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Left-tailed test: the area under the density curve from the critical value to the left is equal to α In particular, if the test is one-sided, then there will be just one critical value, if it is two-sided, then there will be two of them: one to the left and the other to the right of the median value of the distribution.Ĭritical values can be conveniently depicted as the points with the property that the area under the density curve of the test statistic from those points to the tails is equal to α: The alternative hypothesis determines what "at least as extreme" means. These values are assumed to be at least as extreme at those critical values. Critical values are then the points on the distribution which have the same probability as your test statistic, equal to the significance level α. To determine critical values, you need to know the distribution of your test statistic under the assumption that the null hypothesis holds. Critical values depend also on the alternative hypothesis you choose for your test, elucidated in the next section. The choice of α is arbitrary in practice, we most often use a value of 0.05 or 0.01.