Sample size determination for Bayesian ANOVAs with informative hypotheses

Qianrao Fu; Mirjam Moerbeek; Herbert Hoijtink

doi:10.3389/fpsyg.2022.947768

Sample size determination for Bayesian ANOVAs with informative hypotheses

Qianrao Fu^*
, Mirjam Moerbeek
, Herbert Hoijtink

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Researchers can express their expectations with respect to the group means in an ANOVA model through equality and order constrained hypotheses. This paper introduces the R package SSDbain, which can be used to calculate the sample size required to evaluate (informative) hypotheses using the Approximate Adjusted Fractional Bayes Factor (AAFBF) for one-way ANOVA models as implemented in the R package bain. The sample size is determined such that the probability that the Bayes factor is larger than a threshold value is at least η when either of the hypotheses under consideration is true. The Bayesian ANOVA, Bayesian Welch's ANOVA, and Bayesian robust ANOVA are available. Using the R package SSDbain and/or the tables provided in this paper, researchers in the social and behavioral sciences can easily plan the sample size if they intend to use a Bayesian ANOVA.

Original language	English
Article number	947768
Number of pages	11
Journal	Frontiers in Psychology
Volume	13
DOIs	https://doi.org/10.3389/fpsyg.2022.947768
Publication status	Published - 22 Nov 2022

Bibliographical note

Funding Information:
QF was supported by the China Scholarship Council. HH was supported by a fellowship from the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS-KNAW) and the Consortium on Individual Development (CID) which was funded through the Gravitation program of the Dutch Ministry of Education, Culture, and Science and the Netherlands Organization for Scientific Research (NWO Grant No. 024.001.003).

Publisher Copyright:
Copyright © 2022 Fu, Moerbeek and Hoijtink.

Funding

QF was supported by the China Scholarship Council. HH was supported by a fellowship from the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS-KNAW) and the Consortium on Individual Development (CID) which was funded through the Gravitation program of the Dutch Ministry of Education, Culture, and Science and the Netherlands Organization for Scientific Research (NWO Grant No. 024.001.003).

Keywords

Bayes factor
Bayesian ANOVAs
informative hypothesis
sample size
SSDbain

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title = "Sample size determination for Bayesian ANOVAs with informative hypotheses",

abstract = "Researchers can express their expectations with respect to the group means in an ANOVA model through equality and order constrained hypotheses. This paper introduces the R package SSDbain, which can be used to calculate the sample size required to evaluate (informative) hypotheses using the Approximate Adjusted Fractional Bayes Factor (AAFBF) for one-way ANOVA models as implemented in the R package bain. The sample size is determined such that the probability that the Bayes factor is larger than a threshold value is at least η when either of the hypotheses under consideration is true. The Bayesian ANOVA, Bayesian Welch's ANOVA, and Bayesian robust ANOVA are available. Using the R package SSDbain and/or the tables provided in this paper, researchers in the social and behavioral sciences can easily plan the sample size if they intend to use a Bayesian ANOVA.",

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Sample size determination for Bayesian ANOVAs with informative hypotheses

Abstract

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Keywords

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