Which statement best defines statistical significance?

Which statement best defines statistical significance?

• A. If it falls in the critical region (past the critical value), the result is statistically significant.
• B. A large sample always makes results significant.
• C. A low p-value always implies practical importance.
• D. Statistical significance depends on the direction of the effect.

Answer: (A)

Statistical significance concerns whether an observed effect is unlikely to occur if the null hypothesis is true, given a chosen alpha level. In many tests, this is determined by whether the test statistic falls into the critical region beyond the critical value. If it does, we reject the null and call the result statistically significant. This captures the practical rule researchers use: crossing the boundary means the data are unlikely under the null hypothesis. The other ideas miss important nuances. A large sample does not automatically guarantee significance; it increases power and can detect very small effects, but significance still depends on the actual effect size and variability. A low p-value signals statistical significance but does not imply the result has practical importance. Lastly, significance is not about the direction of the effect; a result can be statistically significant in either direction, depending on the test type (one- or two-tailed) and where the observed statistic falls relative to the critical values.

Statistical significance concerns whether an observed effect is unlikely to occur if the null hypothesis is true, given a chosen alpha level. In many tests, this is determined by whether the test statistic falls into the critical region beyond the critical value. If it does, we reject the null and call the result statistically significant. This captures the practical rule researchers use: crossing the boundary means the data are unlikely under the null hypothesis.

The other ideas miss important nuances. A large sample does not automatically guarantee significance; it increases power and can detect very small effects, but significance still depends on the actual effect size and variability. A low p-value signals statistical significance but does not imply the result has practical importance. Lastly, significance is not about the direction of the effect; a result can be statistically significant in either direction, depending on the test type (one- or two-tailed) and where the observed statistic falls relative to the critical values.