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: | |
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| Format: | Article |
| Language: | English |
| Published: |
Springer
2024-10-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/s44199-024-00089-5 |
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| Summary: | 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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| ISSN: | 2214-1766 |