Sampling: the design is the inference
Introduced| English | Meaning |
|---|---|
| sample/ˈsæmpl/ | A subset of a population selected for observation, measurement or analysis. |
| population/ˌpɒpjʊˈleɪʃn/ | The entire set of individuals, items or outcomes about which a statistical study seeks information. |
| data dictionary/ˈdeɪtə ˈdɪkʃənəri/ | data dictionary |
| simple random sample/ˈsɪmpl ˈrændəm ˈsæmpl/ | simple random sample |
| bias/ˈbaɪəs/ | A systematic tendency for a measurement, estimate or selection process to differ from the true or representative value. |
Where did this number come from?
- Every number in a business report was selected by SOME process. Before you interpret it, ask what was selected, how, and who was missed.
- This lesson is the course's front door: the 40 delivery times, their dictionary, and the designs that would — or would not — let you trust a claim.
Sample, population, dictionary
- The 40 times are a sample 样本; all weekday orders are the population 总体. What the sample can say depends entirely on how it was drawn.
- The data dictionary 数据字典 records each field's meaning, unit and coding:
delivery_min(ratio, minutes, one decimal, 3 missing cases),hour(ordinal),rider_id(nominal). Reading one critically is step zero.
What kind of data is this field?
Classify fields by type and measurement scale, and each design by the claim it supports.
Match each field to its measurement scale.
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Scales decide operations: ratios divide, ordinals rank, nominals only count.
A data dictionary is optional paperwork once the analysis is already written.
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Units, codings and missingness decide whether the analysis computes what it claims - the dictionary is read first, not filed.
Four designs, four claims
- A simple random sample 简单随机样本 gives every order the same chance — unbiased for any question about the population.
- Stratified (20 Saturday + 20 Wednesday) answers comparisons; systematic (every 5th) is cheap but risky if orders cycle; convenience (what the manager saw) answers nothing.
Nimbus wants to know whether weekends run slower than weekdays. Which design answers it?
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The claim compares days, so the sample must represent both. Saturday-only or convenience samples cannot answer it at any size.
A Saturday-only sample of 40 supports which claim?
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The design matches the population sampled: Saturday claims only. Slower-than-weekday needs weekday data; whole-week claims need both in proportion.
Systematic sampling takes every 5th order. Its specific risk is:
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Systematic sampling is fine when the ordering is unrelated to the question, and biased when the interval matches a cycle in the process.
Bias is a property of the design
- Bias 偏差 is systematic error: selection bias (who is reachable), non-response (who answers), survivorship (who remains).
- If the design is biased, 10,000 observations are precisely 10,000 times wrong. Sample size buys precision; only design buys truth.
A convenience sample of 10,000 orders is more trustworthy than a random sample of 40.
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Bias is systematic; size multiplies it. The random 40 estimates the population honestly, within a stated margin; the 10,000 estimates the convenient part precisely and wrongly.
Customers who never answer the feedback survey can be ignored because they produced no data.
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Non-response is itself data: unhappy and very happy customers answer at different rates. The responders are a self-selected sample inside your sample.
Read the missingness
- The 3 missing
delivery_minvalues are not zero minutes, and not random — riders forget the timer more when busy. - The honest report: mean on the 37 complete cases AND the missingness stated. A silent average is a small lie with a decimal point.
Three delivery_min values are missing because riders forgot the timer when busy. The honest report is:
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The missingness is informative (busy runs are slower), so it must be reported; silently averaging or zero-filling biases the mean.
Three sampling slips
- Trusting a big convenience sample. Size multiplies the design's error, it does not dilute it.
- Confusing non-response with absence. The customers who did not answer are data.
- Analysing before the dictionary. Units and codings are where analyses die.
Recap
- The design is the inference; random sampling earns population claims.
- Bias is systematic; sample size cannot cure it.
- The dictionary and the missingness are part of the data.