Final answer:
Option C is answer. Using multifactorial ANOVA allows for the detection of interactions among variables, a benefit not provided by direct comparisons of means or one-way ANOVA.
Step-by-step explanation:
One benefit of using a multifactorial ANOVA with two or more factors is that it can detect interactions among the variables, whereas multiple direct comparisons of means cannot. Unlike one-way ANOVA, which compares the means across multiple groups to see if at least one is different, multifactorial ANOVA (also known as factorial ANOVA) can test for interactions, which are situations where the effect of one factor on the outcome variable depends on the level of another factor. This is in addition to testing for main effects, which are the independent contributions of each factor to the outcome variable.
A one-way ANOVA looks at a single factor and tests the null hypothesis that all group means are equal, using the F distribution for the test statistic. However, it cannot assess the interactive effects between multiple factors, which is a crucial aspect of multifactorial ANOVA tests. Therefore, the ability to detect interactions is a distinct advantage of multifactorial ANOVA over one-way ANOVA and direct comparisons of means, which typically involve t-tests that can only compare two means at a time.