BEST-package {BEST} R Documentation

## 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)

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)