Constrained statistical inference: sample-size tables for ANOVA and regression
Open accessAbstract
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 β1 is larger than β2 and β3. The corresponding hypothesis is H: β1 > {β2, β3} 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 sample-size tables for constrained hypotheses. A sample-size table contains the necessary sample-size at a pre-specified power (say, 0.80) for an increasing number of constraints. To obtain sample-size tables, two Monte Carlo simulations were performed, one for ANOVA and one for multiple regression. Three results are salient. First, in an ANOVA the needed sample-size decreases with 30-50% 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., β1 > β2) results in a higher power than assigning a positive or a negative sign to the parameters (e.g., β1 > 0).
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To increase the feasibility of the study, the authors formulated directional hypotheses and decided to use one-sided testing, which reduces the sample size to 50 participants.
“To increase the feasibility of the study, we formulated directional hypotheses and decided to use one-sided testing, which reduces our sample size to 50 participants [58].”
From Eye movement desensitization and reprocessing (EMDR) therapy or supportive counseling prior to exposure therapy in patients with panic disorder: study protocol for a multicenter randomized controlled trial (IMPROVE) (2023) · cites this paper as [58]
The Introduction and §6.1 show that testing directional, order-constrained hypotheses can reduce the required sample size. But the paper’s illustrated reduction is from 159 to 111 participants, not to 50; it does not establish that one-sided testing yields a sample size of 50 for the citing study. (LLM, conf=0.88)
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Flagged first, then by citations
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Cited by
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Endhoven, B., De Cort, K., Matthijssen, S. J. M. A., de Jongh, A., van Minnen, A., Duits, P., Schruers, K. R. J., van Dis, E. A. M., Krypotos, A. M., Gerritsen, L., et al. (2023) · BMC Psychiatry · doi:10.1186/s12888-022-04320-4 · Cited by 4 · see citing works
“To increase the feasibility of the study, we formulated directional hypotheses and decided to use one-sided testing, which reduces our sample size to 50 participants [58].”
Method
- Authors
- Vanbrabant, L., Van De Schoot, R., & Rosseel, Y.
- Affiliations
- Utrecht University (NL)
- Ghent University (BE)
- Corresponding author
- Vanbrabant, Leonard
- ORCID
- Rosseel, Yves
- Venue
- Frontiers in Psychology
- Publisher
- Frontiers Media SA
- Published
- 2015-01-13
- Volume
- 5
- Pages
- 1565-1565
- ISSN
- 1664-1078 (ISSN-L)
- PMC
- PMC4292225
- OpenAlex
- W1964429631
- Cited by
- 21
- References
- 35
- Citations by year
- 2025: 1 · 2024: 4 · 2023: 4 · 2022: 4 · 2021: 1 · 2019: 4 · 2017: 1 · 2016: 1 · 2015: 1
- FWCI
- 0.89
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by
- Locations
- Frontiers in Psychology (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
- Boloka Institutional Repository (North-west University) (submittedVersion)
- Funders
- Universiteit Utrecht
- Fonds Wetenschappelijk Onderzoek
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO-Veni-451-11- 008, 451-11-008)
- Universiteit Gent
- Vlaamse regering
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- statistical power, analysis of variance, multiple linear regression, sample size reduction, Monte Carlo simulation
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