Which statistical test should be used for comparing two independent samples with continuous data?

The Student t-test is the appropriate statistical test for comparing two independent samples with continuous data when the following conditions are met: the data in each group should be normally distributed, and the variances of the two groups should be approximately equal. This test evaluates whether the means of the two samples are statistically significantly different from each other.

When using the Student t-test, you are typically looking to answer a question such as whether the average scores (or measurements) from two different groups (for example, two different treatment groups) differ in a statistically significant manner. This test is specifically designed for situations where you have two distinct sets of observations, enhancing the robustness and reliability of the hypothesis testing.

In contrast, other options presented involve different scenarios or types of data. The Mann Whitney U test is a non-parametric alternative to the t-test but is best used when the assumptions of normality are not met or when dealing with ordinal data. The Chi-square test is used for categorical data, not continuous data, to assess the associations between variables. The paired t-test is meant for dependent samples—or situations where there are matched pairs—where measurements are taken on the same subjects under different conditions.

Thus, for comparing two independent samples of continuous data, the Student t-test