BEST-package: Bayesian Estimation Supersedes the t Test

In BEST: Bayesian Estimation Supersedes the t-Test

Description

An alternative to t tests, producing posterior estimates for groups means and standard deviations and their differences and effect sizes. Bayesian estimation provides a much richer picture of the data, and can be summarized as point estimates and credible intervals.

Details

The core function, BESTmcmc, generates posterior distributions to compare the means of two groups, or to compare the mean of one group with a standard, taking into account the standard deviation(s). It is thus similar to a t test. However, our Bayesian approach results in probability statements about the values of interest, rather than p-values and significance levels.

In addition, the procedure accounts for departures from normality by using a t-distribution to model the variable of interest and estimating a measure of normality.

Functions to summarize and to visualize the output are provided.

The function BESTpower allows simulation-based estimates of power, either retrospective power directly with BESTmcmc output or prospective power analysis with makeData.

Author(s)

Original code by John K. Kruschke, packaged by Mike Meredith.

References

Kruschke, J. K. 2013. Bayesian estimation supersedes the t test. Journal of Experimental Psychology: General 142(2):573-603. doi: 10.1037/a0029146

Kruschke, J. K. 2011. Doing Bayesian data analysis: a tutorial with R and BUGS. Elsevier, Amsterdam, especially Chapter 18.

Examples

## Comparison of two groups:
## =========================
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)

# Run an analysis, takes up to 1 min.
BESTout <- BESTmcmc(y1, y2, parallel=FALSE)

# Look at the result:
BESTout
summary(BESTout)
plot(BESTout)
plot(BESTout, "sd")
plotPostPred(BESTout)
plotAll(BESTout, credMass=0.8, ROPEm=c(-0.1,0.1),
          ROPEeff=c(-0.2,0.2), compValm=0.5)
plotAll(BESTout, credMass=0.8, ROPEm=c(-0.1,0.1),
          ROPEeff=c(-0.2,0.2), compValm=0.5, showCurve=TRUE)
summary(BESTout, credMass=0.8, ROPEm=c(-0.1,0.1), ROPEsd=c(-0.15,0.15),
          ROPEeff=c(-0.2,0.2))
pairs(BESTout)

head(BESTout$mu1)
muDiff <- BESTout$mu1 - BESTout$mu2
mean(muDiff > 1.5)
mean(BESTout$sigma1 - BESTout$sigma2)
hist(BESTout$nu)

# Retrospective power analysis
# ----------------------------
# This takes time, so we do 2 simulations here; a real analysis needs several hundred

powerRet <- BESTpower(BESTout, N1=length(y1), N2=length(y2),
            ROPEm=c(-0.1,0.1), maxHDIWm=2.0, nRep=2, parallel=FALSE)
powerRet
# We only set criteria for the mean, so results for sd and effect size are all NA.

## Analysis with a single group:
## =============================
y0 <- c(1.89, 1.78, 1.30, 1.74, 1.33, 0.89)

# Run an analysis, takes up to 40 secs.
BESTout1 <- BESTmcmc(y0, parallel=FALSE)
BESTout1
summary(BESTout1)
plot(BESTout1)

head(BESTout1$mu)
mean(BESTout1$sigma)
 

BEST documentation built on Oct. 13, 2021, 9:08 a.m.