Hi,
can someone explain to me why p-values for a correlation test (t-test) and a chi-square test on the same set of data do not return the same p-values? Computing phi and r returns the same values, but the p-value for the t-test for the correlation is different from the chi-square test (or fisher z-test). Values are perfectly correlated but p-values for chisquare tests are always larger.
Here is reproducible r-code (psych package needed):
set.seed(1)
n
Hello Lukas!
First of all, for reasons of brevity I will completely disregard the question of which test would be more fitting for this hypothetical data.
In order to perform both the chi-square and t-tests, the sample data are used in equations (attached) to come up with test statistics. These test statistics results are used in conjunction with the sample's degrees of freedom to look up the p-value on a table, the table being specific for each distribution.
So, all in all, to calculate the P-value for each test you need 1. the actual result, 2. the degrees of freedom and 3. the table which is test-specific. All three test "ingredients" are different between these tests (yes, even the degrees of freedom), so it's really not surprising that the p-values are different!
Lukas Röseler ,
1) First, ask chisq.test() to not use Yate's correction.
2) Use an even larger sample size to overcome issues with continuity.
Then I _think_ they are essentially equivalent.
n
Each test works asumming a distribution, chis-square values has one distribution, and t values another.
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