The answer to this question is found by understanding the basic principles of a two-way ANOVA (Analysis of Variance). ANOVA is a statistical method used to test differences between two or more means. A two-way ANOVA test is a statistical method used to understand the effect of two nominally scaled variables (also known as factors) on an interval scaled variable.
The options provided in this question are all parts of the ANOVA but are different from each other.
A. The effect of changing the levels of a factor on the dependent scores: This can be seen as the main effects of a factor. Changing the level of one factor does change the dependent score, but this does not consider interactions between factors.
B. The effect of changing the levels of a factor on the dependent scores, ignoring all other factors in the study: This is again referring to the main effects and does not involve interactions between factors.
C. The extent to which the effect of one factor depends on the action of the other factor: This is the definition of the interaction effect in a two-way ANOVA. The interaction effect happens when the effect of one factor (independent variable) on the dependent variable depends on the level of another factor. For example, if the effect of a drug on patients' recovery speed might depend on the age of the patients.
D. The effect on the independent variable of changing the levels of a factor: This is more of a cause-and-effect process in an experiment. However, in ANOVA we mainly focus on the variations in the dependent variable caused by different factors.
Therefore, the answer to this question is C. The interaction effect in a two-way ANOVA is the extent to which the effect of one factor depends on the action of the other factor.