4 independent variables and nominal data
Message posted by thiGGer (via 66.68.79.13) on October 2, 2001 at 6:08 PM (ET)

hi,

i'm doing a study that's like a consumer report type deal... 4 products, with yes-no type questions... my research question is, "is there a best product out of these 4 products?"

i was told that chi-square was the only way to analyze nominal data... i read up on chi-square and concluded that this is the wrong test for my study design.

what other tests can i do for the data/design i have, for the research question i'm after?

thanks so much for your input,
thi

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Re: 4 independent variables and nominal data
Message posted by Tomi (via 154.32.143.47) on October 5, 2001 at 10:16 AM (ET)

Let's assume that for these questions yes is a favourable response and no is an unfavourable response. If this is not true, then you could categorise all the answers as favourable/unfavourable and proceed as I descibe.

Let's also assume that all questions are equal in their importance. If this is not true, then a weighting method can be used (I won't bother explaining this).

Method 1 (bit dodgy)

If the number of questions is large, then simply adding up the number of yes replies will give a score for each product. You could use a t-test to see if the score for the highest scoring product is significantly greater than the other scores.

Now this is dodgy because you fail a key assumption for the t-test - that the underlying distribution is normal. But if you have a large number of questions with random possible answers yes/no then it will be roughly normal, so why not give it a try?

Method 2 (bit better)

Calculate (Total number of yes answers for all four products)/(Total number of questions). This gives you a number between 0 and 1. Let's call it p.

If all the answers are being answered randomly yes or no, then p represents the probability of getting a yes.

OK, for your particular product, the number of yes answers should follow a binomial distribution and you can do a test to see if the number observed is significantly greater than what could occur by random.

Method 3

What's so wrong with the chi squared test? On reflection, I think it might actually be the best option. Create the following contingency table:

Yes No Total
Product 1 54 26 80
Product 2 32 48 80
Product 3 11 59 80
Product 4 16 54 80
Totals 113 187 320

Do a chi square on the table and you shouild be OK.