Imagine a study investigating calorie estimation using a factorial design with two independent variables: participant major and food type. In this scenario, what does running a factorial ANOVA produce separate $F$ ratios and $p$-values for?

A health psychologist is investigating calorie estimation using two independent variables: Participant Major (Psychology vs. Nutrition) and Food Type (Cookie vs. Hamburger). Match each specific effect produced by a factorial ANOVA to the specific research question it evaluates.

In a study using a factorial ANOVA to analyze calorie estimates based on participant major (Psychology vs. Nutrition) and food type (Cookie vs. Hamburger), a significant interaction effect would indicate that the difference in calorie estimations between cookies and hamburgers is consistent across both majors.

A health psychologist is investigating calorie estimation using two independent variables: participant Major and Food Type. In the resulting factorial ANOVA, the component that evaluates whether the difference in estimations between hamburgers and cookies is inconsistent across the two majors is the ________ effect.

A health psychologist is evaluating the results of a factorial ANOVA for a study on calorie estimation with two independent variables: Participant Major (psychology vs. nutrition) and Food Type (cookie vs. hamburger). Arrange the following steps in the correct order of interpretation priority, starting with the effect that determines the context for all other findings.

Suppose you are writing the 'Data Analysis' section for a research proposal investigating how calorie estimation is influenced by participant major (Psychology vs. Nutrition) and food type (Cookie vs. Hamburger). To properly structure the factorial ANOVA results you intend to generate, which of the following represents the complete set of primary statistical effects you must plan to report?

In a factorial ANOVA analyzing calorie estimation based on participant major and food type, the analysis produces a single $F$ ratio that represents the aggregate significance of all variables combined.

In the health psychologist's study of calorie estimation based on Participant Major and Food Type, what is the primary purpose of the 'separate' $F$ ratio and $p$-value generated for the interaction effect?

A health psychologist conducts a factorial ANOVA on calorie estimation data using two independent variables: participant major (psychology vs. nutrition) and food type (cookie vs. hamburger). The analysis yields separate F ratios for each effect. Match each factorial ANOVA component on the left to the specific research question it analyzes on the right.

After running a factorial ANOVA on calorie estimation data (participant major × food type), a researcher obtains a non-significant main effect of participant major (p = .34) but a significant major × food type interaction (p = .02). A colleague advises omitting the interaction from the write-up because it is 'too complicated to explain.' Evaluating this advice: following it would produce a _____ account of the results, because a significant interaction is the primary evidence that the effect of participant major on calorie estimates is not consistent across food types.

In a factorial design where a health psychologist investigates calorie estimation with the independent variables of participant major (psychology versus nutrition) and food type (cookie versus hamburger), a factorial ANOVA is performed. Recall and state the three specific effects for which this analysis generates separate $F$ ratios and $p$-values.

Explain what each of the three separate statistical outputs (the main effect of major, the main effect of food type, and the interaction effect) measures in the context of this calorie estimation study. How does the researcher use these outputs to understand the factors influencing calorie estimation?

Imagine a health psychologist runs the calorie estimation study and wants to know if the difference in calorie estimates between psychology and nutrition majors is larger when estimating a cookie than when estimating a hamburger. Based on the outputs produced by a factorial ANOVA, which specific statistical output should they examine to directly answer this question, and why?