On the Equivalence Test and Sample Size Procedures for Simple Linear Regressions with Applications to ANCOVA and Moderation Analysis

Abstract Traditional comparisons of slope coefficients and mean responses in linear regression analysis mainly focus on the significant difference rather than the practical equivalence. There has been a growing awareness and demand for appropriate techniques for assessing similarity and comparabilit...

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Main Author: Gwowen Shieh
Format: Article
Language:English
Published: Springer 2024-10-01
Series:Journal of Statistical Theory and Applications (JSTA)
Subjects:
Online Access:https://doi.org/10.1007/s44199-024-00089-5
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author Gwowen Shieh
author_facet Gwowen Shieh
author_sort Gwowen Shieh
collection DOAJ
description Abstract Traditional comparisons of slope coefficients and mean responses in linear regression analysis mainly focus on the significant difference rather than the practical equivalence. There has been a growing awareness and demand for appropriate techniques for assessing similarity and comparability in applied research. Because of the simplicity of the two one-sided tests of mean equivalence, this study describes the corresponding extensions for appraising slope coefficients and mean responses in one and two linear regression lines. The equivalence tests can help assess the negligible trends and similar responses in a single regression line and evaluate the unimportant interaction-moderation effects and comparable simple effects between two linear regression lines. Exact power and sample size formulas are also derived for design planning, and the proposed procedures have the distinct property of accommodating the random properties of both the response and predictor variables. Their usage and validity are illustrated and justified through numerical illustrations and simulation assessments.
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series Journal of Statistical Theory and Applications (JSTA)
spelling doaj-art-5de5d0a2c5a74d0bb5de69b6d0f8c5df2024-12-29T12:49:54ZengSpringerJournal of Statistical Theory and Applications (JSTA)2214-17662024-10-0123439040710.1007/s44199-024-00089-5On the Equivalence Test and Sample Size Procedures for Simple Linear Regressions with Applications to ANCOVA and Moderation AnalysisGwowen Shieh0Department of Management Science, National Yang Ming Chiao Tung UniversityAbstract Traditional comparisons of slope coefficients and mean responses in linear regression analysis mainly focus on the significant difference rather than the practical equivalence. There has been a growing awareness and demand for appropriate techniques for assessing similarity and comparability in applied research. Because of the simplicity of the two one-sided tests of mean equivalence, this study describes the corresponding extensions for appraising slope coefficients and mean responses in one and two linear regression lines. The equivalence tests can help assess the negligible trends and similar responses in a single regression line and evaluate the unimportant interaction-moderation effects and comparable simple effects between two linear regression lines. Exact power and sample size formulas are also derived for design planning, and the proposed procedures have the distinct property of accommodating the random properties of both the response and predictor variables. Their usage and validity are illustrated and justified through numerical illustrations and simulation assessments.https://doi.org/10.1007/s44199-024-00089-5ANCOVATOSTModerationPowerSample size
spellingShingle Gwowen Shieh
On the Equivalence Test and Sample Size Procedures for Simple Linear Regressions with Applications to ANCOVA and Moderation Analysis
Journal of Statistical Theory and Applications (JSTA)
ANCOVA
TOST
Moderation
Power
Sample size
title On the Equivalence Test and Sample Size Procedures for Simple Linear Regressions with Applications to ANCOVA and Moderation Analysis
title_full On the Equivalence Test and Sample Size Procedures for Simple Linear Regressions with Applications to ANCOVA and Moderation Analysis
title_fullStr On the Equivalence Test and Sample Size Procedures for Simple Linear Regressions with Applications to ANCOVA and Moderation Analysis
title_full_unstemmed On the Equivalence Test and Sample Size Procedures for Simple Linear Regressions with Applications to ANCOVA and Moderation Analysis
title_short On the Equivalence Test and Sample Size Procedures for Simple Linear Regressions with Applications to ANCOVA and Moderation Analysis
title_sort on the equivalence test and sample size procedures for simple linear regressions with applications to ancova and moderation analysis
topic ANCOVA
TOST
Moderation
Power
Sample size
url https://doi.org/10.1007/s44199-024-00089-5
work_keys_str_mv AT gwowenshieh ontheequivalencetestandsamplesizeproceduresforsimplelinearregressionswithapplicationstoancovaandmoderationanalysis