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I have two groups of people (for example male and female) and I performed an experiment on both groups with a single binary measurement. (for example I observed if each subject has performed a specific action (noted as 1) and if the subject didn't performed that particular action (noted as 0). Now I want to compare the two groups and see if these two groups are similar or not regarding performing this action. So I have two groups (male and female) and my dependent variable is a single binary measurement. I wanted to ask what statistical method can I use to compare these two groups. (note that my sample size are small like 23 subjects for each group. Is independent t-test a good approach for it or because my measurement is binary then I need another statistical analysis. thanks in advance.

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  • $\begingroup$ I personally don't have background in statistics, and I am a bit confused because when we have binary measurement how could we have a normal distribution. But I am sure there should be test for this kind of experiment. at first I tried to perform independent t test, but I need to calculate the mean value, and by binary data, I have seen that we don't have mean value. $\endgroup$ Commented Mar 9 at 10:52

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The two options that spring to mind first are chi-square and logistic regression. Chi-square looks at whether there is an association between the two variables. Logistic regression treats one variable as dependent and the other as independent. That seems more like what you've got (if your "for instance" reflect what you really did ... It's better to use your actual case, rather than "for instance").

However, there is also a t-test for proportions. This tests, not surprisingly, whether two proportions are equal.

All of these are discussed in many books and websites, and right here on CrossValidated. If you have questions after doing some reading, feel free to ask a new question.

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Since you are dealing with binary data (1 for performing the action, 0 for not performing it) the summary statistic in question is the sample proportion (In contrast to sample mean for continuous data) and your groups are independent (male and female), you can use a chi-square test or Fisher's exact test to compare the proportions of individuals who performed the action between the two groups.

Chi-square test is commonly used when you have larger sample sizes, whereas Fisher's exact test is recommended when sample sizes are small. Given your sample size of 23 subjects for each group, Fisher's exact test would be more appropriate.

A similar question has appeared before here on CrossValidated

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