What's the REAL difference between moderation and interaction, in ANOVA, in this case? And more

I think the people here will appreciate this. This is a reading assignment/puzzle.

I don't see a difference between #1 and #6. This refers to the subject of my question here (moderation and interaction).

Note: I've changed ALL the items names in #1 - #6, but I have otherwise left the sentence structures alone. For example, "Male vs. Female" could be "Tall vs. Short."

Match the answers below with each question.  An answer can only be used once.
(Use 6 of 7 of the answers.)  The entire set is marked as right or wrong.

**Hypothesis**

1. The impact of personal health interest level (minimal, average, high) on
average spending on raw vegetables per week is moderated by the state of
residence: California or Florida.

2. Food group choice A: [low-carb/high-fat/med-protein], B: [high-carb/low-
fat/med-protein], and C: [med-carb/med-fat/med-protein] affects a persons
energy level two hours later. The energy level is interval.

3. Tips received by a waitress predicts whether she will look for another
job (Boolean outcome).

4. Advertising experience (rating - interval) and experience researching
competitors (rating - interval) predicts net income.

5. There is a curviliniear relationship between hours spent on a secondary
work assignment and productivity on the primary assignment.

6. There is an interaction effect between age group (A:25-30 or B:35-40) and
gender on spending on clothing.

**Models**
A. Logistic regression
B. Linear regression
C. One-way ANOVA with post-hoc testing
D. One-way ANOVA without post-hoc testing
E. Factorial ANOVA with post-hoc testing
F. Factorial ANOVA without post-hot testing
G. None of these


The whole set gets marked right or wrong.

#1    #2
C.    E.
D.    D.
A.    A.
B.    B.
G.    G.
E.    F.


This is from a reading resource in an online graduate course in statistics I'm taking. You have to be logged in to the course to see this. It is not graded, and I don't even have to complete it. My responses are not recorded. I've made two attempts (shown above) and I've done a lot of related reading. What are the correct answers? It only reports if the whole set is right or wrong. I don't see how I've gotten any of the other items wrong (other than the top and bottom ones). Is there a way to test for a curvilinear relationship with ANOVA? I picked "none" for that one, as linear regression is used, and you need to do linear regression + others things for curvilinear.

I will post the correct answer once I get it, unless the people here say I shouldn't.

Your answers to 3, 4, and 5 appear correct to me, so let's talk about the others.

First, you need to understand when we need or don't need post-hoc testing in ANOVA. When a factor has more than two levels, rejecting the null hypothesis for the main effect of that factor doesn't tell us which groups differ from each other; it merely tells us that not all levels are equal to each other. To figure out which levels differ from each other, we need to perform post-hoc testing. When a factor only has two levels, however, we don't need post-hoc testing; we already know that the only two levels differ from each other. In this problem set, knowing how many levels are in each factor is critical for deciding whether to use post-hoc testing or not.

For 1), we have one categorical, 3-level factor, one two-level factor, and a continuous outcome. This is clearly a case for factorial ANOVA. Because one of the factors has more than two levels, we need post-hoc testing to decide which groups differ from each other and how. So, I suspect E is the correct answer.

For 2), we have one 3-level factor and a continuous outcome. This is a case for one-way ANOVA. Because we have more than two levels, we need post-hoc testing to decide which groups differ from each other. So, I suspect C is the correct answer.

For 6), we have two 2-level factors and a continuous outcome. This is a case for factorial ANOVA. However, because each factor only has two levels, we don't need post-hoc testing; if we were to reject the null hypothesis for the main effect of each factor, we would already know which groups differ from each other and how (e.g., we would know that older individuals spend more on the clothing than younger individuals by rejecting the null hypothesis for the main effect of age group and looking at the group means, which we could not do with health interest level in question 1). So, I suspect F is the correct answer.

There are advanced ways to test for curvilinear relationships using ANOVA and using linear regression to model nonlinear relationships, but those are clearly beyond the scope of the question, so you shouldn't worry about them for now.

• Thanks. That worked. I was thinking that with 6 you'd need some kind of post-hoc test to establish there's an interaction between the independent variables. I guess that will be shown in the resulting statistics. Your explanation is very clear. Also, it appears there's not a difference here between "interaction" and "moderation." – user179810 Jul 16 at 3:38
• In the context of ANOVA, there isn't a difference. In epidemiology they mean two different things conceptually, but in experiments, they are analyzed in the same way. – Noah Jul 16 at 4:04