mean and variance. If the distribution of the test statistic is completely fixed by the null hypothesis we call the hypothesis simple, otherwise it is called composite. Select a significance level (α), a probability threshold below which the null hypothesis will be rejected. Common values are 5% and 1%. The distribution of the test statistic under the null hypothesis partitions the possible values of T into those for which the null hypothesis is rejected—the so-called critical region—and those for which it is not. The probability of the critical region is α. In the case of a composite null hypothesis, the maximal probability of the critical region is α. Compute from the observations the observed value tobs of the test statistic T. Decide to either reject the null hypothesis in favor of the alternative or not reject it. The decision rule is to reject the null hypothesis H0 if the observed value tobs is in the critical region, and not to reject the null hypothesis otherwise. A common alternative formulation of this process goes as follows: Compute from the observations the observed value tobs of the test statistic T. Calculate the p-value. This is the probability, under the null hypothesis, of sampling a test statistic at least as extreme as that which was observed (the maximal probability of that event, if the hypothesis is composite). Reject the null hypothesis, in favor of the alternative hypothesis, if and only if the p-value is less than (or equal to) the significance level (the selected probability) threshold (α), for example 0.05 or 0.01. The former process was advantageous in the past when only tables of test statistics at common probability thresholds were available. It allowed a decision to be made without the calculation of a probability. It was adequate for classwork and for operational use, but it was deficient for reporting results. The latter process relied on extensive tables or on computational support not always available. The explicit calculation of a probability is useful for reporting. The calculations are now trivially performed with appropriate software. The difference in the two processes applied to the Radioactive suitcase example (below): "The Geiger-counter reading is 10. The limit is 9. Check the suitcase." "The Geiger-counter reading is high; 97% of safe suitcases have lower readings. The limit is 95%. Check the suitcase." The former report is adequate, the latter gives a more detailed explanation of the data