Bayesian Estimation Supersedes the t Test
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Citations
Using Bayes to get the most out of non-significant results
Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan
Extensive impact of non-antibiotic drugs on human gut bacteria
Is psychology suffering from a replication crisis? What does "failure to replicate" really mean?
The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective
References
Stopping rules for clinical trials incorporating clinical opinion
Inference by Eye: Pictures of Confidence Intervals and Thinking About Levels of Confidence
Practical Bayesian design and analysis for drug and device clinical trials.
Bayesian Inference and Application of Robust Growth Curve Models Using Student's t Distribution
Related Papers (5)
Frequently Asked Questions (8)
Q2. What packages are required to run BEST?
BEST also requires the packages rjags and coda, which should normally be installed at the same time as package BEST if you use the install.
Q3. What is the way to extract the data?
Since BEST objects are also data frames, the authors can use the $ operator to extract the columns the authors want:> names(BESTout)[1] "mu1" "mu2" "nu" "sigma1" "sigma2"> meanDiff <- (BESTout$mu1 - BESTout$mu2) > meanDiffGTzero <- mean(meanDiff > 0) > meanDiffGTzero[1]
Q4. what is the package for rjags?
Once installed, the authors need to load the BEST package at the start of each R session, which will also load rjags and coda and link to JAGS:> library(BEST)The authors will use hypothetical data for reaction times for two groups (N1 = N2 = 6), Group 1 consumes a drug which may increase reaction times while Group 2 is a control group that consumes a placebo.>
Q5. What is the method for estimating the power of experimental designs?
If you want to know how the functions in the BEST package work, you can download the R source code from CRAN or from GitHub https://github.com/mikemeredith/BEST.Bayesian analysis with computations performed by JAGS is a powerful approach to analysis.
Q6. What is the package for estimating statistical power?
You can specify your own priors by providing a list: population means (µ) have separate normal priors, with mean muM and standard deviation muSD; population standard deviations (σ) have separate gamma priors, with mode sigmaMode and standard deviation sigmaSD; the normality parameter (ν) has a gamma prior with mean nuMean and standard deviation nuSD.
Q7. What is the default prior for the other parameters?
We’ll use the default priors for the other parameters: sigmaMode = sd(y), sigmaSD = sd(y)*5, nuMean = 30, nuSD = 30), where y = c(y1, y2).> priors <- list(muM = 6, muSD = 2)The authors run BESTmcmc and save the result in BESTout.
Q8. What is the way to calculate the reaction times?
y1 <- c(5.77, 5.33, 4.59, 4.33, 3.66, 4.48) > y2 <- c(3.88, 3.55, 3.29, 2.59, 2.33, 3.59)Based on previous experience with these sort of trials, the authors expect reaction times to be approximately 6 secs, but they vary a lot, so we’ll set muM = 6 and muSD = 2.