Trying to discover the interaction of 11 beliefs (IV) and how those influence acceptance mean scores (DV) and which combination are most influential when found together.
What is "acceptance mean score"? Assuming it is not created from any of the factors and it is a variable appropriate for OLS (inc. ANOVA) analyses, and assuming that you are not really interested in things like a ten way interaction but are in two way interactions, and assuming you want to look at the interactions not conditional on the others (so Y ~ X1*X2, but not conditional on X3), then you have 11 choose 2 (55) interactions to run. If you are just interested in the interaction terms (and for "simplicity" let's assume all factors only have 2 levels each), then you can conducted these 55 tests, find the p values, adjust these using something like Holm's procedure.
But, I am assuming a lot here about what you want. You should probably say more about what your research hypothesis (or ses) is (or are) if you want more helpful answers.
I wonder if ANOVA is the best statistic to use. It is hard to interpret more than a 3-way interaction, and it would be unusual to see more than a 4-way. If you want to look at configurations, you might look into Qualitative Comparative Analysis. It enables you to see which combinations of your predictors best relates to your DV. You might find that there is more than one configuration.
If the variables are not related to each other try to check step regression to achieve model from them; let me know if this works for you
I understand that you collected questionnaire data and want to find the relation between these variable. In this situation I would rather think about linear regression in pairs (each IV with the DV) and compare the R2 – the higher the better, than only compare means.
Since it is important to know whether the high value of IV relates to the high value or low value of DV and whether it is a tendency.
Did you include interaction terms in your model? Did you do interaction plots?. This should be some sort of a factorial design. So you might check these terms in a standard work such as: Design and Analysis of Experiments, 9th Edition | Douglas C. Montgomery (Author) | download (b-ok.cc) Good luck. David Booth
What do you mean by interaction? As you use the term 'combinations', are you interested in intersectionality? As others have pointed out, you will need a very large sample size to tackle that number of factors as interactions.. You may be interested in
Article Uncovering interactions in multivariate contingency tables: ...
Preprint Using shrinkage in multilevel models to understand intersect...
What is "acceptance mean score"? Assuming it is not created from any of the factors and it is a variable appropriate for OLS (inc. ANOVA) analyses, and assuming that you are not really interested in things like a ten way interaction but are in two way interactions, and assuming you want to look at the interactions not conditional on the others (so Y ~ X1*X2, but not conditional on X3), then you have 11 choose 2 (55) interactions to run. If you are just interested in the interaction terms (and for "simplicity" let's assume all factors only have 2 levels each), then you can conducted these 55 tests, find the p values, adjust these using something like Holm's procedure.
But, I am assuming a lot here about what you want. You should probably say more about what your research hypothesis (or ses) is (or are) if you want more helpful answers.
Since you are from a psychology deparment, I wonder which 11 factors/predictors you have. For me as a psychologist, it is hard to imagine how you could enter 11 factors at once and have hypotheses for their interactions. Besides that, I find it hard to come up with 11 psychological variables, which are totally unrelated to each other. Therefore, multicollinearity may also be a problem, but please tell us more about your design.
ps. I had a different take than Rainer Duesing . I was assuming that you had 11 different experimental factors so that each was orthogonal. This would be about 2000 cells. If you were interested in all the interactions (i.e., up to the 11-way) then you'd need a lot of participants, but with just the 2-way method I suggest above you would not need all of these. But, if Rainer Duesing 's reading is correct and these are not orthogonal factors, then you should have a theoretical model for how they relate and should avoid the ANOVA framework.
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