SAT-62: Experimental Design — Random Assignment and Cause-and-Effect

SAT-62: Experimental Design — Random Assignment and Cause-and-Effect

Description: SAT-61 warned that correlation is not causation. This lesson explains the one situation where you can claim cause-and-effect: a well-designed experiment with random assignment. Knowing the difference between an experiment and an observational study is a guaranteed SAT question.

Two kinds of studies

• Observational study: you only watch and record; you don't change anything. It can show an association, but lurking variables may explain it.
• Experiment: you actively apply a treatment to subjects and compare groups. Done right, it can show causation.

(Oʻzbekcha: kuzatuv tadqiqotida faqat qarab turamiz; eksperimentda esa biror taʼsir (davolash) qoʻllaymiz.)

The three pillars of a good experiment

• Control group vs treatment group: one group gets the treatment, one doesn't, so you have something to compare.
• Random assignment: subjects are placed into groups by chance. This spreads hidden differences evenly, so the only systematic difference left is the treatment.
• Replication: enough subjects that the result isn't just luck.

Random assignment (to groups) is what allows causal claims; random selection (SAT-60) is what allows generalizing to a population. The SAT loves this distinction. (Oʻzbekcha: tasodifiy taqsimlash — sababiy xulosa uchun; tasodifiy tanlash — umumlashtirish uchun.)

Worked Example 1 — classify the study

Researchers record the diets people already follow and compare their health. Experiment or observational?

• Nothing was assigned — they only observed existing diets → observational study. It can't prove the diet caused the health difference.

Worked Example 2 — what makes it causal

A company randomly assigns 100 volunteers to take a new vitamin or a placebo, then compares energy levels. Can they claim the vitamin caused any difference?

• Yes — random assignment plus a control (placebo) group means the groups were alike except for the vitamin, so a difference can be attributed to it. Causal claim is justified.

(Oʻzbekcha: tasodifiy taqsimlash va nazorat guruhi boʻlgani uchun sababiy xulosa chiqarish mumkin.)

Worked Example 3 — scope of the conclusion

In that vitamin study the 100 volunteers were not randomly selected from any population — they just volunteered. What can and can't the company conclude?

• They can say the vitamin caused the effect within these subjects (random assignment).
• They cannot generalize to all people, because the subjects weren't randomly selected.

Rule: random assignment → causation; random selection → generalization. You need both for "this causes that for everyone." (Oʻzbekcha: ikkalasi ham boʻlsa — "hamma uchun sabab" deyish mumkin.)

The four-box summary (a fast way to answer)

Every SAT design question fits into one of four boxes formed by two yes/no questions: Was there random assignment? and Was there random selection?

• Assignment yes + selection yes → can claim cause and generalize.
• Assignment yes + selection no → can claim cause, but only for the subjects studied.
• Assignment no + selection yes → can generalize an association, but not claim cause.
• Assignment no + selection no → only an association among these subjects; no cause, no generalizing.

Decide the two yes/no answers first, and the correct conclusion falls out automatically. (Oʻzbekcha: ikkita savolga (taqsimlash tasodifiymi? tanlash tasodifiymi?) javob bering — xulosa oʻzidan kelib chiqadi.)

Practice 1

A study finds students who eat breakfast score higher, by surveying current habits. Can it claim breakfast causes higher scores?

Practice 2

To test a teaching app, a school randomly assigns half its students to use it and half not, then compares grades. Which type of study is this, and can it show cause?

Key words — Kalit soʻzlar

• Experiment — tajriba (eksperiment)
• Observational study — kuzatuv tadqiqoti
• Treatment — taʼsir (davolash usuli)
• Control group — nazorat guruhi
• Random assignment — tasodifiy taqsimlash
• Placebo — platsebo (soxta dori)
• Cause-and-effect — sabab-natija
• Lurking variable — yashirin omil
• Replication — takrorlash

Summary

• Observational study → association only; experiment → can show causation.
• Good experiments need a control group, random assignment, and replication.
• Random assignment → causal claims; random selection → generalizing to a population.