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Colleagues, can't wrap my mind on simple question, please help!

I have two products and list of their attributes. My respondents make an answer which product on each attribute they prefer. Finally they choose which product they are preferred overall.

This is an example of an answer from a single respondent:

           Product_A    Product_B No_Preference
  Attr 1       1           0           0
  Attr 2       1           0           0
   ...
  Attr 20      0           0           0
Final_Choice   1           0           1 

There are two goals:
1) to learn the final choice drivers, which attributes impacts more on the final choice
2) Is there difference between drivers between two products. Example: Imagine, Product_A has great color, and Product_B has great scent. All the rest attribs are very similar. I want to detect that scent and color are drivers that differ significantly and all the rest do not.

The problem is that that Product_A is 25% more popular (on the final choice) and people tended to choose its attributes even more often (every preferred Product_A has on average 20% more preferred attributes than Product_B).

I tried to apply 2-samples Z-test of proportions and Chi-squared test on every attribute but both yield significance on every attribute since the proportions are rather different. It gives me no information. It seems I need to compare kind of relative impact (meaning I have to somehow exclude different "popularity" of the products and different level of their attributes' "attractiveness" per product)

I also tried logistic regression but it does not work either: people tended to prefer attributes of the product that they are finally chosen, so logistic gives me just perfect fit.

The problem seems logically similar to McNemar test but since every respondent was able to make only one choice (per attribute) I can't apply this test too.

What have I missed?

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I would say your second question is invalid with this data. With 2 groups you can't say that one atribute drives for the first product and the other for the second product. It is always fully related.

In future with such questions (both 1st and 2nd) I would suggest to gather data in design suitable for conjoint analysis.

As far as the 1st question is concerned with current data, I would say correlation tests between final choice question and the rest give you the answer. Items with biggest correlation are the best predictosr and can be assumed to be the most influencial drivers. Obviously some interactions can matter. That's why you could consider multidimensional scaling (on the final map you will have to look for the whole group closest to the final choice item).

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  • $\begingroup$ For the 1st question, I just took simple percentage count. I believe obtained result very much similar to the correlation analysis. For the 2nd question (the key question) I think there should be a solution. Imagine, product A has great color, and product B has great scent. All the rest attribs are very similar. So, the list of attribute's preferences for two products would be alike except these two attributes. I want to detect this difference. Conjoint is not applicable since these are real products so I can't rotate level of attributes between them. $\endgroup$ – Niksr Jul 17 '17 at 6:45

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