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6 - Paired Data

Published online by Cambridge University Press:  17 April 2022

Michael P. Fay
Affiliation:
National Institute of Allergy and Infectious Diseases
Erica H. Brittain
Affiliation:
National Institute of Allergy and Infectious Diseases
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Summary

This chapter covers paired data, such as comparing responses before and after a treatment in one group of individuals. The sign test (also called the exact McNemar’s test when responses are binary) is compared to a median test on the differences of responses within pairs, and we show that the sign test is often more appropriate. We give confidence intervals compatible with the sign test. We discuss parameters associated with the Wilcoxon signed-rank test (often more powerful than the sign test) and assumptions needed to give associated confidence intervals. When we can assume symmetric distribution on the differences within pairs, the t-test is another option, and we discuss asymptotic relative efficiency for choosing between the t-test and Wilcoxon signed-rank test. We compare parameterizing the treatment effect as differences or ratios. We discuss tests using Pearson’s and Spearman’s correlation and Kendal’s tau, and present confidence intervals assuming normality. When the paired data represent different assays or raters, then agreement coefficients are needed (e.g., Cohen’s kappa, or Lin’s concordance correlation coefficient).

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Chapter
Information
Statistical Hypothesis Testing in Context
Reproducibility, Inference, and Science
, pp. 84 - 103
Publisher: Cambridge University Press
Print publication year: 2022

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