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Question 524:



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When we speak of a directional test, this refers to whether we want to know if a mean we are testing is greater than a specified amount or mean or less than a specified amount or mean. If we speak in terms on non-directional testing, then we want to know if there is a difference (either greater or less than) an amount or mean from another distribution. For example, if we knew from prior research that people with a particular disease tapped their fingers more slowly than healthy people and we wanted to test a treatment. It would make sense for us to use a directional test. We'd reject the null hypothesis if say the people who took the treatment tapped significantly more than those who did not. In this example we would not be interested in whether they tapped more slowly than those who did not receive treatment.

This of course raises an important point, one should have a strong reason to use a directional test prior to conducting an experiment and analyzing data. The use of a directional test has a lower critical value from the t-distribution, making it easier to reject the null hypothesis. For example, for a non-directional t-test, we'd use the critical value of 2.06 and for a directional test we'd use the critical value of 1.71 given the same sample size. When in doubt use the non-directional test (2-sided test).

The t-test is more appropriate than using the z-test when we're dealing with a small sample size and don't know the population standard deviation.  As the sample size gets larger (>30) the t and z begin to get closer and closer. For example, if we wanted to study the effects of a memorization technique on a sample of 20 students we would use the t-test (small sample and unknown population standard deviation). In most research applications we use the t-score to test-hypothesis rather than the z-score, and therefore conduct more t-tests than z-tests.

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