Chapter 7. Hypothesis Testing: Introduction to Hypothesis Testing (Critical Region Approach
One-tailed Tests
When there are good reasons to suspect that a treatment effect, difference, or relationship has a specific direction, it may be beneficial to use a one-tailed test.
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One-tailed Tests
There are two ways in which a one-tailed or directional test differs from a two-tailed test:
- A directional prediction is incorporated in the hypotheses of the test.
- The critical region is located entirely in one tail of the sampling distribution.
There are two types of one-tailed tests: left-tailed and right-tailed.
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A left-tailed test should be used when the population parameter is suspected to be less than a particular value. The hypotheses of a left-tailed test are:
- #H_0:\mu \geq \mu_0#
- #H_a:\mu \lt \mu_0#
The critical region of a left-tailed test is located entirely in the left tail of the sampling distribution.
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A right-tailed test should be used when the population parameter is suspected to be greater than a particular value. The hypotheses of a right-tailed test are:
- #H_0:\mu \leq \mu_0#
- #H_a:\mu \gt \mu_0#
The critical region of a right-tailed test is located entirely in the right tail of the sampling distribution.
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The advantage of using a one-tailed test is that, compared to the two-tailed alternative, a one-tailed test has increased power in the direction specified by the test. However, if the direction of the effect is not what you suspect it to be, this effect cannot be detected by a one-tailed test.
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