02 Section A, Key question 2 - Probability sampling (part 2)

Population, frame and sample

Sampling begins by deciding whose experiences the research aims to describe.

The target population is the whole group to which the research question refers. A sample is a smaller group selected for research. Interviewing a sample usually takes less time and money than interviewing everyone, but the selection process affects whose experiences appear in the findings.

Consider an invented teaching example: a researcher wants to investigate insecure work among all 600 adults currently working for Riverford Care, including agency workers. The target population is these 600 workers. A verified register with one entry for each worker is the sampling frame. Selecting 60 entries produces the selected sample; if only 42 agree to participate, those 42 form the responding sample. Selection and participation are different stages.

The researcher must first check what the register contains. If Riverford's payroll lists only directly employed staff, agency workers may be missing. This is coverage error: the frame does not match the target population. Randomly choosing names from that payroll cannot include missing workers. If agency workers face different employment conditions, the results may misrepresent insecurity across the workforce. Updating the register or limiting the stated population honestly is necessary; a larger draw from the same incomplete list does not solve the omission.

Probability sampling uses a chance procedure under which each unit covered by the design has a known, non-zero probability of selection. The three procedures in this lesson all use random selection, although they organise it differently. Equal chances are a feature of simple random sampling, but probability designs can deliberately use unequal known chances. Statistics Canada explains probability selection.

The unit also matters. A random sample of addresses is not automatically a random sample of individuals: several adults may share one address. A household study needs a rule for selecting people within selected households if it intends to make probability-based claims about individuals.

Simple random selection

Simple random sampling chooses the sample by chance from the whole sampling frame.

In simple random sampling, each frame member has the same chance of inclusion, and every possible set of the chosen size has the same chance of being selected. A well-mixed lottery can do this, as can a suitable random-number generator. The researcher does not choose people because they seem typical, cooperative or easy to contact.

For the invented Riverford study, assume the register has now been checked and includes all 600 current workers. To select 60:

1. Give every worker a unique number from 1 to 600.
2. Use a random-number generator to select 60 distinct numbers from that range. Select without replacement, so nobody occupies two places in the sample.
3. Match each number to its worker and invite those workers. A possible selection might include 12, 38, 149, 277, 406 and 589; these are illustrative entries, not reported fieldwork.

Each worker's selection probability is 60 out of 600, or one in ten. A refusals policy should preserve the planned selection procedure: casually substituting the nearest willing colleague changes the design. Researchers can plan random reserve selections, report non-response and explain any adjustments.

The main strength is removing personal discretion from selection. A manager cannot simply nominate workers expected to praise the organisation. However, a chance draw may still contain very few members of a small subgroup. It does not guarantee the exact workforce proportions of contract type, age or ethnicity. It also needs a suitable frame, and contacting widely scattered selected people can be expensive.

Opportunity sampling means recruiting whoever is conveniently available. Approaching workers who happen to be in the staff room is opportunity selection, even if the researcher informally says they picked people “at random”. Night workers or those too busy to take breaks may be excluded. Everyday unpredictability is not a procedure with known selection chances.

Systematic random selection

Systematic sampling selects entries at a fixed interval after choosing a random starting position.

In the invented Riverford study, the frame contains 600 workers and the desired sample is 60. Divide 600 by 60 to obtain an interval of 10. Randomly choose a start from positions 1 to 10. If the start is 7, select positions 7, 17, 27 and so on through 597. This yields 60 selected workers. Positions are used, rather than assuming staff identification numbers run consecutively.

Only the start needs to be drawn randomly; the rest follow the rule. In this exact example, every entry belongs to one of the ten possible start sequences and has a one-in-ten selection chance. However, it is not a simple random sample: two adjacent entries cannot both be selected by this interval rule. Statistics Canada's methodological guide distinguishes these designs.

The method is quick to administer and spreads selections along a list. Its weakness depends on the list's ordering. Imagine an invented alternative register arranged in repeating teams of ten, with each supervisor always in the first position. An interval of ten would select the same position in every team. One random start would select only supervisors; the other starts would select none. Individual selection chances may be equal, yet the realised sample may give a poor account of differences in authority and insecurity. This is the danger of periodicity, a repeating pattern that coincides with the interval.

A researcher should inspect the ordering and avoid such cycles, for example by randomising the list before applying the interval. Choosing the first willing worker and then every tenth willing worker would alter the frame and selection rule; it is not the procedure taught here. Practical convenience must be evaluated alongside the social pattern in the list.

Stratified random selection

Stratified sampling builds relevant group membership into the sample design before selecting people.

A stratum is a subgroup used in the sampling design; strata is the plural. In stratified random sampling, the researcher divides the frame into non-overlapping groups and selects randomly within each. Every member must belong to an appropriate stratum, and the groups together must cover the population included in the design. The researcher therefore needs accurate group information in advance.

In the invented Riverford study, contract type is relevant because the question concerns insecure work. The complete 600-worker register contains these groups. A proportionate sample of 60 takes one tenth of each:

The allocation is only the first step. The researcher separately numbers the members of each stratum, randomly draws 30 distinct permanent workers, 20 fixed-term workers and 10 agency workers, then invites those selected. Merely collecting these totals from whichever workers are easiest to find would not complete stratified random selection.

Compared with a simple random draw, this design ensures the selected sample contains the planned numbers from each contract group. It supports comparison and can improve precision when the stratifying characteristic is relevant to the outcome. But it requires a more detailed frame, and exact contract proportions do not guarantee balance on every other characteristic. Non-response can also change the achieved proportions. ONS explains the role of stratification.