Final answer:
The correct identification of sources of variation in two-way between-subjects ANOVA are Factor A, Factor B, Main effect, and Interaction effect, representing various influences on the dependent variable, including individual and combined effects of the independent variables.
Step-by-step explanation:
The correct identification of each source of variation in the two-way between-subjects ANOVA is Factor A, Factor B, Main effect, and Interaction effect. These variations include:
- Factor A: This represents the variation due to the first independent variable.
- Factor B: This represents the variation due to the second independent variable.
- Main effect: This refers to the individual effect of each factor on the dependent variable.
- Interaction effect: This refers to the effect of the combination of both factors A and B on the dependent variable, beyond their individual main effects.
When analyzing the results, the variation between groups (Factor A and B) and the variation within groups (Error) are considered. The main effects and the interaction effects collectively help determine if the independent variables have a significant impact on the dependent variable.
In experiments such as medical trials, researchers may administer a placebo to control for psychological effects on the treatment outcomes. Also, by assigning subjects randomly, lurking variables are evenly distributed across groups, ensuring that any measured differences in response variables are due to the treatments (Factor A and B), thereby establishing a potential cause-and-effect relationship. If a two-way ANOVA analysis encounters violations of assumptions, such as differing standard deviations among groups, further statistical testing may be necessary.