If a 95% confidence interval includes the null value, what can be inferred about statistical significance at the 0.05 level?

If a 95% confidence interval includes the null value, what can be inferred about statistical significance at the 0.05 level?

• A. The result is not statistically significant.
• B. The result is statistically significant.
• C. The result has high precision.
• D. The result is inconclusive due to sample size.

Answer: (A)

A 95% confidence interval represents a range of plausible values for the true effect given the data. If the null value (no effect, such as zero difference or a relative risk of one) lies inside that interval, we cannot rule out no effect at the 5% significance level. In practical terms, the observed data do not provide enough evidence to conclude an effect, so the result is not statistically significant at 0.05. The p-value would be greater than 0.05. This interpretation hinges on the link between confidence intervals and significance: excluding the null value would indicate a significant result, while including it means non-significance. Precision or sample size aren’t the primary conclusions here; a narrow interval can still include the null, and a wide interval can sometimes exclude it, but the key takeaway at the 0.05 level is whether the null lies inside the interval.

A 95% confidence interval represents a range of plausible values for the true effect given the data. If the null value (no effect, such as zero difference or a relative risk of one) lies inside that interval, we cannot rule out no effect at the 5% significance level. In practical terms, the observed data do not provide enough evidence to conclude an effect, so the result is not statistically significant at 0.05. The p-value would be greater than 0.05.

This interpretation hinges on the link between confidence intervals and significance: excluding the null value would indicate a significant result, while including it means non-significance. Precision or sample size aren’t the primary conclusions here; a narrow interval can still include the null, and a wide interval can sometimes exclude it, but the key takeaway at the 0.05 level is whether the null lies inside the interval.