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Learn through experiments

When two improvements cancel each other

Is the effect of one intervention independent of the other?

Entering midway? Revisit Same people, different order for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

Original synthetic scenario. Two fictional process changes A and B alter a 40-point baseline. You control the individual effects and their interaction.

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?

With A +6, B +4 and interaction −8, will adding A help when B is already present?

3 · Experiment

Change one thing. Inspect what happens.

  1. Compare neither, A only, B only and both; compute the two A contrasts.
  2. Set interaction to zero and describe the additive case.
  3. Find an interaction for which A helps alone but harms when B is present.
  4. Specify a four-condition experiment, a measured outcome, and controls that would distinguish interaction from unequal starting groups.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
A effect with B absent6 points
A effect with B present-2 points
Interaction-8 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.
046
  • Neither (points)40
    Neither (points): 40Horizontal bar from zero to 40, on the shared zero to 46 numeric axis.
  • A only (points)46
    A only (points): 46Horizontal bar from zero to 46, on the shared zero to 46 numeric axis.
  • B only (points)44
    B only (points): 44Horizontal bar from zero to 44, on the shared zero to 46 numeric axis.
  • A and B (points)42
    A and B (points): 42Horizontal bar from zero to 42, on the shared zero to 46 numeric axis.

Follow the calculation

  1. Neither intervention: 40 points.
  2. A only: 40 + 6 = 46; B only: 40 + 4 = 44.
  3. Both: 40 + 6 + 4 + (-8) = 42.
  4. A contrast without B = 46 − 40 = 6. With B = 42 − 44 = -2.
  5. Difference between contrasts = -2 − (6) = -8.

A one-factor trial at a single B setting cannot reveal how A behaves when B changes. A factorial design observes all four combinations.

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

What the experiment explains

Original synthetic scenario. Two fictional process changes A and B alter a 40-point baseline. You control the individual effects and their interaction.

An interaction means the effect of A depends on the setting of B. It does not mean the two effects are merely both present.

At defaults the four scores are 40, 46, 44 and 42. A adds 6 without B but changes the score by 42 − 44 = −2 with B. The difference between those effects is −8.

Testing changes one at a time only at the baseline misses this reversal. A factorial design compares all combinations, with assignment and measurement controls needed in a real experiment.

Read the relationship

Score = 40 + aA + bB + iAB. A and B are 0/1 indicators; a and b are individual effects, i is the interaction, all in points.

Inspect the evidence

The numerical trace is recalculated from your current settings. Compare a controlled pair of trials before changing several inputs together. Inspect intermediate quantities as well as final metrics; state which assumptions make the comparison meaningful.

Boundaries of the model

  • Cell means are exact and deterministic; no sample-size or significance claim.
  • Only two binary factors and one outcome are modeled.

Return to the scientific reasoning and experimental design course and project to connect this mechanism to the broader investigation.

5 · Apply

Try a fresh case

Fresh four-cell results: neither 20, A only 27, B only 25, both 29. What is the interaction in 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 safe paper-design experiment with two factors and all four conditions.

College investigation

Implement a factorial regression and evaluate uncertainty with independently sampled replicates.

Workplace investigation

Propose a process experiment that can detect whether two policy changes interfere.

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.