Sampling Bias Simulator | mysimulator.uk

Sampling method

Sample size 40

Result

Population mean

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Sample mean

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Bias (error)

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Sample n

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How it works

The town holds 400 households split across four neighborhoods, each with its own typical income and its own population share — Downtown is the biggest group and the poorest, Estate Row is the smallest and the richest. A survey never measures everyone; it measures a sample and uses the sample mean to estimate the true population mean. How that sample is drawn determines whether the estimate is trustworthy.

x̄ = (1/n) · Σ xᵢ        (sample mean, i = 1…n)
bias = x̄ − μ            (μ = true population mean)

Random — every household has an equal chance of being picked, regardless of neighborhood. The sample mean scatters around μ but is not systematically off in either direction.
Convenience — the surveyor only knocks on doors near the marker, all inside Downtown. Because Downtown's income differs from the town average, every convenience sample is pulled the same direction — a bias that more interviews cannot fix.
Stratified — the sample is split across neighborhoods in the same proportions as the real population, so each group contributes its fair share and the estimate tracks μ closely even at small n.
Sample size — larger random or stratified samples shrink random scatter around μ, but a larger convenience sample just repeats the same bias more confidently.

Real-world relevance: mall-intercept surveys, online-only polls and volunteer studies are all convenience samples — easy to run, but systematically skewed toward whoever is easiest to reach.

Downtown (55%) Suburbs (22.5%) Uptown (15%) Estate Row (7.5%) Surveyor start point

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