Population and Sample

Definition

The population is the complete set of things you want to learn about; the sample is the subset you actually observe. Statistical inference asks what the sample says about the population, and the answer is only as good as the way the sample was chosen.

In plain terms

A number computed from a sample (a statistic) estimates the corresponding number for the population (a parameter). If the sample is drawn at random, the difference between them is ordinary chance, called sampling variability, and it can be measured. If the sample is selected some other way, there is also bias, and collecting more data does not remove it.

Before sampling, say precisely what the population is: which items, in which period, in which place.

Example

A population of 10,000 listings, sampled at random, 100 at a time. The ratings have a standard deviation of 0.8.

The means differ by chance. The typical size of that wobble, the standard error, is about 0.8 / √100 = 0.08, so a plausible range for the population mean is roughly the sample mean ± 0.16. A sample taken as “the 100 most reviewed listings” would not have this property: its error is mostly bias.

Common misunderstandings

• “A bigger sample is always better.” It reduces chance error only; a biased selection stays biased.
• “A sample must be a fixed percentage of the population.” Precision depends mainly on the sample size, not on its share of the population.
• “If I have all the data there is no sampling.” All the data for one period is still one sample of what could have happened.