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This is not really a coding question but more of a statistical question.

I'm doing a proportions test on multiple proportions for many subjects.

For example, subject 1 will have multiple proportions (multiple "successes per total trials"), and subject 2 will have multiple proportions. And for each subject we're testing if all these proportions are the same. For each subject, there are multiple proportions where there is number of successes per total trials. The proportions could range from being 30 successes out of 60 to like 300 successes out of a 1000 (just to show the range of trials and successes for each subject). Furthermore, for each subject, there could be varying number of proportions. Subject 1 could have 50 proportions, whereas subject 2 could only have 2. The idea is that we're trying to test that for each subject that all of their proportions are the same, and then reject if they are different.

However, I'm realizing that subjects that have many more proportions, will have more significant p-values than subjects that only have 2 proportions, when using the prop.test. I was wondering if there is a way to approach this problem in a different way. Any sort of correction I could do, or take into account the number of positions.

Any suggestions would be helpfil.

user3799576
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  • SO is for code-based questions. Your question would be better suited for [Cross Validated](http://stats.stackexchange.com/). – talat Jul 22 '14 at 09:05
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    This question appears to be off-topic because it is about statistics and should be asked on crossvalidated.com. – josliber Jul 25 '14 at 01:33

1 Answers1

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One way you can approach your example of comparing proportions for a single subject is by performing null hypothesis testing is by using the Z-statistic to compare one proportion with the other proportions. The Z-statistic inherently normalizes data for different sample sizes. As an example, assuming that one subject has 50 proportions, you would have 50 tests, and in the method below 5% error is allowed for each subject. You can set this up with the following:

Research Question:

For a single subject with 50 proportions, is the first proportion the same as the other proportions?

Hypothesis

  • Null hypothesis: u_1 = u_2 = ... = u_50
  • Alternative hypothesis: u_i != 1/49 sum (u_j) where j != i

Calculate the Statistic

  • Use the Z-test to compare the mean to the average mean of the other 49 proportions (for all 50 samples)
  • N is your number of trials

Compute the appropriate test statistic and rejection criteria

  • 5% error is allowed for each subject
  • p-value, 5% / 50

You would repeat this method for each proportion for this subject (i.e. perform null hypothesis testing 50 times for this subject).

Pam
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