Question: Imagine that your cousin, a high school student, has been assigned to an algebra class based on previous performance. Like many high schools, his high school has three levels of algebra classes: (1) one that includes the standard curriculum plus remedial lessons, (2) one that

includes the standard curriculum, and (3) one that includes the standard curriculum plus an advanced component. At the end of the semester, students’ performance will be assessed on a statewide standardized mathematics exam. These data will be analyzed using a one-way between-groups ANOVA.

1. Using this example, explain the concept of between-groups variance.
2. Using this example, explain the concept of within-groups variance.
3. How would you draw a curve for each distribution (1, 2, and 3) that demonstrates the concepts of between-groups variance and within-groups variance, while also showing what you’d expect these three distributions to look like in comparison with one another?

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