What is the critical value?

What is the critical value?

• A. The calculated value is the boundary used to decide significance.
• B. The critical values table is given to you.
• C. The p-value of the test.
• D. The observed effect size.

Answer: (B)

A critical value is the threshold on the test statistic that determines whether the result is statistically significant. It marks the boundary between the rejection and non-rejection regions for the null hypothesis at a chosen alpha level. In practice, you look up these cutoffs in a critical values table for the appropriate distribution (z, t, chi-square, F), and those values are provided to you in exams or reports. You then compare your calculated test statistic to that boundary to decide significance; if it exceeds the critical value, you reject the null. This is why the statement that a critical values table is given to you best captures how the boundary is obtained. The calculated value refers to the test statistic itself, which is compared to the boundary rather than being the boundary. The p-value is a related way to assess significance but is not the boundary itself. The observed effect size describes how big the effect is, not whether the result crosses the significance threshold.

A critical value is the threshold on the test statistic that determines whether the result is statistically significant. It marks the boundary between the rejection and non-rejection regions for the null hypothesis at a chosen alpha level. In practice, you look up these cutoffs in a critical values table for the appropriate distribution (z, t, chi-square, F), and those values are provided to you in exams or reports. You then compare your calculated test statistic to that boundary to decide significance; if it exceeds the critical value, you reject the null.

This is why the statement that a critical values table is given to you best captures how the boundary is obtained. The calculated value refers to the test statistic itself, which is compared to the boundary rather than being the boundary. The p-value is a related way to assess significance but is not the boundary itself. The observed effect size describes how big the effect is, not whether the result crosses the significance threshold.