The Art of Statistics: Learning from Data

by David Spiegelhalter

In Chapter 7 we saw a quarterly change in unemployment of 3,000 had a margin of error of ± 77,000, based on ± 2 standard errors. This means the 95% confidence interval runs from −80,000 to +74,000 and clearly contains the value 0, corresponding to no change in unemployment. But the fact that this 95% interval includes 0 is logically equivalent to the point estimate (−3,000) being less than 2 standard errors from 0, meaning the change is not significantly different from 0. This reveals the essential identity between hypothesis testing and confidence intervals: A two-sided P-value is less than 0.05 if the 95% confidence interval does not include the null hypothesis (generally 0). A 95% confidence interval is the set of null hypotheses that are not rejected at P < 0.05.

A 95% confidence interval with p=.05 0nly gives range of null hypothesis