Question

You are the School Resources Officer for a large metropolitan high school. Recently, a controversy has emerged regarding arrest rates for youth that attend the school. The issue is related to the current national controversy called Disproportionate Minority Contact. Essentially, this controversy alleges that criminal justice practitioners arrest a higher proportion of minority individuals.

You have been asked to analyze the arrests you and your colleagues make at the school. You have a list of all of the students that were brought to your attention last year that could have been arrested, totaling about 400 students, and you know their races. Of these 400 students, 150 were arrested (this includes arrests at school sponsored events like football games).  

So, you have two variables. First, you have the race of the students (Black, Hispanic or Caucasian). Second, you have whether they were arrested or not (yes or no). In order to be sure that the differences in arrest rates are not due to chance (i.e. statistically significant) you want to use a statistical model for analyzing these data. Of the statistical models we have discussed in this learning module (Chi-square, t-score, F-ratio*) which would be the most appropriate for these data?

*F-ratio is also referred to as Analysis of Variance or ANOVA.

The table below will be helpful in determining the type of hypothesis.

If the independent variable is measured at the    level of measurement, and

The dependent variable is measured at the           level of measurement, then

The hypothesis is              .

Nominal

Nominal, Ordinal, Scale*

Difference

Ordinal, Scale

Ordinal, Scale

Association

*Interval and Ratio level variables are collapsed into one category called Scale because the statistical tests available for variables measured at both of these levels are the same.

The information below will help you determine which statistical model would be appropriate for these data.

For a hypothesis of difference,

If the independent and dependent variables are both measured at the nominal level of measurement, use a Chi-Square model.

If the independent variable is measured at the nominal level of measurement and the dependent variable is measured at the scale level of measurement,

Use a t-test model when there are two groups to compare, or

Use an Analysis of Variance (F-ratio) model if there are more than two groups to compare.

For a hypothesis of association,

If the independent and dependent variables are both measured at the scale level of measurement, use a Pearson R model.

If the independent and dependent variables are both measured at the scale level of measurement and you want to use the independent variables to predict the value of the dependent variable, use a Regression model.

Answer 1

If the independent variable is measured at the Nominal level of measurement, and

The dependent variable is measured at the Nominal level of measurement, then

The hypothesis is . Chi-square

Reason:

For a hypothesis of difference,

If the independent and dependent variables are both measured at the nominal level of measurement, use a Chi-Square model.

The model which would be the most appropriate for these data is . Chi-square model because the independent variable: the race of the students is Nominal because it can take only the values: Black, Hispanic or Caucasian. The dependent variable : whether they were arrested or not is Nominal because it can take only the values: yes or no.