What is the difference between a one-tailed and a two-tailed test of significance? Under what circumstances would each be used?

     The difference between a one-tailed and two-tailed test of significance is that a one-tailed test looks for an increase or decrease in the parameter and a two-tailed test looks for any change in the parameter (Stockburger, n.d.). The one-tailed hypothesis-testing procedure is for a directional hypothesis and the two-tailed hypothesis-testing is a procedure for a nondirectional hypothesis. A one- or two-tailed t-test is determined by whether the total area of a is placed in one tail or divided equally between the two tails (Stockburger, n.d.). When the results are interesting only if they turn out in a particular direction a one-tailed test is performed and  if the results would be interesting in either direction a two-tailed test is performed. In a one-tailed test the area associated with a is in either one tail or the other, and the selection of the tail depends which direction would be positive or negative (Stockburger, n.d.) A two-tailed test divides a in half by placing half in the each tail, therefore the null hypothesis is a particular value with two alternative hypotheses, one positive and one negative (Stockburger, n.d.). The hypothesis-testing procedure is effected in different ways depending on the choice of one- or two-tailed tests.

Reference

 Stockburger, D.W. (n.d.). Introductory Statistics: Concepts, Models, and Applications . Retrieved from http://www.psychstat.missouristate.edu/introbook/sbk25m.htm