Basically, I want to identify whether there is an interation effect bewteen these two variables onto the continuous variable. Hence, I wanted to conduct a factorial ANOVA. However, there are 2 issues:
1) the two categorical variables come from the sam eparticipants (eg each respondent to my survey had to answer both questions) and
2) a Chi Square test to test the two categorical variables for independence was highly significant.
Can I still do a factorial ANOVA?
Let V be que quanti, W1, W2 be the two nominal variables. You can still do the ANOVA. As long as W1 is not almost the same as W2. This may very well be the case even if chi(W1,W2) is statistically significant. It may be the case though that anova V W1 and anova V W2 are both significant but that anova V W1 W2 shows that one (or even both) of them is not. You may also want to do anova V W1 W2 W1#W2. Two final remarks. Beware that "predictors" has a somewhat weak sense in an anova, for an anova is no regression. And beware that with some statistical packages you have to indicate that your "predictors" are categorical.
Regards from Madrid,
Andrés
Interesting situation! If I follow, it sounds like the predictors are partially confounded/correlated. This will make any test for an interaction underpowered (see McClelland, 1997, Psych Methods). You’ll need to do a repeated measures ANOVA or multilevel model to capture the data dependence caused by the within-subject design, but there’s nothing stopping you. just be aware of the impact of the confounding on the interaction test.
The measurements of the variables are done on the same individuals. The samples are dependent. No wonder the chi-square test of independence is significant. Paired t-test may be done to compare the two variables. To test for their interaction a factorial ANOVA may still be done.
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