A sample is useful only when the process that produced it supports the conclusions we want to draw. Random sampling uses a probability mechanism to select observations from a population.

Simple random sampling

In a simple random sample of size $n$, every subset of $n$ population members has the same probability of being selected.

Randomization does not guarantee a perfectly representative sample, but it makes the sampling process analyzable and prevents systematic preference for particular members.

Sources of bias

A convenience sample selects units because they are easy to reach. A self-selected sample lets participation depend on the subjects themselves. Both mechanisms can overrepresent some parts of the population.

Nonresponse bias arises when selected units do not respond and their behavior differs systematically from that of respondents.

Measurement bias arises when the measurement process itself systematically distorts the recorded values.

Sample size and bias are different issues

A larger random sample usually reduces random sampling variability. It does not repair a biased sampling mechanism.

A survey of one million self-selected website visitors can therefore be less informative about a population than a much smaller well-designed random sample.

Sampling design determines which population the data can represent; sample size determines how much random variability remains within that design.