As we said, the chance of this happening is low in a single trial, but we increase our chances of it happening by conducting multiple trials. It just so happened we were very unlucky to witness such an unusual event. If it happened to us we may conclude the coin is unfair, but that would be the wrong conclusion if the coin truly was fair. Think of flipping a fair coin 10 times and getting 9 or 10 heads (or 0 or 1 heads). When we run a hypothesis test, we always run a risk of finding something that isn’t there. rejecting a null hypothesis that should not have been rejected. Making multiple comparisons leads to an increased chance of making a false discovery, i.e. The outcome of these pairwise comparisons will hopefully tell us which schools have significantly different proportions of students flossing. But where are the differences? This leads us to pairwise comparisons of proportions, where we make multiple comparisons. If we reject the null, we have evidence of differences. The null would be no difference between the proportions versus some difference. An obvious first step would be to conduct a hypothesis test for any differences between these proportions. When finished we’ll have 8 proportions of students who answered “Yes”. Let’s say we go to 8 high schools in an area, survey 30 students at each school, and ask them whether or not they floss their teeth at least once a day. We sometimes want to make pairwise comparisons to see where differences occur.
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