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Consider the following survey question:

Q: Choose one or more of the following 5 items:

A B C D E

  • How can one test which items are more frequently chosen for a sample with 100 individuals? Is it advisable to fit a distribution to the data?
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I'm not an expert on this, so I'll leave it as a comment and see what other people think. You could use Bayes theorem with a Dirichlet prior to compute the probability that someone chooses a particular value. Alternatively, you could take a frequentist approach and run a significance test on the population statistics (% of people who chose each value) using a chi-squared test. – rm999 Jun 15 '11 at 23:43
Does the order of choice matter this time (cf. your recent question about Testing the importance of an item among a finite set of items)? What would be the rationale for model fitting on the response patterns or on the marginal distribution? – chl♦ Jun 16 '11 at 9:25
Your language confuses me a bit. Usually I would describe a multiple choice test as consisting of as set of "items" where each item has response "options". When you say "items" do you mean "options"? I.e., you are trying to describe the frequency of selection of a set of response options for a single item? – Jeromy Anglim Jun 16 '11 at 14:09
@Jeromy @chl @rm999 @Thomas I thank you for your help. I hope now to use a more precise language. What I have is a question like the following: "Q: For what services do you contract company X: * Cleaning; * Transportation of waste; * Surveillance; etc. And I would like to test which are the most important services for which company X is contracted. – Paul Smith Jun 16 '11 at 14:40

2 Answers

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It seems like you are not interested in how choosing one item relates to choosing another.

If this is the case, you can just treat each of the five items as separate questions with binary responses, and you can estimate the proportion of people who would select a particular item with a binomial or normal model.

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Like Thomas, I think you should simply convert your items into 5 binary variables (0 or 1), and then get the frequencies for those variables. You'll then be able to order the items by popularity. If you want to "test" the difference between the proportions, I would advise using a tool such as this one to get confidence intervals (typically 95%). If the intervals overlap, the differences may then be due to sampling error.

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