A statistical procedure whereby a quantity computed from data samples is compared with theoretical values of standard probability distributions. Formally it is a comparison between a null-hypothesis, H₀ (for example that there is no difference between the means of two populations), and an alternative hypothesis, H₁, (that a real difference exists). If H₀ is assumed to be true, the probability distribution of the test statistic can be computed or tabulated. If the test statistic exceeds the critical value corresponding to a probability level of α‎ per cent, the null-hypothesis is rejected at the α‎ per cent significance level. The most commonly used levels of significance are 5%, 1%, and 0.1%. Care must be taken to specify exactly what alternative hypothesis is being tested. Tests involving both tails of the probability distribution are known as two-tailed tests; those involving only one tail are one-tailed tests. See also analysis of variance, chi-squared distribution, goodness-of-fit test, multiple-range tests, Student’s t distribution.