I Two-sample t test vs. chi-squared test for homogeneity

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The two-sample t-test is used to determine how close the means of two samples are, specifically when the samples are drawn from a normal distribution. In contrast, the chi-squared test for homogeneity assesses the similarity of distributions between two populations or samples. The t-test is appropriate for comparing means, while the chi-squared test is suitable for categorical data and can be applied in a wider range of situations. Understanding when to use each test is crucial for accurate statistical analysis. Both tests serve distinct purposes in hypothesis testing and data analysis.
Leo Liu
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The purpose of t test is to find how close the two means of the two samples given are; whereas the result of ##\chi^2## homogeneity test indicates the likeness of the two distributions of two populations (or maybe samples--I am not sure). Can anyone please tell me the differences between them, when one should use which one, and whether one may conclude that chi-squared test is applicable to more situations than t test? Thanks.
 
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I think that your own statement has described the difference between the t-test and the chi-squared test. One thing to add is that the Student's t-test is for a sample drawn from a normal distribution.
 
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