Learning Statistics with R - A tutorial for psychology students and other beginners, 2018a

--------------
[1] Non-indep. (a=1) : 8.294321 ˘0%
Against denominator:
Null, independence, a = 1
---
Bayes factor type: BFcontingencyTable, hypergeometric
The Bayes factor of 8:1 provides modest evidence that the labels were being assigned in a way that
correlates gender with colour, but it’s not conclusive.
17.5
Bayesian t-tests
The second type of statistical inference problem discussed in this book is the comparison between two
means, discussed in some detail in the chapter on t-tests (Chapter 13). If you can remember back that
far, you’ll recall that there are several versions of the t-test. The BayesFactor package contains a function
called ttestBF() that is flexible enough to run several different versions of the t-test. I’ll talk a little
about Bayesian versions of the independent samples t-tests and the paired samples t-test in this section.
17.5.1 Independent samples t-test
The most common type of t-test is the independent samples t-test, and it arises when you have data that
look something like this:
> load( "harpo.Rdata" )
> head(harpo)
grade tutor
1 65 Anastasia
2 72 Bernadette
3 66 Bernadette
4 74 Anastasia
5 73 Anastasia
6 71 Bernadette
In this data set, we have two groups of students, those who received lessons from Anastasia and those
who took their classes with Bernadette. The question we want to answer is whether there’s any difference
in the grades received by these two groups of student. Back in Chapter 13 I suggested you could analyse
this kind of data using the independentSamplesTTest() function in the lsr package. For example, if you
want to run a Student’s t-test, you’d use a command like this:
> independentSamplesTTest(
formula = grade ~ tutor,
data = harpo,
var.equal = TRUE
)
Like most of the functions that I wrote for this book, the independentSamplesTTest() is very wordy. It
prints out a bunch of descriptive statistics and a reminder of what the null and alternative hypotheses
- 574 -