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Learn through experiments

Who answered the survey?

Can a large survey still give the wrong answer?

1 · Try

Start with a concrete question

An original synthetic campus has 100 commuters and 100 residents. Support for a later opening time is 80% among commuters and 20% among residents. Change invitations and response rates.

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 whether equal invitations are enough when commuters rarely answer.

3 · Experiment

Change one thing. Inspect what happens.

  1. Set invitations to 50% commuters and response to 100%. Check the population answer.
  2. Lower commuter response to 25%, holding invitations fixed. Explain the direction of error.
  3. Find an invitation mix that recovers 50%. Explain why this cancellation does not prove a generally unbiased sampling method.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Population support50 %
Respondent support50 %
Absolute error0 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.
050
  • Population support (%)50
    Population support (%): 50Horizontal bar from zero to 50, on the shared zero to 50 numeric axis.
  • Respondent support (%)50
    Respondent support (%): 50Horizontal bar from zero to 50, on the shared zero to 50 numeric axis.

Follow the calculation

  1. Population: commuters 80/100 support; residents 20/100 support. True support = 100/200 = 50%.
  2. Per 100 invitations: 80 commuters and 20 residents.
  3. Expected responses: 20 commuters + 20 residents (resident response is 100%).
  4. Expected supporters: 16 + 4. Divide by expected responses: 50%.

Compare who was invited with who actually responded. A larger biased survey can preserve the same error.

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

Who answered the survey?

An original synthetic campus has 100 commuters and 100 residents. Support for a later opening time is 80% among commuters and 20% among residents. Change invitations and response rates.

Before you change anything

Predict whether equal invitations are enough when commuters rarely answer.

Follow the mechanism

A population is everyone we want to describe. A sample contains only the people we observe. Here both population groups have the same size.

At 50% invitations and 25% commuter response, 12.5 expected commuter replies and 50 resident replies yield 20/62.5 = 32% support. Fractional people represent expected counts over repeated surveys.

The weighted mean gives each group weight according to its responses. More replies reduce random uncertainty, but do not automatically fix underrepresentation.

Calculate it yourself

Respondent support = expected supporting replies ÷ expected total replies × 100%.

Try a counterexample

  1. Set invitations to 50% commuters and response to 100%. Check the population answer.

  2. Lower commuter response to 25%, holding invitations fixed. Explain the direction of error.

  3. Find an invitation mix that recovers 50%. Explain why this cancellation does not prove a generally unbiased sampling method.

What this model leaves out

  • Exact synthetic group rates are known here. Within each group, response is assumed unrelated to support; real nonrespondents may differ in unknown ways.

  • This is an expectation calculation, not a random sample or a confidence interval.

Take it further

High school: Design a class survey and identify who an online-only invitation might miss.

College: Derive inverse-response weights, then explain which assumptions make them valid.

Working professionals: Draft a customer-feedback sampling plan including nonusers and a plan to investigate nonresponse.

5 · Apply

Try a fresh case

A fresh survey has 30 replies with 60% support and 70 replies with 20% support. What percentage of all replies support the proposal?

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

Design a class survey and identify who an online-only invitation might miss.

College investigation

Derive inverse-response weights, then explain which assumptions make them valid.

Workplace investigation

Draft a customer-feedback sampling plan including nonusers and a plan to investigate nonresponse.

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.