### 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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