Discussion
The test is named after the "tail" of data under the far left and far right of a bell-shaped normal data distribution, or bell curve. However, the terminology is extended to tests relating to distributions other than normal. In general a test is called 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. For example, if the alternative hypothesis is, rejecting the null hypothesis of for small or for large values of the sample mean, the test is called "two-tailed" or "two-sided". If the alternative hypothesis is, 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.
The statistical tables for Z and for t provide critical values for both one- and two-tailed tests. That is, they provide the critical values that cut off an entire alpha region at one or the other end of the sampling distribution as well as the critical values that cut off the 1/2 alpha regions at both ends of the sampling distribution.
Read more about this topic: One- And Two-tailed Tests
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