Description Usage Arguments Details Value Note Author(s) References See Also Examples

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.

1 2 | ```
meta.ttestBF(t, n1, n2 = NULL, nullInterval = NULL, rscale = "medium",
posterior = FALSE, callback = function(...) as.integer(0), ...)
``` |

`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 |

`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 |

`callback` |
callback function for third-party interfaces |

`...` |
further arguments to be passed to or from methods. |

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.

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.

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

Richard D. Morey (richarddmorey@gmail.com)

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
## 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)
``` |

```
Loading required package: coda
Loading required package: Matrix
************
Welcome to BayesFactor 0.9.12-2. If you have questions, please contact Richard Morey (richarddmorey@gmail.com).
Type BFManual() to open the manual.
************
Bayes factor analysis
--------------
[1] Alt., r=1 0<d<Inf : 38.68248 <U+00B1>0%
Against denominator:
Null, d = 0
---
Bayes factor type: BFmetat, JZS
Independent-candidate M-H acceptance rate: 100%
Iterations = 1:1000
Thinning interval = 1
Number of chains = 1
Sample size per chain = 1000
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
0.17085 0.04682 0.00148 0.00148
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
0.07384 0.13974 0.16967 0.20257 0.26746
```

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