“In general a test is called two-sided or two-tailed if the null hypothesis is rejected for values of the test statistic falling into either tail of its sampling distribution, and it is called one-sided or one-tailed if the null hypothesis is rejected only for values of the test statistic falling into one specified tail of its sampling distribution” [1]. For example, if our alternative hypothesis is , rejecting the null hypothesis of μ = 42.5 for small or for large values of the sample mean, the test is called two-tailed or two-sided. If our alternative hypothesis is μ > 1.4, rejecting the null hypothesis of only for large values of the sample mean, it is then called one-tailed or one-sided.

If the distribution from which the samples are derived is considered to be normal, Gaussian, or bell-shaped, then the test is referred to as a one- or two-tailed T test. If the test is performed using the actual population mean and variance, rather than an estimate from a sample, it would be called a one- or two-tailed Z test.