Suppose that you are asked to conduct a study to determine w

Suppose that you are asked to conduct a study to determine whether smaller class sizes lead to improved student performance of fourth graders. If you could conduct any experiment you want, what would you do? Be specific. More realistically, suppose you can collect observational data on several thousand fourth graders in a given state. You can obtain the size of their fourth-grade class and a standardized test score taken at the end of fourth grade. Why might you expect a negative correlation between class size and test score? Would a negative correlation necessarily show that smaller class sizes cause better performance? Explain.

Solution

a. I will study corelation between class size and student performance. We can also study regression analysis between two variables.

b. On the basis of common sense we can expect a negative correlation between calss size and test score. In smaller class, teacher is able to give more attention on each and every child. Children are closely connected and have harmonious relation with each other. It makes us predict that there will be a negative correlation between class size and test score.

c. No, a negative correlation does not mean that smaller class sizes cause better performance because in statistics correlation does not mean cause and effect relationship. It simply means that when X falls Y rises and vice versa but it does not mean that rise in Y is caused by fall in X.