Random and systematic sampling | AQA A-Level Psychology Revision

For 7182 specification, first teach in September 2025

AQA A-Level Psychology | Free Revision Notes

Estimated study time: 45 minutes

These Random and systematic sampling A-Level Psychology revision notes explain two methods psychologists use to select participants from a target population. You will learn how researchers use sampling frames, random selection and fixed sampling intervals. You will also evaluate whether each method reduces researcher bias, produces a representative sample and supports generalisation. These methods build directly on the distinction between target populations and participating groups 

Learning Objectives 🎯

By the end of this revision page, you should be able to:

• Explain how random sampling is carried out.

• Explain how systematic sampling is carried out.

• Distinguish random sampling from systematic sampling.

• Evaluate the strengths and limitations of each method.

• Apply both methods to unfamiliar research scenarios.

• Explain how each method may affect bias and generalisation.

Revision Notes 📚

Random and systematic sampling A-Level Psychology revision overview

Sampling is the process used to select participants from a target population.

The AQA specification identifies five sampling methods:

• Random sampling.

• Systematic sampling.

• Stratified sampling.

• Opportunity sampling.

• Volunteer sampling.

Random and systematic sampling both use planned selection procedures.

They differ in how people are chosen:

Random sampling	Systematic sampling
Selection is determined by chance	Selection follows a fixed interval
Each population member should have an equal chance of selection	Every nth person is selected from an ordered list
Random numbers or another chance method are used	A sampling interval and starting point are used
Each selection is based on the random procedure	After the start, selection is determined by position on the list

Neither method guarantees a perfectly representative sample.

Their success depends on:

• The quality of the sampling frame.

• Whether selected people agree to participate.

• The size of the sample.

• How the target population is organised.

• Whether the final participants reflect relevant population characteristics.

Sampling frames

What is a sampling frame?

A sampling frame is an organised list of the members of the target population from which a sample can be selected.

Examples include:

• A school register.

• A list of employees.

• A membership database.

• A list of patients using a service.

• An electoral register.

• A university enrolment list.

For example:

A researcher wants to select 40 students from all 800 students attending a college.

The college register could be used as the sampling frame.

Why is a sampling frame needed?

Random and systematic sampling require researchers to identify the people who could be selected.

A sampling frame allows the researcher to:

• Identify eligible population members.

• Assign numbers to individuals.

• Apply a consistent selection procedure.

• Check who has been selected.

• Avoid repeatedly selecting the same person.

• Describe the procedure clearly enough for replication.

Without a suitable list, genuine random or systematic selection may be difficult.

A sampling frame should match the population

The sampling frame should include the members of the target population and exclude people outside it.

Suppose the target population is:

All Year 12 students attending Westbridge College.

A suitable sampling frame would be:

The current Year 12 student register.

An unsuitable sampling frame might be:

The list of students attending an optional revision session.

The second list excludes Year 12 students who do not attend the session.

Incomplete sampling frames

A sampling frame may be incomplete.

It might exclude:

• Newly enrolled members.

• People whose details have not been updated.

• People who are temporarily absent.

• People without registered contact information.

• Members incorrectly removed from the list.

If excluded people differ from those included, the resulting sample may be biased.

Out-of-date sampling frames

A list may contain people who are no longer members of the target population.

For example, a staff list might include employees who have left the organisation.

This creates practical problems because:

• Selected people may be ineligible.

• Replacement participants may be required.

• The final sample may not reflect the current population.

• Additional time is needed to verify the list.

Sampling frames and generalisation

Even an accurately selected sample cannot represent people who were absent from the sampling frame.

For example, a random sample selected from one college register may represent that college reasonably well.

It does not automatically represent:

• Students at other colleges.

• Students studying different qualifications.

• Young people who are not in education.

• All teenagers in the UK.

The scope of generalisation should match the target population and sampling frame.

Random sampling

What is random sampling?

Random sampling is a method in which every member of the target population has an equal chance of being selected.

Selection is determined by chance rather than by the researcher’s personal choice.

A random sample normally requires:

1. A complete sampling frame.

2. A way of identifying every population member.

3. A chance procedure.

4. Selection of the required number of participants.

Random does not mean unplanned

In everyday speech, random can mean careless or without a clear method.

In research, random sampling is a planned procedure.

The researcher must decide:

• Who belongs to the target population.

• Which list will be used.

• How many participants are required.

• Which random process will select them.

• How non-response will be handled.

The outcome is produced by chance, but the procedure is organised.

Random sampling procedure

A psychologist could carry out random sampling using these steps.

Step 1: define the target population

For example:

All 600 students attending a sixth-form college.

Step 2: obtain a sampling frame

The researcher obtains a current list of all 600 students.

Step 3: assign each person a number

Students are numbered from 001 to 600.

