Final answer:
The correct source of variation in the two-way between-subjects ANOVA is 'a. two main effects, one interaction, and error', which includes the effects of two independent variables, their interaction, and unexplained variability.
Step-by-step explanation:
The question relates to two-way between-subjects ANOVA, which is a statistical method used to test for differences in a dependent variable across two or more groups that have been split on two independent variables (factors).
The correct identification of each source of variation in the two-way between-subjects ANOVA is: a. two main effects, one interaction, and error. This means:
- The first main effect is the impact of the first independent variable alone on the dependent variable.
- The second main effect refers to the impact of the second independent variable alone on the dependent variable.
- The interaction effect occurs when the effect of one independent variable on the dependent variable depends on the level of the other independent variable.
- Error refers to the variability in the dependent variable that cannot be explained by the two main effects or the interaction effect, often thought of as random variation or noise.
These sources of variation are essential for interpreting the results of ANOVA tests. In particular, they allow researchers to understand the extent to which independent variables and their combinations affect the dependent variable, beyond what could be expected by chance.