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I'm doing a Chi Square analysis to look at whether two variables are dependent or independent when it comes to the pass rate on a test with two variables: the origin of a participant and the year they take the test. The result comes out as non-significant (.07, so maybe a trend toward significance.)

| Year | PlaceX | PlaceY | |------|--------|--------| | 2015 | 30 | 10 | | 2016 | 30 | 2 |

However, when I look at the fail rate, shown below, the p value is much 'less' significant:

| Year | PlaceX | PlaceY |
|------|--------|--------|
| 2015 | 270    | 30     |
| 2016 | 270    | 38     |

I don't understand why I don't get the exact same significance value given that the two sets of numbers are mirror images of one another - one is the pass rate, one is the fail rate, and the total pass / fail rate for each Place add up to the same total sample size for the two years.

Any light shed on this would be great - I feel like I'm being dishonest by looking at the pass rate as this shows a specific result that trends toward significance, when I could just as easily look at the fail rate and have this be highly non-sig.

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You get different results because you are asking different questions and the computer has no way of knowing that these are mirror images. I don't think chi-square is appropriate here, as you have two independent variables (area and year). What you are testing here is not anything about pass or fail rates, but about whether year is independent from area.

I suggest logistic regression with pass as the dependent variable and area and year as independent variables.

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