ttestBF | R Documentation |

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

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

`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. |

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.

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.

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.

Richard D. Morey (richarddmorey@gmail.com)

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

`integrate`

, `t.test`

```
## 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"])
```

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