# ttest.tstat: Use t statistic to compute Bayes factor for one- and two-... In BayesFactor: Computation of Bayes factors for common designs

## Description

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

## Usage

 ```1 2``` ``` ttest.tstat(t, n1, n2 = 0, nullInterval = NULL, rscale = "medium") ```

## 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

## 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.

## Value

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. For each Bayes factor, a vector of length 2 containing the computed log(e) Bayes factor (against the point null), along with a proportional error estimate on the Bayes factor is returned.

## Author(s)

Richard D. Morey ([email protected]) and Jeffrey N. Rouder ([email protected])

## 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, 752-760

`integrate`, `t.test`; see `ttestBF` for the intended interface to this function, using the full data set.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```## Classical example: Student's sleep data data(sleep) plot(extra ~ group, data = sleep) ## t.test() gives a t value of -4.0621 t.test(extra ~ group, data = sleep, paired=TRUE) ## Gives a Bayes factor of about 17 ## in favor of the alternative hypothesis result <- ttest.tstat(t = -4.0621, n1 = 10) exp(result[['bf']]) ```

### Example output

```Loading required package: coda
************

Type BFManual() to open the manual.
************

Paired t-test

data:  extra by group
t = -4.0621, df = 9, p-value = 0.002833
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-2.4598858 -0.7001142
sample estimates:
mean of the differences
-1.58

[1] 17.25829
```

BayesFactor documentation built on May 31, 2017, 4:17 a.m.