Constrained statistical inference: samplesize tables for ANOVA and regression
 Author
 Leonard Vanbrabant (UGent) , Rens van de Schoot and Yves Rosseel (UGent)
 Organization
 Abstract
 Researchers in the social and behavioral sciences often have clear expectations about the order/direction of the parameters in their statistical model. For example, a researcher might expect that regression coefficient beta(1) is larger than beta(2) and beta(3). The corresponding hypothesis is H: > {beta(2), beta(3) } and this is known as an (order) constrained hypothesis. A major advantage of testing such a hypothesis is that power can be gained and inherently a smaller sample size is needed. This article discusses this gain in sample size reduction, when an increasing number of constraints is included into the hypothesis. The main goal is to present samplesize tables for constrained hypotheses. A samplesize table contains the necessary samplesize at a prespecified power (say, 0.80) for an increasing number of constraints. To obtain samplesize tables, two Monte Carlo simulations were performed, one for ANOVA and one for multiple regression. Three results are salient. First, in an AN OVA the needed samplesize decreases with 3050% when complete ordering of the parameters is taken into account. Second, small deviations from the imposed order have only a minor impact on the power. Third, at the maximum number of constraints, the linear regression results are comparable with the ANOVA results. However, in the case of fewer constraints, ordering the parameters (e.g., beta(1) > beta(2)) results in a higher power than assigning a positive or a negative sign to the parameters (e.g., beta(1) > 0).
 Keywords
 inequality/order constraints, linear model, VARIANCE, Fbar test statistic, HOMOGENEITY, TESTS, EQUALITY, PARAMETERS, ORDERED ALTERNATIVES, INEQUALITY CONSTRAINTS, LINEARMODEL, RESTRICTED EM ALGORITHM, ONESIDED HYPOTHESES, power, samplesize tables
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU5819667
 MLA
 Vanbrabant, Leonard, Rens van de Schoot, and Yves Rosseel. “Constrained Statistical Inference: Samplesize Tables for ANOVA and Regression.” FRONTIERS IN PSYCHOLOGY 5 (2015): 1–8. Print.
 APA
 Vanbrabant, L., van de Schoot, R., & Rosseel, Y. (2015). Constrained statistical inference: samplesize tables for ANOVA and regression. FRONTIERS IN PSYCHOLOGY, 5, 1–8.
 Chicago authordate
 Vanbrabant, Leonard, Rens van de Schoot, and Yves Rosseel. 2015. “Constrained Statistical Inference: Samplesize Tables for ANOVA and Regression.” Frontiers in Psychology 5: 1–8.
 Chicago authordate (all authors)
 Vanbrabant, Leonard, Rens van de Schoot, and Yves Rosseel. 2015. “Constrained Statistical Inference: Samplesize Tables for ANOVA and Regression.” Frontiers in Psychology 5: 1–8.
 Vancouver
 1.Vanbrabant L, van de Schoot R, Rosseel Y. Constrained statistical inference: samplesize tables for ANOVA and regression. FRONTIERS IN PSYCHOLOGY. 2015;5:1–8.
 IEEE
 [1]L. Vanbrabant, R. van de Schoot, and Y. Rosseel, “Constrained statistical inference: samplesize tables for ANOVA and regression,” FRONTIERS IN PSYCHOLOGY, vol. 5, pp. 1–8, 2015.
@article{5819667, abstract = {Researchers in the social and behavioral sciences often have clear expectations about the order/direction of the parameters in their statistical model. For example, a researcher might expect that regression coefficient beta(1) is larger than beta(2) and beta(3). The corresponding hypothesis is H: > {beta(2), beta(3) } and this is known as an (order) constrained hypothesis. A major advantage of testing such a hypothesis is that power can be gained and inherently a smaller sample size is needed. This article discusses this gain in sample size reduction, when an increasing number of constraints is included into the hypothesis. The main goal is to present samplesize tables for constrained hypotheses. A samplesize table contains the necessary samplesize at a prespecified power (say, 0.80) for an increasing number of constraints. To obtain samplesize tables, two Monte Carlo simulations were performed, one for ANOVA and one for multiple regression. Three results are salient. First, in an AN OVA the needed samplesize decreases with 3050% when complete ordering of the parameters is taken into account. Second, small deviations from the imposed order have only a minor impact on the power. Third, at the maximum number of constraints, the linear regression results are comparable with the ANOVA results. However, in the case of fewer constraints, ordering the parameters (e.g., beta(1) > beta(2)) results in a higher power than assigning a positive or a negative sign to the parameters (e.g., beta(1) > 0).}, articleno = {1565}, author = {Vanbrabant, Leonard and van de Schoot, Rens and Rosseel, Yves}, issn = {16641078}, journal = {FRONTIERS IN PSYCHOLOGY}, keywords = {inequality/order constraints,linear model,VARIANCE,Fbar test statistic,HOMOGENEITY,TESTS,EQUALITY,PARAMETERS,ORDERED ALTERNATIVES,INEQUALITY CONSTRAINTS,LINEARMODEL,RESTRICTED EM ALGORITHM,ONESIDED HYPOTHESES,power,samplesize tables}, language = {eng}, pages = {1565:11565:8}, title = {Constrained statistical inference: samplesize tables for ANOVA and regression}, url = {http://dx.doi.org/10.3389/fpsyg.2014.01565}, volume = {5}, year = {2015}, }
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