The power of a paired t-test with a covariate

•The paired t-test is a basic but popular statistical test.•Use of regression to improve power in t-tests is also common.•We provide guidance on computing power for such a design. Many researchers employ the paired t-test to evaluate the mean difference between matched data points. Unfortunately, in...

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Bibliographic Details
Published in:Social science research 2015-03, Vol.50, p.277-291
Main Authors: Hedberg, E.C., Ayers, Stephanie
Format: Article
Language:English
Subjects:
Computational methods
Correlation
Covariance
Data Interpretation, Statistical
Economic efficiency
Families & family life
Humans
Intervention
Means testing
Models, Statistical
Paired t-tests
Regression
Regression Analysis
Statistical power
Statistics
Statistics as Topic - methods
Variables
Variance analysis
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Summary:•The paired t-test is a basic but popular statistical test.•Use of regression to improve power in t-tests is also common.•We provide guidance on computing power for such a design. Many researchers employ the paired t-test to evaluate the mean difference between matched data points. Unfortunately, in many cases this test in inefficient. This paper reviews how to increase the precision of this test through using the mean centered independent variable x, which is familiar to researchers that use analysis of covariance (ANCOVA). We add to the literature by demonstrating how to employ these gains in efficiency as a factor for use in finding the statistical power of the test. The key parameters for this factor are the correlation between the two measures and the variance ratio of the dependent measure on the predictor. The paper then demonstrates how to compute the gains in efficiency a priori to amend the power computations for the traditional paired t-test. We include an example analysis from a recent intervention, Families Preparing the New Generation (Familias Preparando la Nueva Generación). Finally, we conclude with an analysis of extant data to derive reasonable parameter values.
ISSN:0049-089X
1096-0317
DOI:10.1016/j.ssresearch.2014.12.004