Final answer:
The correct statistical test for four categorical independent variables with multiple levels and two interval ratio-dependent variables is multivariate analysis of variance (MANOVA) or multiple regression analysis if MANOVA is unavailable as an option.
Step-by-step explanation:
If you have four categorical independent variables with 2 or more levels and 2 interval ratio-dependent variables, the appropriate statistical test to use is not one-way ANOVA, two-way ANOVA, or the chi-square test. Instead, you should consider using multivariate analysis of variance (MANOVA). MANOVA is an extension of one-way ANOVA that can handle multiple dependent variables and can test for the main and interaction effects of multiple categorical independent variables on interval ratio-dependent variables. If MANOVA is not available as an answer choice, another alternative would be multiple regression analysis, as it can handle multiple predictors and dependent variables, although it does not directly test for all effects of the predictors.
A one-way ANOVA would only be appropriate if there was a single categorical independent variable (factor) and one dependent variable. A two-way ANOVA extends this to two categorical independent variables. However, the chi-square test is designed for categorical dependent variables, and hence not suitable for interval ratio variables. A regression analysis could be applicable but would not provide the full benefits of a complete MANOVA approach.