# Two-Tailed Test

A statistical test for significance of the relation between two variables, where no prior assumption about the direction of the relationship is made (e.g., that a correlation between two is not equal to 0.0, regardless if that correlation is positive or negative;  or that the means in two samples are not the same, regardless of the direction of the difference). The name “two-tailed test” reflects the fact that the probability (i.e., the area under the curve representing the distribution of the test statistic) is determined from the area under two of the “tails” (i.e., sides) of the distribution of the test statistic (usually the normal distribution). If no a priori directional research hypothesis has been formulated (e.g., “male and female rats differ in their level of inquisitiveness” as opposed to, for example, “female rats are more inquisitive that male rats”), then the same observed test statistic value will be associated with half the statistical significance probability (alpha error rate for rejecting the null hypothesis when it holds true in the population), compared to a one-tailed test.