Acceptance Region

TL;DR

• The area of test-statistic values that, according to the source, causes rejection of the null hypothesis.
• Determined by the chosen significance (alpha) level and the corresponding critical value(s).
• Example: for a two-tailed test with significance level 0.05, the critical values are 1.96 standard deviations away from the mean in each direction.

Definition

Acceptance region, also known as critical region, is a specific area in a statistical hypothesis test where the null hypothesis is rejected. It is a range of values of the test statistic that leads to the rejection of the null hypothesis.

Explanation

• The acceptance region is identified after selecting a significance level (alpha), which is the probability of rejecting the null hypothesis when it is true. A commonly used significance level is 0.05.
• Once the significance level is selected, the researcher determines the critical value of the test statistic. The critical value separates the acceptance region from the rejection region.
• For example, in a two-tailed test with significance level 0.05, the critical value is the value that is 1.96 standard deviations away from the mean in each direction. Any test statistic that falls outside of this range would be considered significant and the null hypothesis would be rejected.
• Per the source text, if the calculated test statistic falls within the acceptance region, the null hypothesis is rejected and the alternative hypothesis is accepted.

Examples

Drug effectiveness (blood pressure)

• Null hypothesis: the drug has no effect on blood pressure.
• Alternative hypothesis: the drug has an effect on blood pressure.
• The acceptance region is the range of test-statistic values that indicates the drug is effective in reducing blood pressure.
• If the calculated test statistic falls within this range, the null hypothesis would be rejected and the alternative hypothesis accepted.

Difference in average height (men vs. women)

• Null hypothesis: there is no difference in the average height between men and women.
• Alternative hypothesis: there is a difference in the average height between men and women.
• The acceptance region is the range of test-statistic values that indicates a significant difference in average height.
• With a significance level such as 0.05 and a two-tailed test, the critical value would be the value that is 1.96 standard deviations away from the mean in each direction; any test statistic outside this range would be considered significant and lead to rejection of the null hypothesis.

Related terms

• Critical region
• Significance level (alpha)
• Test statistic
• Critical value
• Null hypothesis
• Alternative hypothesis