Which statistical method is designed to assess differences among group means under two independent variables?

The statistical method that assesses differences among group means under two independent variables is indeed the two-way ANOVA. This technique is specifically designed to evaluate the impact of two different independent variables on a continuous dependent variable, allowing researchers to understand not only the main effects of each independent variable but also any interaction effects that may occur between them.

With two-way ANOVA, you can analyze how variations in one independent variable influence the dependent variable while simultaneously considering the effects of the other independent variable. This is beneficial in research scenarios where multiple factors may influence an outcome, providing a more comprehensive analysis of the data compared to methods that assess only one factor at a time.

In contrast, other choices like one-way ANOVA only allow for the comparison of means across a single independent variable, while linear regression focuses on modeling the relationship between dependent and independent variables through an equation. The chi-square test, on the other hand, is used for categorical data to assess relationships between categorical variables rather than analyzing means. Therefore, two-way ANOVA is indeed the suitable choice for this specific scenario involving two independent variables.