## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

# ADAPTIVE CONFIDENCE INTERVALS AND ESTIMATES

## 12.1 THE RELATIONSHIP BETWEEN TESTS AND CONFIDENCE INTERVALS

Often researchers publish confidence intervals, instead of p-values from tests of significance, because they provide more useful information to the reader. Tests are used to determine if a value c, when used in a test of H0 : β = c, is reasonably consistent with the data, whereas confidence intervals give a range of values of c that are consistent with the data. Although tests and confidence intervals are often used in different situations, there is a close relationship between the two approaches.

One way to construct confidence intervals is to determine the interval that contains values of c that, when used in a test of significance, would lead to acceptance of the null hypothesis. To illustrate this idea, suppose we want to construct a 100(1 − α)% confidence interval for a regression parameter β in a regression model. Let denote the confidence interval for β. If , then the test of H0 : β = c versus Ha : βc would produce a two-sided p-value that is greater than α. If c ∉ [βL, βU], then the p-value would be less than α.

In the first ten chapters of this book we have described how to calculate p-values for many kinds of adaptive tests, so we should be able to construct ...

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required