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Let's say in a research study, participants receive training, and I measure their learning gains before and after the therapy. At the beginning of the study, before the training, I also administered a questionnaire to measure participations' motivation using a LIKERT-type scale. I want to find out if the training has an effect, considering the role of motivation.

Is this simply a two-way repeated-measures ANOVA?

What if, instead of pre- and post-tests, I compared two types of training (with different participations in each training) and measured learning gains after each training while also measuring participants' motivation at the very beginning? Would this be simply a two-way independent-measures ANOVA?

Normally, instead of motivation, if I used gender, a categorical variable, I would be sure about the design. But, I am not sure how to interpret it when a continuous (or ordinal) variable is involved.

I appreciate any insight.

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The first scenario described could be analyzed as a one between-factor repeated-measures ANOVA (where the pre and post is the repeated measure and the motivation classification is the between factor).

The second scenario would be two-way ANOVA where motivation and treatment are the factors.

In the first scenario, the dependent variable is the score (observed at pre and post). In the second scenario, the dependent variable is the gain (from pre to post).

However, in these cases, if motivation was measured as an ordinal variable, you would be treating it here as a categorical variable. Thus, if you have a statistically significant effect (or interaction), then you can only deduce that there is some difference for at least one of the levels of the motivation factor.

If you wish to model the motivation variable as a true ordinal variable or as a scalar variable (if it was measured as such), then the key is to remember that ANOVA analyses are just multiple regression models. And, in these models, we can include categorical variables using an ordinal dummy coding scheme (using k-1 instrumental variables, where k is the number of k Likert-type options) or we can include the variable as a single scalar predictor variable.

Happy to elaborate more if needed.

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  • $\begingroup$ I could not find any resources that explain between-factor ANOVA. It is not that common I guess? $\endgroup$
    – renakre
    Commented May 30, 2023 at 3:16
  • $\begingroup$ Also, from your comments, I understand that if a factor in ANOVA MUST be a categorical variable; is this correct? Could this be a solution: dividing the users into two halves or quartiles to categorize them like low vs high motivation? $\endgroup$
    – renakre
    Commented May 30, 2023 at 3:34
  • $\begingroup$ Sorry for the confusion, this would be one between-subjects factor...the variation in the factor occurs between subjects (from one to another)...as opposed to a repeated measures that is measured within the same subject. As for the ANOVA hypothesis test, yes, the factors must be categorical...however, you do not need to restrict yourself to just an ANOVA (even more so if the design/data calls for a different analysis). $\endgroup$
    – Gregg H
    Commented May 30, 2023 at 12:04
  • $\begingroup$ I thought the learning gains were the dependent variable. $\endgroup$
    – Gregg H
    Commented May 30, 2023 at 18:45
  • $\begingroup$ It was a mistake --> Thanks for the clarification @GreggH. Then, what would be an alternative analysis in this case? For example, what analysis would be suitable if I want to know if there is an interaction between motivation levels and training? Also, I believe categorizing the ordinal variable would not be proper for the case I shared in my question. $\endgroup$
    – renakre
    Commented May 30, 2023 at 19:10

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