Critical value

Definition

A critical value is a point on the scale of the standard normal distribution that is compared to a test statistic to determine whether to reject the null hypothesis. It separates the region where the null hypothesis is not rejected from the region where it is rejected.

5 Must Know Facts For Your Next Test

1. Critical values are determined based on the significance level (alpha) of a test.
2. Commonly used critical values correspond to alpha levels of 0.05, 0.01, and 0.10.
3. For a two-tailed test with alpha = 0.05, the critical values are approximately ±1.96 on the standard normal distribution.
4. The area under the curve to the left of a positive critical value or right of a negative critical value equals alpha/2 in a two-tailed test.
5. Critical values can be found using statistical tables or software functions like `qnorm` in R or `scipy.stats.norm.ppf` in Python.

Review Questions

• How do you find critical values for a given significance level?
• What are the critical values for a two-tailed test at an alpha level of 0.05?
• Why are critical values important in hypothesis testing?

Related terms

Significance Level:

The probability of rejecting the null hypothesis when it is actually true, denoted by alpha (α).

Null Hypothesis: A statement that there is no effect or no difference, often denoted as H₀.

Test Statistic:

A standardized value that is calculated from sample data during a hypothesis test and compared against a critical value.