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

In summary, the purpose of the t-test is to compare the means of two samples, while the chi-squared homogeneity test determines the similarity of two population distributions. The t-test is used for samples drawn from a normal distribution, while the chi-squared test may be applicable to a wider range of situations.
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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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FAQ: Two-sample t test vs. chi-squared test for homogeneity

What is the difference between a two-sample t test and a chi-squared test for homogeneity?

A two-sample t test is used to compare the means of two independent groups, while a chi-squared test for homogeneity is used to determine if there is a significant difference in the distribution of categorical data between two or more groups.

When should I use a two-sample t test instead of a chi-squared test for homogeneity?

A two-sample t test should be used when the data is continuous and normally distributed, and the groups being compared are independent. A chi-squared test for homogeneity is more appropriate when the data is categorical and the groups being compared are not independent.

What are the assumptions for a two-sample t test and a chi-squared test for homogeneity?

The assumptions for a two-sample t test include normality of the data, independence of the groups, and equal variances between the groups. The assumptions for a chi-squared test for homogeneity include independence of observations, expected cell counts of at least 5, and a large enough sample size.

Can a two-sample t test and a chi-squared test for homogeneity be used for the same data?

No, a two-sample t test and a chi-squared test for homogeneity are used for different types of data and have different assumptions. It is important to carefully consider the type of data and the research question before deciding which test to use.

How do I interpret the results of a two-sample t test and a chi-squared test for homogeneity?

In a two-sample t test, the results will include a p-value which indicates the probability of obtaining the observed difference in means if the null hypothesis (no difference between groups) is true. A p-value less than the chosen alpha level (typically 0.05) suggests that there is a significant difference between the two groups. In a chi-squared test for homogeneity, the results will also include a p-value, but this indicates the probability of obtaining the observed distribution of data if the null hypothesis (no difference in distribution between groups) is true. A p-value less than the chosen alpha level suggests that there is a significant difference in the distribution of data between the groups.

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