Which statistical test is most appropriate for comparing the means of three different groups?

The most appropriate statistical test for comparing the means of three different groups is the one-way ANOVA. This test is specifically designed to detect whether there are any statistically significant differences between the means of three or more independent groups.

The one-way ANOVA assesses the impact of a single factor on the dependent variable by analyzing variance among group means. It helps determine if at least one group mean is different from the others without conducting multiple t-tests, which could increase the risk of type I error.

Using a one-way ANOVA allows researchers to evaluate multiple groups simultaneously, making it a more efficient and powerful option compared to individual t-tests, which are limited to comparing two groups at a time. This reduces the likelihood of false positives that might occur if multiple t-tests were performed independently.

In contrast, a t-test is suitable only for comparing the means of two groups, while a paired t-test is used when there are two related groups (like measurements taken from the same subjects before and after an intervention). Additionally, the Chi-square test evaluates the association between categorical variables, not means, so it is not applicable for comparing group means. Thus, one-way ANOVA is the optimal choice for this scenario.