The Bayesian independent samples t-test

For our last example in the chapter, we will be performing a sort-of Bayesian analogue to the two-sample t-test using the same data and problem from the corresponding example in the previous chapter-testing whether the means of the gas mileage for automatic and manual cars are significantly different.

Note

There is another popular Bayesian alternative to NHST, which uses something called Bayes factors to compare the likelihood of the null and alternative hypotheses.

As before, let's specify the model using non-informative flat priors, as shown in the following code:

the.model <- " 
model { 
  # each group will have a separate mu 
  # and standard deviation 
  for(j in 1:2){ 
    mu[j] ~ dunif(0, 60)       # prior 
    stddev[j] ~ dunif(0, 20)   # prior 
    tau[j] <- pow(stddev[j], -2) 
  } 
  for(i in 1:theLength){ 
    # likelihood function 
    y[i] ~ dnorm(mu[x[i]], tau[x[i]])    
  } 
}" 

Notice that the construct that describes the likelihood...