
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),
...
)
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.
a vector of observations for the first (or only) group
a vector of observations for the second group (or condition, for paired)
for independent-group designs, a (optional) formula describing the model
for one-sample and paired designs, the null value of the mean (or mean difference)
optional vector of length 2 containing lower and upper bounds of an interval hypothesis to test, in standardized units
if TRUE
, observations are paired
for use with formula
, a data frame containing all the
data
prior scale. A number of preset values can be given as strings; see Details.
if TRUE
, return samples from the posterior instead
of Bayes factor
callback function for third-party interfaces
further arguments to be passed to or from methods.
Richard D. Morey (richarddmorey@gmail.com)
The Bayes factor provided by ttestBF
tests the null hypothesis that
the mean (or mean difference) of a normal population is 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
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
The Bayes factor is computed via Gaussian quadrature.
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
## 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"])
Run the code above in your browser using DataLab