The Difference Between A Left-Tailed, Two-Tailed, And Right-Tailed Test

When researchers conduct tests of statistical significance they are given a p-value somewhere in the output.  If the test statistic is distributed symmetrically, the researcher can select one of three alternative hypotheses. Two of these correspond to one-tailed tests and one corresponds to a two-tailed test.  A left-tailed test or right tailed test is when the critical value for rejection lies to either the left or right side of a bell curve.  A one sided tail can be used to determine if there is too many or too few within a sample number.
The one tailed tests are used under these conditions:
-If there are too many in the sample number, a right side test is used.
-If there are too few in the sample number and if too low, a left sided test is used.
A two-tailed test is used when the rejection regions lies on both sides of the bell curve and only the center is acceptable. This condition allows the researcher to easily decide whether to accept or reject the sample.  For instance any test measuring conditions of less than or greater than or equal to conditions can employ the use of the two tailed test since it will measure from the center to either left or right. The problem statement would then be proved correct if it is stating that the observable data coincides with the variable predicted (I.E. less than, more than, equal to) (Lind, Marchal, & Wathen, 2011).

Lind, D. A., Marchal, W. G., & Wathen, S. A. (2011). Basic statistics for business and economics (7th ed.). New York, NY: McGraw-Hill/Irwin.

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