Pooled significance test

When do you use a pooled significance test oe when do you not use it?

The answer to your question requires a little more context. “Pooled” procedures only come up with two-sample procedures (there’s nothing to pool - aka “combine” - if there’s only one sample!). For a two-sample t-test, we would use a pooled procedure if we know or can assume the population variances are equal. This is… essentially never, so don’t worry about it. In fact, the “unpooled” 2-sample t-test would still be valid, so we should do it anyway.

For a 2-sample z-test for a difference of proportions, we “pool” (combine) the two sample proportions into a big single proportion when calculating the test statistic (that’s the p-hat “c” on your formula sheet). The thing is, your calculator would do that automatically without asking you if you’re “pooling” or not, and you don’t need to include the word “pooled” in naming the 2-sample z-test for a difference of population proportions.

SO… with all of that said? Tomorrow, stay out of the pool :slight_smile:

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So it always pools automatically with 2-sample-z/t- tests?

A 2-sample z test involving pooling the proportions, yes. But honestly: you likely won’t need to explain that level of detail tomorrow. I wouldn’t worry about it.

For a 2-sample t-test, do NOT pick “pooled” for the test.

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