Which statistical method is best for examining differences in multiple groups simultaneously?

The best statistical method for examining differences among multiple groups simultaneously is ANOVA, which stands for Analysis of Variance. This technique allows researchers to compare the means of three or more groups to determine if at least one group mean is significantly different from the others.

ANOVA works by analyzing the variance within each group and the variance between the groups to assess if the observed differences in means are statistically significant. This is particularly useful in experimental designs where multiple treatment groups are compared, as it handles the complexity of multiple comparisons and minimizes the risk of type I errors that can occur when conducting several t-tests independently.

Contrarily, a t-test is limited to comparing the means of only two groups, making it inadequate for tests involving three or more groups. The chi-square test is utilized for examining the association between categorical variables and does not assess mean differences between groups. Linear regression is designed for predicting a dependent variable based on one or more independent variables and isn't focused on comparing means across groups. Thus, ANOVA is the most appropriate choice for examining differences among multiple groups simultaneously.