Step 4: use a random selection method

The researcher uses:

• A random-number generator.

• A random-number table.

• Numbered slips selected from a container.

• Another process in which chance determines the selection.

Step 5: select the required sample

If 50 participants are needed, the researcher selects 50 different eligible numbers.

Step 6: contact the selected people

The people connected with the selected numbers are invited to participate.

Those who consent form the final sample.

Worked example of random sampling

A school has 400 Year 12 students.

A psychologist requires a sample of 40.

The researcher:

1. Obtains the Year 12 register.

2. Numbers students from 001 to 400.

3. Uses a random-number generator to produce 40 different numbers.

4. Contacts the students represented by those numbers.

5. Provides information about the research and requests consent.

Each student has an equal chance of being selected by the random procedure.

Random-number generators

A random-number generator produces numbers through a chance process.

The researcher should set an appropriate range.

For example:

• Lowest possible number: 1.

• Highest possible number: 400.

• Number of selections required: 40.

Repeated numbers should not lead to the same person being selected twice for one sample.

The researcher should follow a predetermined rule for dealing with duplicates or ineligible entries.

Random-number tables

A random-number table contains digits arranged without an intentional pattern.

The researcher might:

1. Choose a starting position without selecting a preferred area.

2. Read numbers of the required length.

3. Accept numbers that fall within the population range.

4. Ignore numbers outside the range.

5. Ignore duplicate selections.

6. Continue until the sample is complete.

The researcher should report the procedure clearly.

Lottery method

A small population may be sampled using a lottery method.

The researcher:

1. Writes each population member’s number on an identical slip.

2. Places all slips in the same container.

3. Mixes them thoroughly.

4. Selects the required number without looking.

The slips should be identical so that:

• No number is easier to identify.

• Size or texture cannot influence selection.

• Every slip has an equal chance of being chosen.

This becomes impractical with very large populations.

Equal chance of selection

The defining principle is that each population member has the same chance of being selected.

The researcher should not:

• Exclude inconvenient people from the list.

• Replace selected people with preferred participants.

• Choose only people who appear cooperative.

• Select friends or familiar individuals.

• Ignore valid random selections without a predetermined reason.

These actions would introduce researcher choice and undermine the random procedure.

Random selection and consent

Random selection does not force anyone to participate.

The procedure identifies who will be invited.

Selected people still have the right to:

• Receive relevant information.

• Decide whether to participate.

• Refuse the invitation.

• Withdraw according to the study’s procedure.

The final sample may therefore differ from the original random selection if some people decline.

Strengths of random sampling

Strength: reduced researcher selection bias

Random sampling reduces the researcher’s personal influence over who is selected.

The researcher cannot deliberately choose people who:

• Appear helpful.

• Are easy to contact.

• Seem likely to support the hypothesis.

• Have particular visible characteristics.

• Are personally familiar.

This makes selection more objective.

Strength: equal opportunity for population members

Each person listed on the sampling frame has an equal chance of selection.

This means that the method does not intentionally favour one member over another.

For example, students who:

• Attend different subjects.

• Have different attainment levels.

• Have different attitudes.

• Are personally unknown to the researcher.

can all be selected.

Strength: reduced systematic bias

Because selection is based on chance, the researcher is less likely to repeatedly include one convenient type of person.

This can reduce sampling bias compared with selecting only:

• Nearby people.

• Available people.

• Volunteers.

• Members of one convenient group.

However, chance can still produce an uneven sample.

Strength: possible representativeness

A random sample may reflect a range of characteristics found in the target population.

For example, it may include people from:

• Different age groups.

• Different courses.

• Different departments.

• Different levels of attainment.

• Different backgrounds.

This may support generalisation to the target population.

The word may is important. Random selection does not guarantee representativeness.

Strength: replicable procedure

Researchers can describe:

• The sampling frame.

• The numbering system.

• The random-selection process.

• The sample size.

• Rules for duplicates and non-response.

Another researcher could repeat the same general procedure.

They would probably obtain different individuals because selection is random, but the method itself is replicable.

Strength: transparent selection

A documented random procedure allows other researchers to see how the sample was selected.

This makes it easier to evaluate whether:

• Everyone was eligible.

• Chance genuinely determined selection.

• Certain people were excluded.

• Replacement rules introduced bias.

Limitations of random sampling

Limitation: a complete sampling frame is required

Random sampling usually requires a full and accurate list of the target population.

This may be difficult when studying:

• A very large population.

• People whose identities are unknown.

• Members of a private group.

• People experiencing an uncommon difficulty.

• A population spread across many locations.

• People without accessible contact details.

Without a complete sampling frame, some population members have no chance of selection.

Limitation: the sampling frame may be biased

A random process cannot correct problems in the original list.

