9: ANOVA (General Linear Models Part II)

Overview Section

 Case-Study: Test scores and socioeconomic status

Moriah is a community and economic development major. She is interested in studying the impact of people who suffer from hunger (food insecurity) in economically depressed urban areas on students’ test scores. Moriah has access to some local schools in an economically depressed urban area to collaborate with teachers to assess how often students go hungry. To make the study easier for teachers, she comes up with a 3 point rating scale of low food insecurity, medium insecurity, and high food insecurity, now she wants to see if the level of food insecurity has any relationship to test scores. Can you help Moriah get started on her study?

As is good practice, the first thing Moriah needs to do is correctly identify her data. Moriah’s test scores are measured as a quantitative variable, so we know she has a quantitative response variable. Unlike regression (where the predictor variable was continuous), from unit 8, Moriah’s predictor variable is a categorical one, low, medium, and high food insecurity. How do we tell if the level of insecurity will make a difference in the test scores?

First, let’s look at the descriptive statistics for Moriah’s data. We can see that the mean test scores for the three groups range from 70 for the high food insecurity group to a high of almost 90 for the low food insecurity group. It looks like there might be a trend but Moriah still needs to test to see if these differences among the groups are significant or not.

Descriptive Statistics: Critical Areas, Cost
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
High Food Insecurity 30 0 70.181 0.168 0.923 67.782 69.692 70.162 70.848 72.704
Medium Food Insecurity 30 0 84.823 0.161 0.882 82.799 84.206 84.978 85.508 86.536
Low Food Insecurity 30 0 89.713 0.182 0.995 87.609 89.032 89.856 90.531 91.667


Upon completion of this lesson, you should be able to:

  • Identify the components used calculating an F test
  • Interpret an F test, including the null and alternative hypothesis
  • Interpret a Post-hoc analysis
  • Differentiate between regression and ANOVA
  • State the assumptions for ANOVA