ttest.tstat: Use t statistic to compute Bayes factor for one- and two- sample designs

Description

Using the classical t test statistic for a one- or two-sample design, this function computes the corresponding Bayes factor test.

Usage

ttest.tstat(
  t,
  n1,
  n2 = 0,
  nullInterval = NULL,
  rscale = "medium",
  complement = FALSE,
  simple = FALSE
)

Value

If simple is TRUE, returns the Bayes factor (against the null). If FALSE, the function returns a vector of length 3 containing the computed log(e) Bayes factor, along with a proportional error estimate on the Bayes factor and the method used to compute it.

Arguments

t: classical t statistic
n1: size of first group (or only group, for one-sample tests)
n2: size of second group, for independent-groups tests
nullInterval: optional vector of length 2 containing lower and upper bounds of an interval hypothesis to test, in standardized units
rscale: numeric prior scale
complement: if TRUE, compute the Bayes factor against the complement of the interval
simple: if TRUE, return only the Bayes factor

Author

Richard D. Morey (richarddmorey@gmail.com) and Jeffrey N. Rouder (rouderj@missouri.edu)

Details

This function can be used to compute the Bayes factor corresponding to a one-sample, a paired-sample, or an independent-groups t test, using the classical t statistic. It can be used when you don't have access to the full data set for analysis by ttestBF, but you do have the test statistic.

For details about the model, see the help for ttestBF, and the references therein.

The Bayes factor is computed via Gaussian quadrature.

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

Examples

Run this code

## Classical example: Student's sleep data
data(sleep)
plot(extra ~ group, data = sleep)

## t.test() gives a t value of -4.0621
t.test(sleep$extra[1:10], sleep$extra[11:20], paired=TRUE)
## Gives a Bayes factor of about 15
## in favor of the alternative hypothesis
result <- ttest.tstat(t = -4.0621, n1 = 10)
exp(result[['bf']])

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