hypothesis test

an abstract procedure for determining whether a set of observations is consistent with a hypothesis under consideration; it is the theoretical basis of most statistical tests. A hypothesis test decides between two hypotheses, one stating that the effect under investigation does not exist (the null hypothesis, H_0>), and the other that some specified effect does exist (the alternative hypothesis, H_a> or H₁>), based on the observed value of a test statistic whose sampling distribution is completely determined by H_{0>. When the test statistic falls in a set of values known as the critical region,} H_{0> is rejected. The level of probability of incorrectly rejecting} H_{0> may be set before the data are collected, usually at 0.05 or 0.01; this is called the} significance level or α level. It is now more common to report the smallest α at which the null hypothesis can be rejected; this is called the significance probability or P value>.