The last step in significance
testing involves calculating the probability that a statistic would
differ as much or more from the parameter specified
in the null hypothesis as does the statistics obtained in the experiment.
A probability computed considering differences in both direction (statistic either larger or smaller than the parameter) is called two-tailed probability. For example, if a parameter is 0 and the statistic is 12, a two-tailed probability would be the he probability of being either ≤ -12 or ≥12. Compare with the one-tailed probability which would be the probability of a statistic being ≥ to 12 if that were the direction specified in advance.