designed to take care of this, and if you find a test that does what you need, the chances are good that it will support frequency weights. Start with help weights for more information on frequency weights, among others.

[Welch Suggs]

William Lisowski Thanks for the suggestion! Others?

[Marcos Almeida]

William suggested an excellent approach on how to tackle aggregated data in Stata.

With regards to comparing a sample with a subsample,I fear that core assumptions concerning benchmark tests would be eventually violated.

Maybe a simulation technique, such as random sampling or bootstrapping or permutation could provide start-up information on whether there might be a difference between the overall sample and this given subsample.