Question

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.
How could randomization be used to select the two groups?

Answer 1

Randomization means assigning students to the new-program or standard-curriculum group by chance rather than by judgment. That prevents selection bias and (on average) balances both measured and unmeasured student characteristics between groups.

Simple random assignment (easy)
- Make a list of all students.
- For each student generate a random number (computer, calculator, phone app) or flip a coin.
- If using random numbers, sort by the random number and put the first half (or the number you want) into the new-program group and the rest into the control group. If using coin flips, assign Heads = new program, Tails = control.
- Keep the person who does the randomization separate from anyone who might influence assignments.

Stratified / blocked randomization (recommended if you want balanced pretest ability)
- Divide students into strata (e.g., low/medium/high ability or quartiles) based on the pretest scores.
- Within each stratum, randomly assign students to the two groups (using the random-number or coin method) so each group has similar ability distribution.
- Optionally use matched pairs: pair students with very similar pretest scores, then randomly assign one of each pair to the new program and the other to control.

Practical notes
- Use a reproducible random-number method (record the seed) and an independent person to do the assignment to avoid bias.
- If whole classes must get the same treatment to avoid contamination, randomize at the classroom level (cluster randomization) rather than individual students.

Either simple randomization or stratified randomization will give you an unbiased comparison of the two instructional programs; stratification improves balance on pretest ability.