Stratified 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 Stratified sampling A-Level Psychology revision notes explain how researchers construct a sample that reflects important groups within a target population. You will learn how to identify strata, calculate the correct number of participants from each group and select individuals using an appropriate procedure. You will also evaluate whether stratification reduces sampling bias and improves generalisation. This lesson builds on chance-based and interval-based participant selection and the distinction between the target population and the participating sample.

Learning Objectives 🎯

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

• Define stratified sampling.

• Explain how a stratified sample is selected.

• Calculate the number of participants required from different population groups.

• Apply stratified sampling to unfamiliar research scenarios.

• Evaluate the strengths and limitations of stratified sampling.

• Explain how stratification affects representativeness and generalisation.

Revision Notes 📚

Stratified sampling A-Level Psychology revision overview

Stratified sampling is a sampling method in which the target population is divided into relevant subgroups and participants are selected from each subgroup in proportion to its size within the population.

The subgroups are called strata.

The singular form is stratum.

Examples of possible strata include:

• Year groups.

• School subjects.

• Departments within a workplace.

• Age groups.

• Types of employment.

• Different geographical areas.

• Levels of qualification.

The aim is to construct a sample that reflects relevant features of the target population.

For example, if a college population contains:

• 60% Year 12 students.

• 40% Year 13 students.

a stratified sample should also contain:

• Approximately 60% Year 12 students.

• Approximately 40% Year 13 students.

The key process is:

Identify the target population → choose relevant strata → calculate each stratum’s proportion → calculate the number required → select participants from each stratum

What is a stratum?

A stratum is one subgroup within a target population.

The plural is strata.

Suppose a college has three year groups:

• Year 11.

• Year 12.

• Year 13.

Each year group could form one stratum.

Alternatively, the researcher could divide the population according to:

• Course studied.

• Location.

• Department.

• Another characteristic relevant to the investigation.

The strata selected should relate meaningfully to the research aim.

What makes stratified sampling different?

Stratified sampling does not leave the proportions of important population groups entirely to chance.

Instead, the researcher deliberately ensures that identified strata appear in the sample in the correct proportions.

For example:

Group	Percentage of population	Percentage of stratified sample
Year 12	60%	60%
Year 13	40%	40%

This differs from a simple random sample, in which chance might produce:

• 70% Year 12.

• 30% Year 13.

The random sample could still be valid, but it would not reproduce the population’s year-group proportions exactly.

Stratified sampling is usually proportionate

In A-Level Psychology, stratified sampling normally means proportionate stratified sampling.

This means that the number selected from each stratum reflects that group’s proportion of the target population.

If one group forms one quarter of the population, it should form approximately one quarter of the sample.

For example:

• Population: 800 employees.

• One department contains 200 employees.

• The department forms 25% of the population.

• Required sample: 80 employees.

• The department should contribute 25% of 80, which is 20 participants.

Stratified sampling requires population information

Before selecting participants, the researcher must know:

• The size of the target population.

• Which strata are relevant.

• The number of population members in each stratum.

• The required total sample size.

The researcher usually needs an accurate sampling frame, such as:

• A college register.

• An employee database.

• A school roll.

• An organisational membership list.

The sampling frame must contain enough information to identify each person’s stratum.

Choosing relevant strata

The researcher should select a characteristic that may be relevant to the behaviour or response being investigated.

Suppose a psychologist wants to investigate examination anxiety across a sixth form.

Potentially relevant strata might include:

• Year 12 and Year 13.

• Different courses.

• Students with different examination schedules.

Year group may be relevant because Year 13 students:

• Have more A-Level examination experience.

• Are closer to final examinations.

• May face different academic pressures.

A characteristic such as eye colour would be unlikely to be relevant.

The research aim guides the choice of strata

Consider this aim:

To investigate attitudes towards remote working among employees in a large company.

Possible relevant strata might be:

• Department.

• Job type.

