Basic Statistics Using R for Crime Analysis

In the previous chapter, I demonstrated that the chi-squared test is employed when examining whether a significant association exists between two categorical variables. For instance, it can be used to test if there is a correlation between the use of credit cards (yes = 1 or no = 0) for online purchases and gender (male = 1 or female = 0). However, what if one of the variables we want to examine is continuous data, not categorical? For instance, suppose we want to investigate whether there is a difference in the number of items purchased online in the past 12 months between men and women. A chi-squared test will not be the most effective statistical tool here. Instead, the t-test is a statistical significance test frequently utilized to evaluate the difference between two group means, such as the average score on antisocial attitudes among inmates who participated in cognitive behavioral therapy (CBT) and those who did not. For example, even if inmates who completed CBT have lower antisocial attitudes than those who did not, it is a different question whether this difference is statistically significant.

There are two main types of t-tests:

In this chapter, we will use two fictitious datasets to conduct these two types of t-tests.