What statistical method would you use to compare mean differences in a study involving more than two groups?

The appropriate statistical method for comparing mean differences across more than two groups is ANOVA, which stands for Analysis of Variance. ANOVA allows researchers to determine if there are statistically significant differences between the means of three or more independent groups. It is preferable in this context because conducting multiple t-tests for each pair of groups would increase the risk of a Type I error, where the probability of wrongly rejecting a true null hypothesis increases.

ANOVA works by assessing the variance within each group and the variance between the groups to ascertain whether the differences observed are more significant than what might be expected due to random chance. If a significant result is found, post-hoc tests can be performed to identify which specific groups differ from one another, providing a comprehensive analysis of the data.

Other methods listed, such as the t-test, are designed for comparing the means of only two groups. The chi-square test is suitable for categorical data to assess relationships between variables, while simple linear regression is used to evaluate the relationship between a dependent variable and one independent variable. Therefore, analyzing more than two groups necessitates using ANOVA as the most relevant and effective method.