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To run a certain activity, a population of companies use a finite set of inputs. There are 8 different inputs, but each company may not use all of them. For instance, company 1 uses inputs A, B and D, whereas company 2 uses inputs B, D, E and F

I have conducted a survey to ask 30 different companies about which inputs they use, and I would like to statistically evaluate the most used input. What statistical test do you recommend for this?

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    – Jeff
    Aug 28, 2011 at 2:53

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I don't think the chi-square test is appropriate because your counts / proportions are not independent. They are generated by the same sample of companies.

  • You might consider the McNemar test (see wikipedia). It is a statistical test specifically designed to compare two proportions that are based on the same sample of individuals. This could be used to see whether the input with the largest sample proportion of use is significantly greater than the proportion of use of any one other input.
  • The Cochran test (see wikipedia) extends the above idea to the case of three or more proportions. This could test the overall null hypothesis of whether the proportions for all inputs are equal.

Here's a tutorial example in R of using Cochran Q first followed by McNemar as a post-hoc test.

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