Probability Sampling

Its merits. It guarantees representation of every stratum, which simple random sampling does not; it permits comparison between strata; and it is usually more precise for the same size.

Its demerit. It requires knowing the strata in advance and having a frame divided by them.

Legal example, and it is the method most often right in this field. A study of clinic users stratified by sex, because section 12(c) makes every woman entitled and a study that happens to draw mostly men will miss what the entitlement does. Or a study of colleges stratified by whether they are government aided.

Cluster sampling

What it is. The population is divided into clusters, usually geographical; some clusters are selected at random; and all units within the selected clusters are studied.

Its merits. No complete frame of the population is needed, only a frame of clusters; and it is far cheaper to reach a sample concentrated in a few places.

Its demerits. Units within a cluster resemble each other, so a cluster sample carries less information than the same number drawn at random; and precision is lower for the same size.

Legal example. Selecting four settlements at random from a list of thirty in a taluk and surveying every household in the four.

Multi-stage sampling

What it is. Sampling in stages: select districts, then within them select taluks, then within them settlements, then within them households.

Its merits. It makes national or State level work possible without a national frame, and each stage needs a frame only for the level below.

Its demerit. Error accumulates at every stage, and the design becomes hard to analyse.

Legal example. A study of legal services clinics across a State: select districts, then clinics within them, then users within those clinics.

Choosing between them

The practical order for a student. If the population is small, take it all. If a list exists, use systematic. If a group must be reported on separately, stratify. If the population is spread over an area with no list, use clusters.

A worked example

A study of whether users of legal services clinics in one district know what they are entitled to under section 12.

Population. Every person who used a clinic in the district in one year.

The frame. The clinics' registers under regulation 20 of the 2011 Regulations, chapter 600, which is a real and complete frame, which is unusual and should be used when available.

Stratify by clinic type, since a clinic in a jail serves a different population from one in a village, and by sex, since section 12(c) makes the position of women distinctive.

Then systematic within each stratum, taking every kth entry from a random start.

Disproportionate for the jail clinic, taking more than its share so that its users can be reported on separately.

And record the reasoning in the methodology chapter, chapter 1310, because a reader who knows the frame was the registers, that the strata were clinic type and sex, and that the jail stratum was over-sampled deliberately, can judge every figure in the study.

Quick revision

Probability sampling: every unit has a known, non-zero chance of selection, which is what licenses inference and permits sampling error to be estimated.

Simple random: equal chance, drawn by lot or random numbers; needs a complete frame; the standard against which others are judged.

Systematic: every kth from a random start; simple and even; fails if the frame has a periodicity matching k.

Stratified: divide into internally similar strata and sample each; proportionate or disproportionate; guarantees representation and permits comparison; needs the strata known in advance.

Cluster: select clusters at random and take all units within them; needs only a frame of clusters and is cheap; less precise because units within a cluster resemble each other.

Multi-stage: sample in stages; makes wide-area work possible; error accumulates.

Order for a student: census if small; systematic if a list exists; stratify if a group must be reported separately; cluster if spread out with no list.

Test yourself

1. What single property defines probability sampling, and what does it license? That every unit of the population has a known, non-zero probability of being included. It licenses inference from the sample to the population and permits sampling error to be estimated, neither of which is available for any other kind of sample.

2. Explain systematic sampling and name its characteristic risk. Every kth unit is taken from a random start, k being the frame size divided by the sample size. Its characteristic risk is periodicity: if the frame repeats with a cycle matching k the sample is systematically distorted, as taking every seventh court sitting day would select the same weekday each time.

3. When should a researcher stratify, and what is the difference between proportionate and disproportionate stratification? When a group must be represented or reported on separately, for example women in a study of clinic users given that section 12(c) makes every woman entitled. Proportionate stratification draws from each stratum in proportion to its size; disproportionate draws more from a small stratum so that it can be analysed on its own.

4. Why does a cluster sample carry less information than a simple random sample of the same size? Because units within a cluster resemble one another, so each additional unit from the same cluster adds less new information than a unit drawn at random from the whole population would.