What analysis is appropriate for assessing mean differences in two groups?

The t-test is the appropriate analysis for assessing mean differences between two groups because it specifically measures whether there is a statistically significant difference between the means of two independent samples. This test works by evaluating the null hypothesis that the two groups have the same population mean against the alternative hypothesis that they do not.

In practice, when researchers want to compare the means of two groups, they would apply the t-test. It calculates the ratio of the difference between the group means to the variability of the samples. A significant result from this test indicates that it is unlikely that the observed differences in sample means occurred by random chance, thus supporting the claim that the groups differ in their means.

In contrast, ANOVA is used for comparing means across three or more groups rather than just two. The chi-square test assesses relationships between categorical variables, rather than mean differences. Regression analysis predicts a dependent variable based on independent variables, rather than directly comparing group means. Together, this illustrates that the t-test is specifically designed for the scenario of assessing mean differences between exactly two distinct groups.