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All courses Math III · S-IC.5 51 of 55
Use randomized-experiment data and simulations to compare treatments and judge significance.

Identify experimental conditions, unit, response, and contrast

Problem
Patients are randomly assigned a new drug or placebo, and pain score is measured. Identify the treatment, control, experimental unit, response, and treatment-minus-control comparison.
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Hint

Identify what receives the random label before naming the outcome.

Treatment/reference are assigned conditions; experimental unit receives assignment; response is measured; contrast order determines effect sign.

Solution walkthrough

01

Identify conditions

\[\text{treatment}=\text{new}~\text{drug};~\text{reference}=\text{placebo}\]

The reference may be placebo, no treatment, standard practice, or active comparator.

02

Identify randomized unit

\[\text{one}~\text{patient}\]

This controls the level of independent assignment and analysis.

03

Identify response

\[\text{pain}~\text{score}\]

The response is measured after assignment.

04

Define signed contrast

\[\text{difference}~\text{in}~\text{mean}~\text{pain}~\text{score},~\text{drug}~\text{minus}~\text{placebo}\]

Order prevents ambiguous positive/negative treatment effects.

05

Submit components

\[\text{treatment}=\text{new}~\text{drug};~\text{control}/\text{reference}=\text{placebo};~\text{experimental}~\text{unit}=\text{one}~\text{patient};~\text{response}=\text{pain}~\text{score};~\text{contrast}=\text{difference}~\text{in}~\text{mean}~\text{pain}~\text{score},~\text{drug}~\text{minus}~\text{placebo}\]

Every design component is separately represented.

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Another way

  1. Complete: assign ₜo each , measure , compare ₘinus .

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Common mistake

Do not confuse treatment with response or ignore an active reference group.