Using Bayesian Independent Sample Inference to perform an independent t-test with prior expectation for difference between means

A small business owner with 474 employees is interested in seeing if there is a difference in mean salary between male and female employees. We assume that the business owner has a prior belief about mean salary for male employees - it follows a normal distribution with a mean of $22,500 and variance of $15,000. Similarly, for female employees the business owner has a prior belief that mean salary also follows a normal distribution with a mean of $20,000 and variance of $10,000. The small business owner wants to use the Bayesian Independent Sample Inference approach to perform an independent t-test with prior expectation for difference between means.

This information is collected in Employee data.sav. See the topic Sample Files for more information.

Note: For the purposes of this case study we are assuming that the salary variable is normally distributed. In practice, a transformation (such as a log transformation) may need to be applied to meet the normal distribution criteria.

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