Combining Evidence Over Multiple Individual Analyses
Rens van de Schoot, Milica Miočević in Small Sample Size Solutions, 2020
The individual Bayes factors can then be aggregated using a function available on the Open Science Framework (https://osf.io/am7pr/). The function requires as input a matrix with rows and columns, where represents the total of individuals and the number of Bayes factors for which the aggregate conclusion is of interest. The output of the individual analyses created in the previous section fulfills this requirement and can be used in the function. The output of the function is a list that contains: a table containing the gPBF for all Bayes factors considered; the individual Bayes factors used as input; and the sample size . gpout <- gPBF(output) gpout
Bayes Factor
Albert Vexler, Alan D. Hutson in Statistics in the Health Sciences, 2018
The Bayes factor is a summary of the evidence provided by the data in favor of one scientific theory, represented by a statistical model, as opposed to a competing model. Jeffreys (1961) provided a scale of interpretation for the Bayes factor in terms of evidence against the null hypothesis; see Table 5.1 for details. It is suggested to interpret in half-units on the scale.
Bayes Factor–Based Test Statistics
Albert Vexler, Alan D. Hutson, Xiwei Chen in Statistical Testing Strategies in the Health Sciences, 2017
The Bayes factor is a summary of the evidence provided by the data in favor of one scientific theory, represented by a statistical model, as opposed to another. Jeffreys (1961) provided a scale of interpretation for the Bayes factor in terms of evidence against the null hypothesis; see Table 7.1 for details. It is suggested to interpret B10 in half units on the log10 scale.
Bayesian rank-based hypothesis testing for the rank sum test, the signed rank test, and Spearman's ρ
Published in Journal of Applied Statistics, 2020
J. van Doorn, A. Ly, M. Marsman, E.-J. Wagenmakers
After obtaining the joint posterior distribution through the MCMC sampling algorithm outlined above, we can either focus on estimation and present the marginal posterior distribution for the parameter of interest θ, or we can conduct a Bayes factor hypothesis test and compare the predictive performance of a point-null hypothesis θ is free to vary; [27,29,38]). The Bayes factor can be interpreted as a predictive updating factor, that is, degree to which the observed data drive a change from prior to posterior odds for the hypothesis of interest:
Top-down Inhibitory Motor Control Is Preserved in Adults with Developmental Coordination Disorder
Published in Developmental Neuropsychology, 2021
William Mayes, Judith Gentle, Irene Parisi, Laura Dixon, José van Velzen, Ines Violante
All variables were examined for normality violations prior to analysis. All analyses were run using R version 4.0.2 and R Studio version 1.3.1073 (R Core Team, 2019) and data manipulation was achieved using functions from dplyr version 0.8.5 (Wickham, François, Henry., & Müller, 2020). For frequentist and Bayesian group comparison analysis on normally distributed data, independent samples t-tests were run using JASP software for use in R (JASP Team, 2020). If normality violations were present, Wilcoxon rank-sum tests were run instead, again using functions from JASP. A Bayes factor indicates the strength of evidence suggesting that one hypothesis is more likely than another (Rouder, Speckman, Sun, Morey, & Iverson, 2009). Factors of less than 1 indicate no evidence against the null hypothesis, while factors of above 10 indicate strong evidence in favor of the alternate hypothesis. The strengths of evidence is proportional to the Bayes Factor, for example, a factor of 0.5 indicates that the data is twice as likely to be observed under the null hypothesis, while a factor of 5 may indicate the likelihood of this observation to be 5 times as likely under the alternate hypothesis.
Bayesian testing for independence of two categorical variables under two-stage cluster sampling with covariates
Published in Journal of Applied Statistics, 2018
Dilli Bhatta, Balgobin Nandram, Joseph Sedransk
We propose a Bayesian method to perform the test of independence with covariates arising from a two-stage cluster sampling design. We consider both unit and cluster level covariates. Our main idea for the Bayesian test of independence is to convert the cluster sample into an equivalent simple random sample that provides a surrogate of the original sample. Then, we compute the Bayes factor on this surrogate data to make an inference about independence. The advantage of this procedure is that the Bayes factor is in a closed form; otherwise it is very difficult to compute the Bayes factor. We apply our methodology to the data from the Trend in International Mathematics and Science Study (TIMSS) [30] for fourth grade US students.
Related Knowledge Centers
- Null Hypothesis
- Likelihood-Ratio Test
- Statistical Hypothesis Testing
- Laplace'S Approximation
- Bayesian Information Criterion
- Overfitting
- Frequentist Inference
- Statistical Significance
- Bayesian Inference
- Occam'S Razor