Say I have the following college enrollment data:


In 1975, 188,234 men and 156,612 women were enrolled in California colleges.
In 2005, 194,416 men and 201,334 women were enrolled in California colleges.


In 1975, 132,261 men and 98,554 women were enrolled in Texas colleges.
In 2005, 140,082 men and 153,305 women were enrolled in Texas colleges.

Consider, for each state, the proportion of those enrolled in colleges who were female.

How would I go about computing the p-value for the null hypothesis that the 1975–2005 increase in this proportion was the same in Texas as in California?

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    $\begingroup$ As stated, the hypotheses apply to the observations - in effect you observed the population quantities about which you wish to make a conclusion, in which case no statistics is required - they plainly differ (in effect the p-value is exactly 0). If that doesn't satisfy your needs, before even attempting inference, you need first to consider these issues: What is the population of interest? What is the model? (Without that, what does the question even mean?) $\endgroup$ – Glen_b Jun 2 '14 at 0:46
  • $\begingroup$ Are you asking about a test for differences (i.e. null hypothesis of no difference), or a test for equivalence (i.e. null hypothesis of difference?). $\endgroup$ – Alexis Jun 2 '14 at 17:19

One way to do it would be logistic regression:

logit(female) ~ year + state + year*state

After being sure to treat both as categorical variables. With N this large, everything will be significant, so you want to look at effect sizes (odds ratios).

  • $\begingroup$ Isn't your proposal testing for differences in proportions? (The OP—"testing for equality"—may have simply been sloppy with language, but it is also possible they are groping for some kind of equivalence test). $\endgroup$ – Alexis Jun 2 '14 at 4:08
  • $\begingroup$ Oh, yes. That's possible. And you're right about my test $\endgroup$ – Peter Flom Jun 2 '14 at 9:49

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