Which statistics help to determine if two means are far apart?

The determination of whether two means are significantly different from each other is specifically the purpose of t-tests. A t-test evaluates the means of two groups and assesses whether the observed differences between those means are greater than would be expected due to random sampling variability. It does this by calculating a t-statistic, which is based on the difference between the group means, the sample sizes, and the variability within each group.

If the calculated t-statistic is beyond a certain threshold (which correlates to a specific significance level, typically set at 0.05), it indicates that the means are significantly different. This test is widely used in experimental and clinical research when comparing two independent or related groups.

Correlation coefficients, ANOVA tests, and regression analysis serve different purposes. Correlation coefficients measure the strength and direction of a relationship between two variables rather than comparing means. ANOVA tests are used when comparing the means of three or more groups to understand if at least one group mean is different from others. Regression analysis is focused on modeling the relationship between dependent and independent variables and does not directly assess the difference between means.