Suppose a researcher randomly selects participants from a list of people registered with an online revision platform.

The sample may be random among registered users.

However, it excludes students who:

• Do not use that platform.

• Lack internet access.

• Use other revision resources.

• Have not created an account.

The sample may therefore be biased relative to all students.

Limitation: chance may produce an unrepresentative sample

A random process can select an uneven group, particularly when the sample is small.

For example, a college population may contain students from several subject areas, but a random sample could contain an unusually high number of Psychology students.

This does not mean the random procedure failed.

It means that chance does not guarantee that population characteristics appear in the correct proportions.

Researchers seeking proportionate representation may use matching population subgroups within a sample.

Limitation: non-response

Some randomly selected people may refuse or fail to participate.

People who respond may differ from those who do not.

For example, participants may be more:

• Interested in psychology.

• Available.

• Confident.

• Comfortable with the topic.

• Motivated by a reward.

The final sample may therefore become less representative than the original random selection.

Limitation: replacing non-responders may introduce bias

Researchers need a predetermined procedure for dealing with non-response.

Poor procedure:

Replace each person who refuses with someone the researcher finds convenient.

This introduces researcher choice.

A better procedure might involve selecting replacements through the same random process.

Even then, repeated non-response by particular population groups may still bias the final sample.

Limitation: time and resources

Researchers may need to:

• Obtain permission to access the population list.

• Check whether the list is current.

• Assign identification numbers.

• Generate selections.

• Contact people individually.

• Follow up non-responses.

• Select replacements.

This can be slower than recruiting people who are immediately available.

Limitation: confidentiality and access

A sampling frame may contain personal information.

Researchers must handle:

• Names.

• Contact details.

• Institutional records.

• Membership information.

Access may be restricted for ethical, legal or organisational reasons.

The researcher should collect and retain only the information required for the study.

Limitation: selected participants may be widely dispersed

A random sample from a broad population may select participants from many locations.

This could increase:

• Travel.

• Cost.

• Scheduling difficulty.

• Differences in testing environments.

Researchers may need online procedures or several research locations.

Limitation: random sampling may be impractical for rare populations

When the target population is small or difficult to identify, researchers may not have a complete list.

For example, people with a rare experience may be reached only through:

• Specialist organisations.

• Support groups.

• Professional referrals.

• Public advertisements.

A different sampling method may be more practical, although generalisation would remain limited.

Systematic sampling

What is systematic sampling?

Systematic sampling is a method in which researchers select every nth member of an ordered sampling frame.

The researcher uses a fixed sampling interval.

For example:

Every tenth person on a college register is selected.

The method normally involves:

1. A sampling frame.

2. A required sample size.

3. A calculated sampling interval.

4. A starting point.

5. Selection of every nth member.

What does “nth” mean?

The expression every nth person means selection at a regular interval.

Examples include:

• Every 5th person.

• Every 10th person.

• Every 20th person.

• Every 50th record.

The value of n depends on:

• Population size.

• Required sample size.

Calculating the sampling interval

A simple sampling interval can be calculated using:

For example:

• Population size: 600.

• Required sample: 60.

600÷60=10

The researcher selects every tenth person.

Worked systematic-sampling example

A college has 1,000 students.

A psychologist requires a sample of 100.

Step 1: calculate the interval

1,000÷100=10

The sampling interval is 10.

Step 2: select a starting point

The researcher selects a starting number between 1 and 10.

Suppose the starting number is 6.

Step 3: apply the interval

The researcher selects:

• 6th person.

• 16th person.

• 26th person.

• 36th person.

The process continues until 100 people have been selected.

Random starting point

Using a random starting point can reduce researcher influence.

If the interval is 10, the researcher can randomly select one number from 1 to 10.

Once the starting point is chosen, the remaining selections follow the fixed interval.

For example:

• Random start: 4.

• Interval: 10.

• Selections: 4, 14, 24, 34 and so on.

Why the starting point matters

Suppose the researcher always begins with the first person on the list.

That person’s position may be connected with the way the list was organised.

A random start reduces the possibility that the researcher chooses a favourable starting position.

However, it does not remove every possible source of systematic bias.

Ordered sampling frame

Systematic sampling requires a list arranged in some order.

The order might be:

• Alphabetical.

• Numerical.

• By date of enrolment.

• By employee number.

• By class register.

• By arrival time.

The researcher should consider whether the ordering is connected with the characteristic being studied.

Systematic sampling without a written list

A systematic procedure may sometimes select people passing a particular point.

For example:

Every tenth customer entering a shop is invited to participate.

The researcher should still define:

• The starting point.

• The counting rule.

• What happens if someone refuses.

• The recruitment time.

• The location.

• Whether the same person could pass more than once.

This samples people present at that location and time, not necessarily the whole target population.

