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Learn through experiments

Did opinions change—or respondents?

Can a headline move while every group holds the same views?

Entering midway? Revisit Investigate apparent disagreement for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

Fictional 100-person community: 75% of group A and 25% of group B support a proposal. You control group sizes and response rates, not opinions.

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 what happens when the higher-support group responds less often.

3 · Experiment

Change one thing. Inspect what happens.

  1. Compare population and respondent support at the initial settings.
  2. Make the two response rates equal; explain the result.
  3. Reduce both response rates to zero and interpret the missing estimate.
  4. Write a headline plus a question to ask the survey organizer about recruitment.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Expected respondents40 people
Respondent support50 %
Population support in fixture65 %

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.
020
  • Group A respondents20
    Group A respondents: 20Horizontal bar from zero to 20, on the shared zero to 20 numeric axis.
  • Group B respondents20
    Group B respondents: 20Horizontal bar from zero to 20, on the shared zero to 20 numeric axis.

Follow the calculation

  1. Fictional population: 100 people; group A 80, group B 20.
  2. Within-group support is fixed at 75% in A and 25% in B. Response is assumed unrelated to support within each group.
  3. Expected responses: A 20; B 20. Expected supporters: 20.
  4. Respondent support: 20/40 × 100 = 50.0%.
  5. Fixture population support: 80×0.75 + 20×0.25 = 65%.

Unequal response rates can shift the headline even when nobody changes their view. This fixture reveals population truth; real surveys generally do not.

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

Did opinions change—or respondents?

Fictional 100-person community: 75% of group A and 25% of group B support a proposal. You control group sizes and response rates, not opinions.

Follow the mechanism

Initially A contributes 20 expected respondents and B also contributes 20. Expected supporters are 15 + 5 = 20, so the respondent headline is 50%.

Yet population support is 80 × 75% + 20 × 25% = 65%. Different response rates changed representation.

The example assumes responders and nonresponders have the same opinions within each group. Real nonresponse can violate that assumption too.

Worked example

Fictional population: 100 people; group A 80, group B 20.

Within-group support is fixed at 75% in A and 25% in B. Response is assumed unrelated to support within each group.

Expected responses: A 20; B 20. Expected supporters: 20.

Respondent support: 20/40 × 100 = 50.0%.

Fixture population support: 80×0.75 + 20×0.25 = 65%.

Calculation

Respondent support = (0.75 × A respondents + 0.25 × B respondents) ÷ all respondents × 100.

Try a controlled comparison

  1. Compare population and respondent support at the initial settings.

  2. Make the two response rates equal; explain the result.

  3. Reduce both response rates to zero and interpret the missing estimate.

  4. Write a headline plus a question to ask the survey organizer about recruitment.

What this does not establish

  • Group support is known only because this is a synthetic fixture; no real political opinion is represented.

  • Expected counts omit sampling randomness. Group adjustment alone cannot guarantee an unbiased real poll.

5 · Apply

Try a fresh case

In a different poll, 30 group-A respondents have 80% support and 20 group-B respondents have 30% support. What is combined respondent support, as a percentage?

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

Compare a voluntary classroom poll with a clearly defined invitation list.

College investigation

Simulate sampling variability separately from systematic nonresponse bias.

Workplace investigation

Audit a fictional stakeholder survey before using it to justify a policy.

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.