Question

When we were children, many of us were told that our punishment would be less severe if we owned up to our mischief than if we lied and were later found to be guilty. A curious social scientist wished to determine if that old adage was true fro criminals in the justice system. He believed that criminals would get lighter sentences if they plead guilty than if they plead not guilty but were convicted by trial. To test the hypotheses, he randomly selected 660 records of burglary trials from all records in toronto. The defendants in the samples cases were cross- classified as to the plea entered and sentence received. What type of test was used?

Chi-square goodness of fit, chi-square homogeneity, chi-square independence or some other type of test. Explain your answer in context.

Chi-square goodness of fit, chi-square homogeneity, chi-square independence or some other type of test. Explain your answer in context.

Answer 1

Here is some set up of the scenario with some dummy data:

We would basically need to see if there is any association between plea entered and sentence received i.e. we need to see whether plea entered and sentence received are independent or dependent variables. Hence the most appropriate test in this scenario would be the chi-square test of independence. We already have two categorical variables and count data.

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!