Consistency of selection

Once the systematic rule begins, the researcher should apply it consistently.

They should not:

• Skip people who appear uncooperative.

• Select someone else because the nth person is busy.

• Change the interval halfway through.

• Restart counting whenever convenient.

• Include additional preferred participants.

Changing the rule introduces researcher bias.

Strengths of systematic sampling

Strength: straightforward procedure

Once the interval and starting point are established, selection is easy to follow.

The researcher does not need to generate a new random number for every participant.

This can make systematic sampling:

• Quick.

• Organised.

• Easy to check.

• Suitable for large lists.

Strength: reduced researcher choice

The fixed interval determines who is selected.

The researcher cannot freely choose the people they prefer.

For example, if every 20th employee is required, the researcher should include the selected employee rather than a more convenient colleague.

This reduces personal selection bias.

Strength: sample is spread across the frame

Systematic sampling usually selects members from different positions throughout the list.

For example, selecting every tenth student spreads selection across the register rather than taking the first 50 names.

This may provide wider coverage of the sampling frame.

However, coverage across a list does not guarantee representation of important population groups.

Strength: efficient for large populations

Systematic sampling can be practical when:

• The population list is long.

• A regular interval can be calculated.

• The researcher needs a manageable proportion of the population.

• Randomly generating hundreds of separate selections would be inconvenient.

Strength: transparent and replicable

Researchers can report:

• Population size.

• Required sample size.

• Sampling interval.

• Starting point.

• Order of the list.

• Rules for non-response.

Another researcher can follow the same procedure.

Strength: can use a random start

A random starting point reduces the researcher’s influence over where selection begins.

This combines:

• Chance for the first position.

• A fixed systematic rule for later selections.

The procedure is more objective than choosing a convenient starting person.

Limitations of systematic sampling

Limitation: a suitable sampling frame is usually required

Like random sampling, systematic sampling normally depends on an organised list.

If the list is:

• Incomplete.

• Out of date.

• Restricted to one group.

• Missing relevant people.

• Filled with ineligible records.

the final sample may be biased.

Limitation: order effects in the sampling frame

The order of the list may influence who is selected.

Suppose a college register is organised by tutor group and each tutor group contains 20 students.

Selecting every twentieth person could repeatedly select students occupying the same position within each tutor group.

If position is connected with another characteristic, this may produce bias.

Limitation: periodic patterns

A periodic pattern occurs when the organisation of the list repeats at regular intervals.

If the sampling interval matches this pattern, one type of person may be selected repeatedly.

For example, a work rota might repeat:

• Day worker.

• Day worker.

• Night worker.

• Day worker.

• Day worker.

• Night worker.

Selecting every third person could produce a sample containing only night workers.

The method would be systematic but unrepresentative.

Limitation: not every selection is independently random

After the starting point has been chosen, later selections are determined by the interval.

For example, with a starting point of 6 and an interval of 10:

• 6 is selected.

• 16, 26, 36 and later positions must follow.

Chance does not independently decide whether each remaining person is selected.

This distinguishes systematic sampling from random sampling.

Limitation: chance imbalance can still occur

Systematic sampling may select an unrepresentative group even without an obvious periodic pattern.

For example, the selected positions may happen to contain more students from one subject or age group.

A fixed interval does not ensure that relevant groups appear in population proportions.

Limitation: non-response

Selected people may refuse to participate.

Researchers must decide whether to:

• Leave the position unfilled.

• Select the next person.

• Continue to the next interval.

• Use a separately specified replacement rule.

Changing to the next available person may alter the selection process and introduce bias.

The rule should be decided before recruitment begins.

Limitation: starting-point bias

If the researcher chooses the starting point deliberately, they may influence who is included.

For example, beginning at a convenient place on the list could exclude earlier population members systematically.

A random start can reduce this problem.

Limitation: the interval may not divide evenly

Suppose:

• Population size: 950.

• Required sample: 100.

950÷100=9.5

The researcher needs a clear procedure for managing the non-whole-number interval.

Possible approaches must be planned carefully so that selection remains systematic.

In an examination question, use the procedure described in the scenario rather than inventing a different rule unnecessarily.

Limitation: practical access remains necessary

Being selected from a list does not mean that the person:

• Can be contacted.

• Is available.

• Meets all eligibility requirements.

• Will consent.

• Can attend the research session.

Systematic selection may therefore produce a final sample that differs from the planned one.

