Embarrassed that I can't figure out this seemingly simple market research question. I have a sample of 2,400 cases who were presented with a list of the same product (cheeseburgers) by different companies (e.g, Whopper, Big Mac, Wendy's etc.). A total of 7 choices were presented and each participant could select only one. Now I need to know if the proportions selecting each are statistically different. For instance, if 35% chose option 1 and 28% chose option 2, is that difference significant.
I have run the two-sample test of proportions but this seems not right because there are not two independent samples.
I have also considered just estimating the confidence intervals around each proportion and assessing whether the CIs for any two overlapped.
Is there a better alternative? Any thoughts on how to run this would be appreciated.
Hello James,
The chi-square goodness of fit may be used as either an overall test (simultaneously comparing the rates of all 7 options being chosen), or any given pair.
For the omnibus test: H0: p1 = p2 = ... = p7, expected cell frequencies for each option would be N / 7. Observed cell frequencies are the actual numbers of selections. The computed chi-square would be referred to the sampling distribution of chi-square with 6 df.
For a pairwise test, such as H0: p1 = p4, the "N" of cases would be the sum of those choosing option #1 or option #4. Expected cell frequencies would be "N"/2. And so on. Alternatively, a binomial test could be used.
However, if your intention is to test lots of pairwise differences, then do note that the risk of at least one Type I error goes up as the number of comparisons increases. There are simple ways to combat this tendency (e.g., Bonferroni adjustment, Benjamini-Hochberg method).
Good luck with your work.
Thanks David… of most interest is the p1=p2 for the top to proportions selected.
Appreciate your taking the time to answer.
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