Methods of Sampling

A sample is only useful for inference if it is drawn in a way that gives it a fair chance of representing the population — this is why how a sample is selected matters as much as how many units are in it. The commonly used methods of scientific (probability/random) sampling are:

1. Simple Random Sampling (SRS). Every unit of the population has an equal and independent chance of being selected. In practice this is done either by the lottery method (writing every unit's identity on a slip, mixing them, and drawing the required number) or by using a table of random numbers to pick unit-serial-numbers. Example: to check the quality of a day's production of 1,000 bottles, a firm numbers every bottle 1 to 1,000 and uses a random-number table to pick 40 bottle numbers for inspection — every bottle had an equal chance of being chosen.

2. Stratified Sampling. The population is first divided into non-overlapping, internally homogeneous groups called strata (based on some relevant characteristic — income group, department, region, product line), and a sample is then drawn independently from every stratum, usually in proportion to the stratum's size. Example: a company with 500 employees — 300 in Production, 150 in Sales, 50 in Administration — wants a sample of 100 employees for an opinion survey. It draws 60 from Production, 30 from Sales and 10 from Administration (proportional to each department's share), rather than picking 100 employees purely at random, which could by chance under-represent a small department like Administration.

3. Systematic Sampling. Units are arranged in some order (a list, a production line), a starting point is chosen at random within the first interval, and thereafter every $k$-th unit is selected, where $k = \dfrac{\text{population size}}{\text{sample size}}$. Example: to sample 50 invoices out of 1,000 issued in a month, $k = 1000/50 = 20$; a random start between 1 and 20 (say, 7) is chosen, and then invoice numbers 7, 27, 47, 67, ... are selected. It is quick to apply on any physically or logically ordered list.

4. Cluster Sampling. The population is divided into groups called clusters that are each meant to be a small-scale, heterogeneous version of the whole population (often based on geography), and a random sample of clusters is drawn — every unit within a chosen cluster is then included, while whole other clusters are left out. Example: a bank wants to survey account-holders across a state; instead of listing every account-holder in the state, it randomly selects 20 out of its 200 branches (clusters) and surveys every account-holder at those 20 branches. This is far cheaper than a state-wide SRS because fieldwork is concentrated in a few locations, though it can be somewhat less precise than stratified sampling for the same sample size.

The table below compares the four methods: