10.4 Wrapping up the Process

Let’s Review the Process

1. Start with a research question: Are job applicants with criminal records less likely to receive call backs for interviews than applicants without criminal records?
2. Develop a theory of how the world works
   • E.g., “Job prospects are, in part, a function of someone’s criminal record.”
3. Construct “null” and “alternative” hypotheses
   • E.g., \(H_o\): “Applicants with a criminal record will receive call backs at similar rates as those without a criminal record” (I.e., no difference)
   • E.g., \(H_A\): “Applicants with a criminal record will be less likely to receive call backs than those without a criminal record” or “Applicants with a criminal record will receive call backs at different rates than those without a criminal record” (I.e., some nonzero difference)
4. Carry out a test of the hypothesis, such as a difference-in-means.
   • Applicants with a criminal record receive 12.5 percentage points fewer call backs than those without a criminal record
5. Calculate the uncertainty around this estimate.
   • We could estimate the standard error with the sample standard deviation and sample size
   • We could also estimate the confidence intervals.
6. Decide whether the result is significant. Can you reject or do you fail to reject the hypothesis of no difference?
   • Use the z-score/t-statistic and p-value
   • The z score is an example of a “test statistic.” The type of statistic might vary across applications, but its purpose will remain similar. Others include t-statistics and Chi-squared statistics.