Definitions for "Two-tailed test"
Keywords:  hypothesis, null, chi, tail, statistic
A significance test in which two critical regions are defined, one in each tail of the probability distribution.  Significance is achieved when the observed value of the test statistic is more extreme than either critical value.  A two-tailed test is used when the sign of the test statistic is not specified by the alternative hypothesis. Thus a two-tailed test would be used if the alternative hypothesis were that two quantities are unequal, without prior specification of which is larger.  Synonymous with nondirectional test.
a test of the prediction that two values are equal, or a test that they are not equal.
If there are two ways to disprove a null hypothesis, the statistical test is two-tailed. EX: “There is no correlation between age at first dental visit and DMF at age 30” is a two-tailed test – there are two ways to disprove it (finding a positive correlation or finding a negative correlation). The operational significance of a two-tail test comes in determining the p-value from the test statistic. Two-tail tests have higher p-values for a given test statistic than do one-tail tests. [See one-tailed test, null hypothesis