We have learned about a "multiple comparisons procedure" for identifying which pairs of population proportions differ: after rejecting the null hypothesis in a chi-square homogeneity, test for the equality of multiple population proportions. You will discover various multiple comparison procedures as well, which are used to identify which pairs of population means differ: after rejecting the null hypothesis in an analysis of variance, F test for the equality of multiple population means.

One concern when making multiple comparisons like this is that since we are making multiple inferences, there are more opportunities to draw an incorrect conclusion or make "false discoveries." Multiple comparison procedures are specifically designed to take account of this problem. But this raises a more general concern. If we exhaustively search for relationships in data, we can uncover all kinds of bizarre patterns, which might suggest a real phenomenon but are actually just coincidence.

Search online for examples of such spurious relationships or correlations. Choose a single example and describe it.