Data and sampling
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Statistics is using data to make a decision. You can't check everyone, so you check a slice (the sample) and let it speak for the whole group (the population).
Why it matters
You can't taste the whole pot, so you stir and taste a spoonful. Statistics is learning to stir well.
Every dashboard, survey and experiment is a spoonful. Whether it speaks for the pot depends on how it was taken.
- ProductSurvey only your happiest users and the product will always look great.
- MarketingIs segment a label or a number? It decides the chart and the math.
- Data workBefore any model, check what each column is and how it was collected.
Tennis example
You want the first-serve percentage of every player on tour (the population). You can't chart every match, so you chart 200 (the sample). The sample's number is p hat; the true one is p.
Check yourself
Describe vs infer?
Describe: summarize what you have. Infer: use a sample to speak for the bigger group.A team's average age describes. A poll predicting an election infers.A gym surveys 150 of its 2,400 members. Population and sample?
Population: all 2,400 members. Sample: the 150 surveyed.N = 2,400 and n = 150.Random, stratified, or risk-based?
Random is fair to all, stratified makes every group show up, risk-based oversamples the riskiest.An auditor looks hardest at the largest expense claims.
The trap
The mistake people make most on this one.
A bigger sample fixes randomness, not bias. 10,000 app users who answered a survey say nothing about the ones who ignore surveys. That is a convenience sample.
Formulas
4 formulas and a way to remember them.
- Quantitative or qualitative
- Quantitative: numbers you can average. Qualitative: labels.
- Discrete or continuous
- Discrete: counted. Continuous: measured.
- Univariate or multivariate
- Univariate: one column. Multivariate: several.
- Population and sample
- Population: N, μ, σ, p. Sample: n, , s, p hat.
- Remember it
- A name is a label, a price is a number. All players on tour are the population; your 200 matches, the sample.
Watch and go deeper
3 free videos and pages.
- Crash Course Statistics #10: Sampling Methods and Bias with SurveysSimple random, stratified, cluster and convenience samples, and the biases that creep into surveys. Watch it once. About 12 minutes.
- OpenIntro: Data Basics, observations, variables and data matricesNumerical versus categorical, discrete versus continuous, and ordinal variables, shown on one real data table. About 4 minutes.
- Khan Academy: Sampling methodsDo the Sampling methods practice set and name the method in each question. About 15 minutes.