How do I test the significance of the difference between two means when the samples are not independent and number of observations is different for each?

Question

Characteristics of data: marketing research study with total sample of 3500 respondents. Topics included ratings of various brands in a product category. But individual brands were rated ONLY by respondents who had used them. Brand A had 270 users; so only 270 of 3500 rated this brand. Brand B had 700 users; so only 700 of 3500 rated Brand B. 90 respondents were common users of the two brands. Since measures for the two brands are drawn from the same sample and have common respondents between them, I assume I should not use an independent sample approach. Ideally I would use the 2 sample paired T test, but of course that won't work since number of observations is different for the two sub samples (270 vs 700). What kind of significance test should I do? Doing a paired t test on just the 90 common observations might make some sense, but it feels like I'd be neglecting the majority of the relevant data. Any helpful thoughts appreciated,

Answer 1

Hi Bob,

I would go with a variation on what David suggested in his comment—matched pairs t-test on the 90 common raters, two sample t-test on everybody else. It might also be possible to do ANOVA, but that would get a little more complicated. I think both of those t-tests will work fine for your purposes.