Random and systematic sampling compared

Feature	Random sampling	Systematic sampling
Main principle	Every population member has an equal chance of selection	Every nth population member is selected
Sampling frame	Usually required	Usually required
Starting point	Selection begins through a random process	A random or predetermined start may be used
Later selections	Each determined through the chance procedure	Determined by the fixed interval
Researcher choice	Reduced	Reduced once the rule is fixed
Ease of use	May require many random selections	Usually quicker for a long list
Risk from list order	Usually lower	May be affected by periodic patterns
Representativeness	Possible but not guaranteed	Possible but not guaranteed
Main practical problem	Obtaining and processing a complete frame	Creating a suitable interval and checking list order
Replicability	Procedure can be repeated	Procedure can be repeated clearly

Central distinction

A strong distinction might state:

Random sampling uses a chance procedure so that every member of the target population has an equal chance of selection. Systematic sampling selects every nth member from an ordered sampling frame, usually after choosing a starting point.

Random selection is not the same as systematic selection

In random sampling, knowing that one person has been selected does not determine the next selected position.

In systematic sampling, once the start and interval are known, the later positions can be predicted.

For example:

• Start: 7.

• Interval: 15.

• Later selections: 22, 37, 52 and so on.

Similarities between the methods

Both methods:

• Require a clearly defined population.

• Usually need a sampling frame.

• Use planned selection procedures.

• Reduce free researcher choice.

• May be affected by non-response.

• Can still produce unrepresentative samples.

• Support generalisation only when the final sample represents the target population.

Representativeness and generalisation

Neither method guarantees representativeness

A common mistake is to assume that random or systematic sampling automatically creates a representative sample.

Representativeness depends on:

• The sampling frame.

• The population’s variation.

• Sample size.

• Chance.

• List organisation.

• Non-response.

• Whether selected people actually participate.

A method can reduce bias without eliminating it.

Random sampling and generalisation

A random sample may support generalisation because researcher choice is reduced and all listed population members can be selected.

However, generalisation may remain limited if:

• The sample is small.

• The frame excludes relevant groups.

• Many selected people refuse.

• The population is highly varied.

• Chance produces an imbalanced sample.

Systematic sampling and generalisation

A systematic sample may support generalisation when:

• The frame represents the target population.

• The list does not contain a problematic periodic pattern.

• The start is selected appropriately.

• The interval spreads selection across the frame.

• Non-response is limited.

Generalisation may be weakened when the list’s organisation causes particular groups to be repeatedly selected or missed.

Sample size

A larger sample may contain more of the population’s variation.

However:

• A large sample selected from an incomplete frame remains biased.

• A large systematic sample can still follow a problematic pattern.

• A large number of volunteers is still self-selected.

• Quality of selection matters as well as quantity.

Population diversity

Random or systematic sampling may be less likely to reproduce every relevant subgroup when:

• The population contains many distinct groups.

• Some groups are very small.

• The sample is relatively small.

• Group membership is not evenly distributed through the sampling frame.

A stratified sample may be more appropriate when representation of identified groups is essential.

Bias in random and systematic sampling

Researcher bias

Both methods reduce the opportunity for researchers to select participants according to personal preference.

However, researchers still make decisions about:

• Population definition.

• Choice of sampling frame.

• Sample size.

• Starting procedure.

• Replacement rules.

• Eligibility criteria.

These decisions can influence the final sample.

Frame bias

Frame bias occurs when the sampling frame does not represent the target population accurately.

For example:

• Target population: all adults living in a town.

• Sampling frame: people registered at one leisure centre.

A random or systematic sample from the leisure-centre list may be unbiased for registered members.

It is not representative of all adults in the town.

Non-response bias

Non-response bias occurs when people who participate differ systematically from selected people who do not.

For example, people experiencing severe stress may be:

• Especially motivated to participate.

• Too overwhelmed to participate.

Either pattern could affect the final findings.

Researchers should report:

• How many people were selected.

• How many responded.

• How replacements were chosen.

Exclusion bias

A study may exclude people who:

• Cannot attend at a particular time.

• Do not speak the language used in the materials.

• Lack internet access.

• Need adjustments that were not provided.

• Cannot be contacted using the available information.

If these people belong to the target population, their exclusion may reduce generalisability.

Random sampling compared with stratified sampling

Random sampling gives population members an equal chance of selection.

It does not deliberately ensure that every subgroup appears in the correct proportion.

Stratified sampling:

• Identifies relevant population groups.

• Calculates how many participants are needed from each group.

• Selects participants within those groups.

For example, if a college population is:

• 60% Year 12.

• 40% Year 13.

a stratified sample of 100 would include:

• 60 Year 12 students.

• 40 Year 13 students.

A random sample of 100 might produce those proportions, but it is not guaranteed.

Random and systematic sampling compared with opportunity and volunteer sampling

Random and systematic sampling use planned procedures based on a population frame or ordered sequence.

Opportunity sampling selects people who are available.

Volunteer sampling recruits people who respond to an invitation.

Random and systematic methods may:

• Reduce researcher choice.

• Provide broader population coverage.

• Offer stronger support for generalisation.

Opportunity and volunteer methods may be:

• Faster.

