Question

(a)

Ms. Harris, a math teacher, wants to compare the effectiveness of a new math instructional program.
She tests each student’s math ability and then divides the students into two groups.

One group uses the new instructional program, while the other group uses the standard curriculum.
At the end of the year, the teacher retests all the students and compares the increase in math ability in the two groups.
Part A:

Is this an observational study or an experiment? Why?



How could randomization be used to select the two groups?

Answer 1

This is an experiment. The teacher is actively assigning students to different instructional programs (the explanatory variable) and then measuring the outcome (change in math ability), so she is manipulating the treatment rather than merely observing naturally occurring differences.

How to randomize the two groups (simple and improved methods):

- Simple random assignment:
1. Give each student a unique ID number.
2. Use a random-number generator (or coin flips, drawing names from a hat, Excel’s RAND function, random.org, etc.) to select half the IDs for the new program and the rest for the standard curriculum.
3. Teach the two groups accordingly and compare post-test gains.

- Better: randomization with blocking/matching (to ensure balance on pretest ability):
1. Use pretest scores to form matched pairs (or small blocks) of students with similar scores, or create strata (low/medium/high).
2. Within each pair/block, randomly assign one student to the new program and the other to the standard curriculum (or randomly assign proportionally within strata).
3. This reduces chance imbalance in baseline ability and increases precision of the comparison.

Randomization helps ensure that other student characteristics are roughly balanced between groups, so differences in post-test gains can more confidently be attributed to the instructional program.