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Learn through experiments

Design a fair comparison

Can easier tasks make a weak treatment look better?

Entering midway? Revisit Audit a dramatic chart for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

An original synthetic task study has easy-task success 80% and hard-task success 40%. Treatment changes both rates by the same chosen number of percentage points.

Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.

Go directly to the experiment · Review basic mathematics

2 · Predict

What do you expect?

Predict the pooled difference when groups receive different difficulty mixes.

3 · Experiment

Change one thing. Inspect what happens.

  1. Keep treatment effect 5; compare 80/20 versus 20/80 task allocations.
  2. Balance both groups at 50% easy tasks.
  3. Set effect to zero and manufacture a favorable headline by changing allocation. State how you would prevent that design error.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Control success72 %
Treatment success53 %
Pooled difference-19 percentage points
Standardized difference5 percentage points

Compare the current results

Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.
072
  • Control success (%)72
    Control success (%): 72Horizontal bar from zero to 72, on the shared zero to 72 numeric axis.
  • Treatment success (%)53
    Treatment success (%): 53Horizontal bar from zero to 53, on the shared zero to 72 numeric axis.

Follow the calculation

  1. Control: 0.8 × 80 + 0.2 × 40 = 72%.
  2. Treatment: 0.2 × 85 + 0.8 × 45 = 53%.
  3. Within each difficulty group, treatment minus control = 5 points.
  4. Use identical 50:50 weights: 0.5 × 5 + 0.5 × 5 = 5 points.

Balance assignment before outcomes are seen. Standardization removes only the difficulty imbalance deliberately modeled here.

Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.

4 · Understand

Explain the mechanism

Design a fair comparison

An original synthetic task study has easy-task success 80% and hard-task success 40%. Treatment changes both rates by the same chosen number of percentage points.

Predict before changing inputs

Predict the pooled difference when groups receive different difficulty mixes.

Understand the mechanism

A fair test must distinguish the intervention from who or what received it. Difficulty affects success even without treatment.

At 80% easy control and 20% easy treatment, control is 72% and treatment 53%: a −19-point pooled gap despite a +5-point within-group effect.

Predefine an outcome, allocation rule and stopping rule. Randomization protects against systematic allocation bias in expectation; this deterministic lab isolates one visible imbalance.

Calculate it yourself

Group rate = easy share × easy rate + hard share × hard rate. Standardize both groups to the same mix.

Guided investigation

  1. Keep treatment effect 5; compare 80/20 versus 20/80 task allocations.

  2. Balance both groups at 50% easy tasks.

  3. Set effect to zero and manufacture a favorable headline by changing allocation. State how you would prevent that design error.

Assumptions and limitations

  • No random assignment or sampling variability is simulated; rates are authored expectations.

  • Adjusting this known difficulty factor cannot remove unmeasured confounding in real observations.

Further investigations

High school: Plan a comparison of revision methods with a clearly defined task.

College: Write a preregistered assignment and analysis protocol.

Working professionals: Design a product experiment with guardrail outcomes and a decision threshold.

5 · Apply

Try a fresh case

Control and treatment both receive half easy and half hard tasks. Control rates are 70% and 30%; treatment rates 76% and 36%. What is the pooled difference in percentage points?

This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.

Take the investigation further

Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.

School investigation

Plan a comparison of revision methods with a clearly defined task.

College investigation

Write a preregistered assignment and analysis protocol.

Workplace investigation

Design a product experiment with guardrail outcomes and a decision threshold.

6 · Continue

Keep the evidence, choose your next step

Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.