What does a 95% confidence interval that does not include the null value indicate?

What does a 95% confidence interval that does not include the null value indicate?

• A. It indicates statistical significance at the 0.05 level; the observed effect is unlikely due to chance alone.
• B. It proves the null hypothesis is true.
• C. It means the study is perfectly precise.
• D. It indicates there is no association.

Answer: (A)

A 95% confidence interval for the effect tells you the range of values that are compatible with the observed data if you repeated the study many times. If that interval does not include the null value (the value representing no effect, such as a difference of zero or a ratio of one), it means the data are inconsistent with no effect at the 5% significance level. In other words, the observed association is unlikely to be due to random chance alone, so we say it is statistically significant at the 0.05 level. This does not prove the null hypothesis true, and it does not mean the study is perfectly precise—the interval simply reflects the range of plausible true effects given the data. It also does not imply there is no association; rather, there is evidence of an association because the null value is outside the interval.

A 95% confidence interval for the effect tells you the range of values that are compatible with the observed data if you repeated the study many times. If that interval does not include the null value (the value representing no effect, such as a difference of zero or a ratio of one), it means the data are inconsistent with no effect at the 5% significance level. In other words, the observed association is unlikely to be due to random chance alone, so we say it is statistically significant at the 0.05 level.

This does not prove the null hypothesis true, and it does not mean the study is perfectly precise—the interval simply reflects the range of plausible true effects given the data. It also does not imply there is no association; rather, there is evidence of an association because the null value is outside the interval.