Mathematics/Lessons/Data Collection/Non-random Sampling
Statistics · Data Collection · Year 1

Non-random Sampling

Not every sample needs a sampling frame or a random number generator. Non-random methods trade the guarantee of a known selection chance for speed and low cost — a trade that's sometimes worth making, and sometimes not.

8 min read 4 worked examples

Why "non-random" doesn't mean "unplanned"

A sampling method is non-random if at least one unit in the population has no fixed, statable chance of being selected — often because selection depends on who happens to be available, or on a researcher's own judgement, rather than on chance alone. Both methods on this course are still deliberate, structured processes — they simply can't guarantee every unit an equal, known opportunity.

Quota sampling

The population is first split into groups based on a characteristic (age, gender, occupation, and so on), and a quota — a target number to interview — is set for each group, usually in proportion to that group's size in the population. An interviewer then approaches people, assesses which group each person belongs to, and interviews them if their group's quota isn't yet full. If someone refuses, or their group is already full, the interviewer simply moves on to the next person. The process continues until every quota is filled.

Quota sampling versus stratified sampling

Both methods split the population into groups first — the difference is entirely in the final selection step. Stratified sampling selects randomly within each group; quota sampling lets the interviewer select non-randomly (typically by whoever is available) until the quota is full. This single difference is what makes stratified sampling random and quota sampling not.

Opportunity sampling

Also called convenience sampling, this method simply takes the sample from whoever is available and willing at the time and place the study happens to be carried out — for example, the first 25 people to leave a train station on a given morning. No groups, quotas, or sampling frame are involved at all; it's the simplest sampling method to carry out, and also the most exposed to bias.

The strategy for classifying any method

Ask: "could I state, before sampling begins, the exact probability that a specific named individual ends up in the sample?" If the answer depends on chance and can be calculated in advance, the method is random. If it depends on who happens to turn up, or on a judgement call, it isn't — regardless of how organised or "fair-sounding" the method appears.

Worked example 1

Setting up a quota sample
A market research company wants to interview 120 shoppers at a shopping centre. Census data shows the shopping centre's typical customers are 40% under 30, 35% aged 30–59, and 25% aged 60 or over. Find the quota for each age group, and describe how the interviewer would proceed.
MethodApply the given percentages, then describe the selection process
1
Under 30: $0.40\times 120 = 48$.
40% of the total quota.
2
30–59: $0.35\times 120 = 42$.
35% of the total quota.
3
60 or over: $0.25\times 120 = 30$.
25% of the total quota.
4
The interviewer approaches shoppers, assesses their age group by sight or by asking, and interviews them if that group's quota isn't yet full — continuing until all three quotas (48, 42, 30) are met.
Describes the non-random selection process.
▪ described
Examiner's eye

The calculation ($48$, $42$, $30$) alone isn't the whole method — a full answer must also describe how the interviewer fills each quota, since that non-random final step is what defines quota sampling.

Worked example 2

Identifying opportunity sampling
A student investigating reaction times asks the first 15 people who happen to be in the college canteen at lunchtime to take a simple test. Name this sampling method, and give one disadvantage specific to this scenario.
MethodName the method, then name who it excludes
1
This is opportunity (convenience) sampling — the 15 people are simply whoever happens to be present, with no predetermined chance of selection.
No frame, no quota, purely availability.
2
Disadvantage: students who don't use the canteen at lunchtime (for example, those with a different lesson at that time) are entirely excluded, so the sample may not represent the whole college.
A specific, named source of bias.
▪ identified
Common mistake

"It's not random" is true but too vague for full marks. A strong disadvantage names who is systematically excluded by the time and place of sampling, and links that to why it could bias the specific quantity being measured.

Worked example 3

Comparing quota and opportunity sampling
A charity wants to survey public opinion on a proposed policy. State one advantage of using quota sampling rather than opportunity sampling for this survey.
MethodCompare what each method can and can't guarantee
1
Quota sampling guarantees the sample reflects the population's structure across the chosen characteristics (such as age or gender), because each group's quota is fixed in advance.
Structure is controlled by design.
2
Opportunity sampling gives no such guarantee — the people available at one time and place could easily skew heavily toward one age group or background.
No control over who happens to be present.
3
So for a survey on public opinion, where age and background may well affect the answers, quota sampling is more likely to produce a broadly representative sample.
Direct comparison, in context.
▪ compared
The key insight

Neither non-random method can promise the freedom from bias that a truly random method can — but between the two, quota sampling at least controls for known, chosen characteristics, while opportunity sampling controls for nothing at all.

Worked example 4

When is a non-random method justified? · Challenge
A researcher has one afternoon and a very limited budget to gauge initial reaction to a new product outside a single supermarket. Explain why opportunity sampling might be a reasonable choice here, despite its limitations.
MethodWeigh the practical constraints against what's actually needed
1
With a single afternoon and minimal budget, there's no time or resource to build a sampling frame or set up formal quotas.
Practical constraints rule out more rigorous methods.
2
The goal is described as gauging "initial reaction" — a rough, exploratory read rather than a formal, statistically representative conclusion.
The purpose doesn't demand the reliability a random method would provide.
3
Opportunity sampling is fast, free, and can be carried out immediately, making it proportionate to both the constraints and the modest aim of the research.
Method matched to purpose and resources.
▪ explained
Look deeper

No sampling method is "best" in the abstract — the right choice always balances statistical rigour against time, cost, and how the results will actually be used. A non-random method used knowingly, for an appropriately modest purpose, is a legitimate choice rather than a shortcut.

Common mistake

Don't describe quota sampling as "random within each group" — the whole point is that the final selection is not random; it's whoever the interviewer approaches until the quota is filled. If the final step were genuinely random, the method would be stratified sampling instead.

Check yourself

A radio station wants 60 listeners' opinions and sets quotas of 24 under-25s, 21 aged 25–49, and 15 aged 50+, based on their known audience breakdown. State the name of this sampling method, and explain why it is not a random method.
(Hint: think about how listeners within each age group are actually chosen once the quotas are set.)

Method
1
This is quota sampling.
2
It isn't random because, once the age groups and quotas are set, listeners within each group are selected by whoever is available or willing to respond, not by a method giving every listener a known chance of selection.
The final selection step is non-random.
▪ solved