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Factorial between group Anova or running ( t-tests then Anova )

I have a question in my study that asks if students attitude vary according to their course level ( 3 levels) and the program ( 2 levels)? In order to answers this research question , I conducted t tests = independent variable is attitude and the dependent variables are the two levels of the course Then Anova= Independent variable is attitude and dependent variables are the three programs

Or should I use factorial Between groups Anova and combine everything together in this test??

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You should use a factorial ANOVA with your two design factors and their interaction included. There are a few reasons to prefer factorial ANOVA:

  1. You will have more power to detect effects with factorial ANOVA. Your p-values will generally be smaller in factorial ANOVA than in the two one-way tests because you are explaining more variability in the outcome.

  2. You get the added bonus of being able to test for an interaction between the two factors. An interaction means that the effect of one factor depends on the level of the other. If an interaction is present, you should be cautious in interpreting the main effects, which are all you would have got with the separated analyses. For example, maybe the relationship between course level and attitudes depends on which program a student is in. The two separate tests would completely miss this phenomenon.

If you can include other covariates in the model in order to do analysis of covariance (ANCOVA), you will have even greater power to detect effects. For example, it may be that students' background characteristics like gender, race, or first-generation student status affect the outcome, in which case controlling for these variables with ANCOVA can improve your ability to find the relationships you are assessing if they are indeed there.

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