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Learn through experiments

Where should the team improve?

Do equal percentage-point improvements produce equal results?

Entering midway? Revisit Find the regression hidden in a revision for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

Synthetic course signup funnel. Visitors may sign up, then signed-up people may finish a task. A repair adds 10 percentage points to exactly one stage.

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 which repair creates more completions at the initial 40% signup and 50% completion rates.

3 · Experiment

Change one thing. Inspect what happens.

  1. Calculate baseline completions, keeping the two denominators separate.
  2. Try both repairs with the same visitors; compare additional completions.
  3. Swap the initial rates and repeat.
  4. Set a rate near 100%; explain how the cap changes the comparison.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Expected signups400 people
Expected completions200 people
Additional completions0 people

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.
01,000
  • Visitors1,000
    Visitors: 1,000Horizontal bar from zero to 1,000, on the shared zero to 1,000 numeric axis.
  • Signups400
    Signups: 400Horizontal bar from zero to 400, on the shared zero to 1,000 numeric axis.
  • Completions200
    Completions: 200Horizontal bar from zero to 200, on the shared zero to 1,000 numeric axis.

Follow the calculation

  1. 1000 visitors × 40% = 400 expected signups.
  2. 400 signups × 50% = 200 expected completions.
  3. Baseline: 200 completions. Change: 0.
  4. The selected repair adds 10 percentage points to one rate, capped at 100%; visitors and the other rate stay fixed.

Compare the same-sized rate changes at different stages. The stage with the lower original rate can offer more additional completions in this model.

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

Where should the team improve?

Synthetic course signup funnel. Visitors may sign up, then signed-up people may finish a task. A repair adds 10 percentage points to exactly one stage.

Follow the mechanism

With 1,000 visitors, 40% signup produces 400 signups; 50% of those produces 200 completions.

Raising signup to 50% produces 250 completions. Raising task completion to 60% produces 240. Equal percentage points need not produce equal final outcomes.

These are expected counts under assumed stable rates; fractions of people represent averages over repeated cohorts.

Worked example

1000 visitors × 40% = 400 expected signups.

400 signups × 50% = 200 expected completions.

Baseline: 200 completions. Change: 0.

The selected repair adds 10 percentage points to one rate, capped at 100%; visitors and the other rate stay fixed.

Calculation

Expected completions = visitors × signup rate/100 × completion rate/100.

Try a controlled comparison

  1. Calculate baseline completions, keeping the two denominators separate.

  2. Try both repairs with the same visitors; compare additional completions.

  3. Swap the initial rates and repeat.

  4. Set a rate near 100%; explain how the cap changes the comparison.

What this does not establish

  • Rates and repair effects are invented, not measured causal effects.

  • Implementation cost, repeat visitors and learning quality are omitted.

5 · Apply

Try a fresh case

A new funnel has 600 visitors, 30% signup and 80% completion among signups. How many expected completions result?

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

Prototype a club signup page and observe where volunteers get stuck.

College investigation

Design a randomized comparison with a predefined completion measure.

Workplace investigation

Prepare an improvement proposal that includes implementation cost and a stop rule.

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.