How can I test possible reasons for the relationship between income and handedness?

Question

For a project, I am trying to determine what accounts for the difference in income between left handed people and right handed people. (For example, whether it is only among males, or only in a certain field, education level etc.)

For independent variables, I will be looking at:

• handedness
• education level
• sex
• job category (jobs will be divided into 3-4 categories)

For the dependent variable, I simply have income.

My theory is that left handed people tend to pick jobs which are lower paying, which is why they have on average a lower income than right handed people. So what kinds of statistical tests could I use to show the following relationship is statistically likely:

left handed --> lower paying job --> lower income

Answer 1

(Converting my comment to an answer.)

You list several questions, and they are different types of questions. For example, the question of whether it is only among males, is a question of moderation. You can test that with an interaction term. That is, you would create a new variable as the product of your indicator variable for sex and your indicator for handedness.

On the other hand, the causal chain at the bottom is a model of mediation. Testing that is more complicated. The traditional approach was to establish that Baron & Kenny's (pdf) 'logical steps' criteria were met. However, that has been criticized (MacKinnon, et al., 2002). Many methods have been suggested since Baron and Kenny's time (1985). You may want to read about some of them on the Wikipedia page, and/or you may want to browse through some of our threads categorized under mediation.