To determine if there was a statistically significant difference between student groups after a physical activity intervention, which type of bivariate data analysis is appropriate?

When determining if there is a statistically significant difference between student groups after a physical activity intervention, the most appropriate analysis is ANOVA (Analysis of Variance). ANOVA is particularly useful when comparing means across three or more groups. In this scenario, if there are multiple student groups who have undergone different levels or types of physical activity interventions, ANOVA can help assess if the differences in outcomes—such as physical fitness levels, participation rates, or other relevant metrics—are statistically significant.

Using ANOVA allows for the analysis of variance among the groups simultaneously, thus providing a comprehensive understanding of where the differences lie. This is crucial in educational and health contexts, as it can inform decisions about the effectiveness of different physical activity interventions on varying student groups.

If only two groups were being compared, a t-test would be more appropriate, but since ANOVA can handle comparisons across multiple groups, it is the superior choice in this context. Additionally, while correlation is used to determine the relationship between two numerical variables, and chi-square tests are for categorical data to identify associations between groups, neither is suited for directly comparing means across groups in the context of intervention outcomes. Hence, ANOVA stands as the most fitting statistical method for the task at hand.