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I have a question about the sample size when using chi-square test of independence or multinomial logistic regression. I would if you provide me with your feedback since I search a lot and I could not find a clear answer:

does the sample size or the number of responses for the dependent variable should be the same for all the different values of the independent variable? if the sample size differs, would it affect the test result?

For example, the independent variable is type of data (location, time, interests) and the dependent variable is about their privacy concern (yes, maybe, no). I can control how many people to answer the privacy question for each condition: whether location, time or interests.

So, should I assign the same number of people for each condition to have the same number of responses across all conditions (values of independent variable) in order to be able to apply these tests or it does not matter or affect the test??

May thanks, Fatma.

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You can apply these tests with (almost) any marginal distribution, but the statistical power of your test will be larger when assign your respondents equally. So if you have a choice, distribute your respondents equally.

In many cases you don't have a choice, e.g. you are doing a survey and you cannot manipulate what their location is. In that case you can still perform those tests, the resulting $p$-values will be correct, but if the distribution is very unequal, the statistical power will suffer. This is something to be aware off, but typically not something you can do much about.

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