What does a two-tailed test test for?
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A two-tailed test tests for the possibility of an effect or relationship in both directions (i.e., it checks for the presence of a relationship that could be either positive or negative).
A two-tailed test is used to test whether a population parameter (e.g., mean, proportion) is significantly different from a specified value in either direction—that is, it tests for the possibility of the parameter being either greater than or less than the hypothesized value.