ttestBF {BayesFactor} | R Documentation |

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

### Description

This function computes Bayes factors, or samples from the posterior, for one- and two-sample designs.

### Usage

```
ttestBF(
x = NULL,
y = NULL,
formula = NULL,
mu = 0,
nullInterval = NULL,
paired = FALSE,
data = NULL,
rscale = "medium",
posterior = FALSE,
callback = function(...) as.integer(0),
...
)
```

### Arguments

`x` |
a vector of observations for the first (or only) group |

`y` |
a vector of observations for the second group (or condition, for paired) |

`formula` |
for independent-group designs, a (optional) formula describing the model |

`mu` |
for one-sample and paired designs, the null value of the mean (or mean difference) |

`nullInterval` |
optional vector of length 2 containing lower and upper bounds of an interval hypothesis to test, in standardized units |

`paired` |
if |

`data` |
for use with |

`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. |

### Details

The Bayes factor provided by `ttestBF`

tests the null hypothesis that
the mean (or mean difference) of a normal population is `\mu_0`

(argument `mu`

). Specifically, the Bayes factor compares two
hypotheses: that the standardized effect size is 0, or that the standardized
effect size is not 0. For one-sample tests, the standardized effect size is
`(\mu-\mu_0)/\sigma`

; for two sample tests, the
standardized effect size is `(\mu_2-\mu_1)/\sigma`

.

A noninformative Jeffreys prior is placed on the variance of the normal
population, while 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 references
below for more details.

For the `rscale`

argument, several named values are recognized:
"medium", "wide", and "ultrawide". These correspond
to `r`

scale values of `\sqrt{2}/2`

, 1, and `\sqrt{2}`

respectively.

The Bayes factor is computed via Gaussian quadrature.

### 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

The default priors have changed from 1 to `\sqrt{2}/2`

. The
factor of `\sqrt{2}`

is to be consistent
with Morey et al. (2011) and
Rouder et al. (2012), and the factor of `1/2`

in both is to better scale the
expected effect sizes; the previous scaling put more weight on larger
effect sizes. To obtain the same Bayes factors as Rouder et al. (2009),
change the prior scale to 1.

### Author(s)

Richard D. Morey (richarddmorey@gmail.com)

### References

Morey, R. D., Rouder, J. N., Pratte, M. S., & Speckman, P. L. (2011). Using MCMC chain outputs to efficiently estimate Bayes factors. Journal of Mathematical Psychology, 55, 368-378

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

### See Also

### Examples

```
## Sleep data from t test example
data(sleep)
plot(extra ~ group, data = sleep)
## paired t test
ttestBF(x = sleep$extra[sleep$group==1], y = sleep$extra[sleep$group==2], paired=TRUE)
## Sample from the corresponding posterior distribution
samples = ttestBF(x = sleep$extra[sleep$group==1],
y = sleep$extra[sleep$group==2], paired=TRUE,
posterior = TRUE, iterations = 1000)
plot(samples[,"mu"])
```

*BayesFactor*version 0.9.12-4.7 Index]