Statistical analysis categorical variable


For my research study I have performed a survey in which 400 people responded. In this survey they were given 3 options and the people had to choose which one they preferred the most. As a result (I rounded the numbers up for now to make it easy to visualize) 175 people chose option A, 125 chose option B and 100 people chose option C. Is there a statistical test I can perform to measure if The differences in results between these options are statistically significant?

I thank you for your help, my sincere apologies if this is a straight forward question or if this has already been asked many times.

I have thought about the chi square but don't I need 2 groups for that? Every time I try it I get stuck. My only 'group' is the total number of participants. The chi square asks for 2 groups such as men and women?


TS Contributor
You have got 3 groups (choice of A, B, or C) within your sample. You do not perform
a Chi² of association (between 2 variables), but a one-sample test. This regards the
question, whether the three options are chosen equally often in the population.

With kind regards



Active Member
It' s still chi square but this would be a goodness of fit test. You have a 3x1 table in which you would expect 400/3 in each if there was no difference. Do all the (e-o)^2/e stuff as usual. There are 2 df.


Less is more. Stay pure. Stay poor.
But won't the chi-square test just be significant if at least one of the groups is different?

I dislike significant testing since it doesn't give estimates. I would think three one sample tests against the constant n/3 with corrected alpha/3 used for confidence interval could work. Or a Bayesian test. I know it depends on what a person wants to do with the results, but a single p value seems trivial. Can a one-sample chi-sq kick out standardized residuals?


Active Member
Can a one-sample chi-sq kick out standardized residuals?
(o-e)/sqrt(e) is more or less a standardized residual (I think) because in this case, the null hypothesis is that the observed are Poisson with an expected rate 400/3 or 133 and the SD of the Poisson is sqrt(133). (Well almost anyway. The role of the df are always a bit fuzzy in my mind when it comes to this sort of question.)