• Cheaper.

• Easier to organise.

• Possible without a complete sampling frame.

Their different sources of bias are explored in convenient and self-selected recruitment.

Random selection and random allocation

Random selection

Random selection determines who enters the sample.

Example:

Forty students are randomly chosen from the college register.

Its purpose is to reduce sampling bias.

Random allocation

Random allocation determines which experimental condition sampled participants enter.

Example:

The 40 selected students are randomly placed in either the music or silence condition.

Its purpose is to distribute participant variables across conditions.

The distinction is developed further in random allocation and other control techniques.

Why the distinction matters

A researcher might:

• Recruit an opportunity sample.

• Randomly allocate those participants to conditions.

The experimental groups may be balanced, but the original sample is still an opportunity sample.

Alternatively, the researcher might:

• Randomly select the sample.

• Place all participants through a repeated-measures procedure.

Random sampling does not determine the experimental design.

The designs are covered in allocation through repeated measures, independent groups and matched pairs.

Designing a random sample

Step 1: define the population

State the exact group of interest.

Example:

All 750 employees working for the company in August.

Step 2: obtain an appropriate frame

Use a current list containing all eligible employees.

Step 3: assign unique identifiers

Each employee receives one number from 001 to 750.

Step 4: decide the sample size

The researcher determines how many people are required.

Step 5: use a genuine chance procedure

A random-number generator or table selects the required numbers.

Step 6: apply rules consistently

The researcher follows predetermined rules for:

• Duplicate numbers.

• Ineligible records.

• Non-response.

• Withdrawal before data collection.

Step 7: report the procedure

The research report should explain how each stage was completed.

Designing a systematic sample

Step 1: define the population

Example:

All 900 students currently enrolled at a college.

Step 2: obtain an ordered sampling frame

Use an accurate student register.

Step 3: decide the required sample

Suppose 90 students are needed.

Step 4: calculate the interval

900÷90=10

Select every tenth student.

Step 5: choose a start

Randomly select a starting number from 1 to 10.

Suppose the starting number is 8.

Step 6: follow the interval

Select:

• 8

• 18

• 28

• 38

Continue until the sample is complete.

Step 7: check the list’s organisation

Determine whether the order contains a repeating pattern that could bias selection.

Step 8: apply a predetermined non-response rule

Do not replace people according to convenience.

Selecting the appropriate method

Random sampling may be appropriate when:

• A complete sampling frame exists.

• Equal opportunity for selection is important.

• The population is manageable.

• The researcher wants to minimise personal selection.

• Sufficient time is available for contacting selected people.

Systematic sampling may be appropriate when:

• An ordered list exists.

• A sample must be selected efficiently.

• The population is large.

• A clear interval can be calculated.

• The list does not contain a problematic repeating pattern.

Random sampling may be less appropriate when:

• No complete population list exists.

• The population is difficult to identify.

• Selected people are geographically dispersed.

• Contacting individuals is impractical.

• The study needs exact subgroup proportions.

Systematic sampling may be less appropriate when:

• The list has a periodic structure.

• Population members are arranged according to a relevant characteristic.

• No sensible sampling interval is available.

• The researcher cannot maintain the fixed rule.

• The sampling frame is incomplete.

Applying sampling methods to scenarios

Scenario 1: school register

A psychologist wants to select 30 students from a school containing 600 pupils.

Random-sampling procedure

• Number the pupils from 001 to 600.

• Use a random-number generator to select 30 different numbers.

• Invite the corresponding pupils.

Systematic-sampling procedure

• Calculate the interval: 600 ÷ 30 = 20.

• Randomly select a starting number from 1 to 20.

• Select that pupil and every twentieth pupil afterwards.

Scenario 2: employee list

A researcher needs 50 participants from a company employing 1,000 people.

Systematic sampling could use:

1,000÷50=20

The researcher selects every twentieth employee after a randomly chosen start between 1 and 20.

A limitation would arise if the list repeatedly places employees from one department in every twentieth position.

Scenario 3: online-service users

A psychologist randomly selects 200 users from an online service’s membership database and generalises the findings to all adults.

The selection may be random within the database.

However, the sample may not represent all adults because it excludes:

• Non-users.

• People without suitable internet access.

• Adults using competing services.

• People who chose not to register.

The limitation concerns the sampling frame rather than the random-number procedure.

Scenario 4: customers entering a shop

Every tenth customer entering a shop between 9.00 am and 11.00 am is invited to complete a survey.

This is systematic selection from customers present during that period.

The sample may not represent:

• Afternoon customers.

• Evening customers.

• People shopping on another day.

• Customers who use other branches.

The researcher should restrict the conclusion accordingly.

A method for evaluating a sampling method

Step 1: identify the method correctly

Look for:

• Chance selection: random.

