# Thread: proper analysis of a 3x3 contingency table

1. ## proper analysis of a 3x3 contingency table

I have some data on how male-female pairs spend their time in an undergraduate level physics lab. Their activity is classified as either: using the *equipment*, using the *computer*, or doing something *other*. An observation is taken every ~5 minutes, say. This means that over the course of a three-hour period, the same pair may be observed 36 times. This allows me to build a contingency table (see attachment).

So, for example, we observed 112 instances of a female student using a computer while the male partner was using the equipment. It is possible that, over the course of our observations, a given pair ends up as a count in each of the cells, as their behaviour changes. It is also possible that a given pair ends up as multiple counts in the same cell, if their behaviour never changes.

I am interested in knowing whether or not females and males spend their time differently in the lab. My initial (and naive) thought was to use a chi-square test of association, but this data fail the assumption of independence of observations (as we are obtaining multiple measurements from the same person). This led me to McNemar's test but this only works for 2x2 contingency tables. I have read that the Bhapkar test is a powerful extension of McNemar's test that allows for larger contingency tables. So here I am. Is Bhapkar's test the right one to use or not? I have found precious little about the assumptions that must be met in order to run the Bhapkar test. Do my data violate any requisite assumptions?

Many thanks in advance for anyone who can help me out.

2. ## Re: proper analysis of a 3x3 contingency table

Do they have to use computer, equipment, other to complete lab? And they both can use the same options at the same time? How many pairs are there? What are the proportions of mm ff or mf pairs?

3. ## Re: proper analysis of a 3x3 contingency table

Using the equipment, the computer, and other (e.g., writing notes, talking to lab partner, etc.: really, anything that isn't equipment or computer) are all requisite for *the group* to complete the lab. It is possible that one of the group members spends no time, say, on the computer.

Yes, they can both be doing the same activity at the same time. So, to be clear, in the attached spreadsheet of the original post, we observed 137 instances of both partners using the equipment at the same time.

There were about 70 pairs of students, observed over three separate three-hour lab periods (for a total of 2133 distinct observations). ALL of the pairs from which these numbers come are female/male partners.

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