R: Function for Bayesian analysis of one- and two-sample designs

meta.ttestBF {BayesFactor} | R Documentation

## Function for Bayesian analysis of one- and two-sample designs

### Description

This function computes mata-analytic Bayes factors, or samples from the posterior, for one- and two-sample designs where multiple t values have been observed.

### Usage

    meta.ttestBF(t, n1, n2 = NULL, nullInterval = NULL, rscale = "medium",
      posterior = FALSE, callback = function(...) as.integer(0), ...)

### Arguments

`t` | a vector of t statistics
`n1` | a vector of sample sizes for the first (or only) condition
`n2` | a vector of sample sizes. If `NULL`, a one-sample design is assumed
`nullInterval` | optional vector of length 2 containing lower and upper bounds of an interval hypothesis to test, in standardized units
`rscale` | prior scale. A number of preset values can be given as strings; see Details.
`posterior` | if `TRUE`, return samples from the posterior instead of Bayes factor
`callback` | callback function for third-party interfaces
`...` | further arguments to be passed to or from methods.

### Details

The Bayes factor provided by `meta.ttestBF` tests the null hypothesis that the true effect size (or alternatively, the noncentrality parameters) underlying a set of t statistics is 0. Specifically, the Bayes factor compares two hypotheses: that the standardized effect size is 0, or that the standardized effect size is not 0. Note that there is assumed to be a single, common effect size delta underlying all t statistics. For one-sample tests, the standardized effect size is (mu-mu0)/sigma; for two sample tests, the standardized effect size is (mu2-mu1)/sigma.

A Cauchy prior is placed on the standardized effect size. The `rscale` argument controls the scale of the prior distribution, with `rscale=1` yielding a standard Cauchy prior. See the help for `ttestBF` and the references below for more details.

The Bayes factor is computed via Gaussian quadrature. Posterior samples are drawn via independent-candidate Metropolis-Hastings.

### Value

If `posterior` is `FALSE`, an object of class `BFBayesFactor` containing the computed model comparisons is returned. If `nullInterval` is defined, then two Bayes factors will be computed: The Bayes factor for the interval against the null hypothesis that the standardized effect is 0, and the corresponding Bayes factor for the compliment of the interval.

If `posterior` is `TRUE`, an object of class `BFmcmc`, containing MCMC samples from the posterior is returned.

### Note

To obtain the same Bayes factors as Rouder and Morey (2011), change the prior scale to 1.

### Author(s)

Richard D. Morey (richarddmorey@gmail.com)

### References

Morey, R. D. & Rouder, J. N. (2011). Bayes Factor Approaches for Testing Interval Null Hypotheses. Psychological Methods, 16, 406-419

Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G. (2009). Bayesian t-tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review, 16, 225-237

Rouder, J. N. & Morey, R. D. (2011). A Bayes Factor Meta-Analysis of Bem's ESP Claim. Psychonomic Bulletin & Review, 18, 682-689

### See Also

`ttestBF`

### Examples

    ## Bem's (2010) data (see Rouder & Morey, 2011)
    t=c(-.15,2.39,2.42,2.43)
    N=c(100,150,97,99)

    ## Using rscale=1 and one-sided test to be
    ## consistent with Rouder & Morey (2011)
    bf = meta.ttestBF(t, N, rscale=1, nullInterval=c(0, Inf))
    bf[1]

    ## plot posterior distribution of delta, assuming alternative
    ## turn off progress bar for example
    samples = posterior(bf[1], iterations = 1000, progress = FALSE)
    ## Note that posterior() respects the nullInterval
    plot(samples)
    summary(samples)

[Package BayesFactor version 0.9.12-4.2 Index]