• Every nth person: systematic.

Step 2: identify the sampling frame

State who could be selected.

Step 3: identify a relevant strength

Explain how the selection procedure:

• Reduces researcher choice.

• Gives equal opportunity.

• Spreads selection through the list.

• Improves efficiency.

Step 4: identify a relevant limitation

Consider:

• Incomplete frames.

• Chance imbalance.

• List periodicity.

• Non-response.

• Time or cost.

Step 5: explain the effect on the findings

Link the limitation to:

• Sampling bias.

• Representativeness.

• Generalisation.

Step 6: apply the point to the scenario

Use the actual population, list and measured behaviour described.

Writing an effective random-sampling explanation

A strong explanation might state:

The researcher would obtain a complete list of the target population and assign each member a unique number. A random-number generator would then be used to select the required number of different participants. This gives every member of the sampling frame an equal chance of selection and reduces researcher selection bias.

Writing an effective systematic-sampling explanation

A strong explanation might state:

The researcher would place the population members in an ordered sampling frame and calculate a sampling interval by dividing the population size by the required sample size. After choosing a starting point, the researcher would select every nth person until the sample was complete.

Writing an effective random-sampling evaluation

One strength of random sampling is that every person on the sampling frame has an equal chance of selection, reducing the researcher’s ability to choose convenient or preferred participants. This may make the sample more representative. However, chance can still produce an imbalanced sample, especially when the sample is small, so relevant population groups may be overrepresented or absent.

Writing an effective systematic-sampling evaluation

One strength of systematic sampling is that selecting every nth person is quick and easy to replicate, particularly with a large population list. The fixed interval also reduces researcher choice. However, if the sampling frame contains a periodic pattern matching the interval, the procedure may repeatedly select one type of person, producing a biased sample and limiting generalisation.

Overall summary

Random sampling

Random sampling:

• Uses a chance procedure.

• Requires an appropriate sampling frame.

• Gives each listed population member an equal chance of selection.

• Reduces personal researcher choice.

• May support generalisation.

Its limitations include:

• Difficulty obtaining a complete sampling frame.

• Chance production of an unrepresentative sample.

• Non-response.

• Time and cost.

• Bias within the original population list.

Systematic sampling

Systematic sampling:

• Selects every nth person.

• Uses a sampling interval.

• Usually begins from a selected starting point.

• Is straightforward and efficient.

• Spreads selection across an ordered frame.

Its limitations include:

• Dependence on an accurate sampling frame.

• Possible periodic patterns in the list.

• Non-response.

• Possible starting-point bias.

• Lack of guaranteed subgroup representation.

The key comparison is:

Random sampling uses chance to select population members, whereas systematic sampling follows a fixed interval after a starting point has been chosen.

Key Words 🔑

Key word	Student-friendly definition	How it may be used in an exam
Random sampling	A sampling method in which every member of the target population has an equal chance of selection.	Describe a chance-based participant-selection procedure.
Systematic sampling	A sampling method in which every nth person is selected from an ordered population.	Explain selection through a fixed interval.
Target population	The complete group about which the researcher wants to draw conclusions.	Identify the people from whom the sample should be selected.
Sample	The smaller group selected to participate in the investigation.	Identify the people who provide the research data.
Sampling frame	A list of the target population from which participants can be selected.	Explain what is required for random or systematic sampling.
Sampling interval	The fixed numerical gap between selections in systematic sampling.	Calculate or explain which population members will be selected.
Random starting point	A starting position selected by chance before systematic selection begins.	Explain how starting-point bias may be reduced.
Random-number generator	A tool that selects numbers through a chance procedure.	Explain how a random sample could be obtained.
Equal chance	The same probability of being selected as every other population member.	Explain the defining principle of random sampling.
Sampling bias	A systematic difference between a sample and its target population.	Evaluate whether the sample may be unrepresentative.
Representative sample	A sample reflecting relevant characteristics of the target population.	Evaluate whether findings may be generalised.
Generalisability	The extent to which findings can be applied beyond the sample studied.	Explain the consequence of a biased sample.
Periodic pattern	A repeated arrangement within a sampling frame.	Explain a possible limitation of systematic sampling.
Non-response bias	Bias caused when selected people who participate differ from those who do not.	Evaluate the final sample after invitations are refused.
Random selection	Using chance to select people for a sample.	Distinguish sampling from assignment to experimental conditions.
Random allocation	Using chance to place participants into experimental conditions.	Explain a control procedure rather than a sampling method.
Researcher bias	The researcher’s expectations or preferences influencing a procedure.	Explain why planned selection methods may be useful.
Stratified sampling	Sampling that represents population subgroups in appropriate proportions.	Compare proportionate representation with random selection.
Opportunity sampling	Selecting people who are available and convenient.	Compare practicality with random and systematic sampling.
Volunteer sampling	Recruiting people who choose to respond to an invitation.	Compare self-selection with researcher-controlled procedures.

