One town. Three hundred households. One number we want: the average commute. Five different ways of choosing who to ask — and five very different kinds of error. Every method below draws a real sample from the same grid, and every standard error you see is computed exactly from the town itself.
Ashford — 300 households
4 min64 min
Where the estimates land
one sample’s estimatethe town, 34.0 minevery sample this method can produce
All five methods, side by side
Dot = the value the method homes in on. Bar = ±2 standard errors, the ordinary reach of its estimates. A method is good when the dot sits on the dashed line and the bar is short.
Same town, five ways inchoose a method, then draw a sample
60
10 min
Zone gap is how far apart the three zones’ average commutes are. Whatever you set it to, the town’s overall average stays exactly 34.0 minutes — only the shape of the town changes, never the target.
Samples drawn0
This estimate—
Off the truth by—
Centre of the pile—
Spread of the pile—
Exact standard error—
All five estimates are the same arithmetic — add up the sample, divide by how many. The only thing that ever changes is who ended up in the sample. In survey work the design is the whole game; the formula is an afterthought.
Strata and clusters are opposites, and they are the classic mix-up. You take a slice of every stratum, and you want each stratum to be internally alike. You take a few whole clusters, and you want each cluster to be a miniature of the entire population. Same grid, opposite goals.