Common Mistakes ⚠️

Mistake: Saying random sampling means choosing people without planning.

Why this is incorrect:Random sampling uses a structured chance procedure based on a defined population.

How to improve:Refer to a sampling frame, numbered population members and a random-selection method.

Mistake: Saying the researcher picks participants they believe are typical.

Why this is incorrect:Personal judgement does not give every population member an equal chance of selection.

How to improve:Use a random-number generator, random-number table or fair lottery procedure.

Mistake: Saying random sampling guarantees a representative sample.

Why this is incorrect:Chance can produce an uneven sample, particularly when the sample is small.

How to improve:State that random selection may reduce bias but does not guarantee representation.

Mistake: Ignoring the sampling frame.

Why this is incorrect:Researchers need an appropriate way to identify the population members who could be selected.

How to improve:Name a complete and current list relevant to the target population.

Mistake: Assuming a random sample from a biased list represents the whole population.

Why this is incorrect:People absent from the sampling frame have no chance of selection.

How to improve:Evaluate both the chance procedure and the quality of the original list.

Mistake: Defining systematic sampling as selecting people in an organised manner.

Why this is incorrect:Many sampling methods are organised. Systematic sampling specifically selects every nth person.

How to improve:Refer to an ordered sampling frame, sampling interval and starting point.

Mistake: Confusing the sampling interval with the sample size.

Why this is incorrect:The sample size is the number of participants required. The interval is the gap between selections.

How to improve:Calculate the interval by dividing population size by required sample size.

Mistake: Choosing a convenient starting point without recognising possible bias.

Why this is incorrect:A researcher-selected start may influence which positions are included.

How to improve:Use a random starting point where appropriate.

Mistake: Ignoring periodic patterns in systematic sampling.

Why this is incorrect:A repeated list structure may cause the same type of population member to be selected repeatedly.

How to improve:Examine how the sampling frame is ordered before applying the interval.

Mistake: Saying systematic sampling gives every person an independently random chance.

Why this is incorrect:After the starting point is chosen, later selections are determined by the fixed interval.

How to improve:Distinguish chance-based selection from interval-based selection.

Mistake: Replacing non-responders with anyone who is available.

Why this is incorrect:Convenient replacement changes the original sampling method and may introduce bias.

How to improve:Decide on a consistent replacement rule before recruitment begins.

Mistake: Confusing random sampling with random allocation.

Why this is incorrect:Random sampling selects participants from a population. Random allocation assigns participants to conditions.

How to improve:Identify whether the procedure concerns recruitment or experimental groups.

Mistake: Saying a large random sample must represent every subgroup exactly.

Why this is incorrect:Chance does not guarantee that groups will appear in their population proportions.

How to improve:Use stratified sampling when exact subgroup representation is required.

Mistake: Evaluating systematic sampling only by saying it is quick.

Why this is incomplete:A developed evaluation should explain why the fixed interval increases efficiency and consider the risk created by list order.

How to improve:Link the procedure to both practicality and possible sampling bias.

Mistake: Generalising beyond the sampling frame.

Why this is incorrect:The selected sample directly represents only the population from which it could be chosen.

How to improve:Keep conclusions within the defined target population and replicate using other populations before making broader claims.

Exam-Style Questions ✍️

Question 1

Which one of the following best describes random sampling?

A. Selecting every tenth person from a list

B. Selecting people who are easiest to contact

C. Giving every member of the target population an equal chance of selection

D. Asking people to respond to an advertisement

[1 mark]

Question 2

Define systematic sampling.

[2 marks]

Question 3

A college has 500 students. A psychologist wants a random sample of 50 students.

Explain how the psychologist could obtain the sample.

[4 marks]

Question 4

A company employs 800 people. A researcher requires a systematic sample of 80 employees.

a) Calculate the sampling interval.

[1 mark]

b) Explain how the researcher could use this interval to select the sample.

[3 marks]

Question 5

Explain one difference between random and systematic sampling.

[3 marks]

Question 6

Explain one strength and one limitation of random sampling.

[6 marks]

Question 7

Explain one strength and one limitation of systematic sampling.

[6 marks]

Question 8

A school register is organised into groups of 25 pupils. The researcher selects every twenty-fifth name.

Explain why this systematic sample may be biased.

[4 marks]

Question 9

A psychologist randomly selects 100 registered users from an online revision platform and concludes that the findings apply to all A-Level students.

Explain why this conclusion may not be justified.

[4 marks]

Question 10

A researcher randomly selects 40 employees from a company and then randomly allocates them to two experimental conditions.

Explain the difference between random selection and random allocation in this study.

[4 marks]