• Working location.

• Seniority level.

Different groups may have different experiences of remote working.

Now consider this aim:

To investigate use of school revision resources among sixth-form students.

Relevant strata might include:

• Year group.

• Subject area.

• Type of course.

Researchers should not divide the population into groups without explaining why those groups matter.

Strata should cover the population

The strata should account for all eligible members of the target population.

For example, if employees are divided by department, every employee should belong to an appropriate department category.

A coding system that includes only:

• Sales.

• Finance.

• Marketing.

would be incomplete if the company also contains:

• Human resources.

• Information technology.

• Operations.

People who cannot be placed into a stratum may be excluded incorrectly.

Strata should not overlap unnecessarily

Each person should normally be placed into one category within the chosen stratification variable.

For example, if the researcher stratifies by year group, a student should be classified as either:

• Year 12.

• Year 13.

A student should not be counted in both strata.

Researchers can stratify using more than one characteristic, but this creates more complex combined groups.

For example:

• Year 12 science students.

• Year 12 humanities students.

• Year 13 science students.

• Year 13 humanities students.

Each participant would belong to one combined category.

Stratification and operationalisation

The strata must be defined clearly.

For example, “younger” and “older” employees are vague categories.

A clearer division might be:

• Employees aged 18 to 34.

• Employees aged 35 to 49.

• Employees aged 50 and over.

The boundaries should be:

• Clear.

• Non-overlapping.

• Relevant to the population.

• Suitable for the research aim.

This links to defining variables and categories precisely.

How to conduct stratified sampling

Step 1: define the target population

The researcher identifies the complete group to which the findings are intended to apply.

Example:

All 1,000 students currently enrolled at Greenfield College.

Step 2: identify relevant strata

Suppose the researcher decides that year group is relevant.

The college contains:

• 600 Year 12 students.

• 400 Year 13 students.

The strata are:

• Year 12.

• Year 13.

Step 3: decide the sample size

Suppose the researcher requires a sample of 100 students.

Step 4: calculate the proportion of each stratum

Year 12:

600 ÷ 1000=0.60

Year 13:

400 ÷ 1000=0.40

Therefore:

• Year 12 forms 60% of the population.

• Year 13 forms 40% of the population.

Step 5: calculate the number needed from each stratum

Year 12:

0.60×100=60

Year 13:

0.40×100=40

The stratified sample should contain:

• 60 Year 12 students.

• 40 Year 13 students.

Step 6: select individuals from each stratum

The researcher then selects the required number from each group.

They might:

• Use random sampling within each stratum.

• Use systematic sampling within each stratum.

For example:

• Randomly select 60 students from the Year 12 register.

• Randomly select 40 students from the Year 13 register.

Using random selection within each stratum reduces personal researcher choice.

Step 7: invite selected people to participate

The selected individuals receive:

• Information about the study.

• An invitation to participate.

• An appropriate consent procedure.

Selection does not remove the right to refuse.

Step 8: check the final sample

The researcher should check whether:

• The required number from each stratum participated.

• Non-response altered the proportions.

• Replacements were selected consistently.

• The final sample still reflects the population.

The stratified sampling formula

The number required from one stratum can be calculated using:

Number required from stratum=(Number in stratum ÷ Total population)×Required sample size

A useful memory structure is:

Part ÷ Whole × Sample

Where:

• Part is the number of population members in the stratum.

• Whole is the total target population.

• Sample is the total number of participants required.

Formula triangle in words

To calculate the sample contribution from a group:

1. Divide the size of the group by the total population.

2. Multiply the answer by the required sample size.

3. Round appropriately if the result is not a whole person.

4. Check that all group totals add to the required sample size.

Why the calculation works

The fraction:

Number in stratum ÷ Total population

shows the proportion of the population belonging to the stratum.

Multiplying by the sample size applies the same proportion to the sample.

For example:

300÷ 500=0.60

If the required sample contains 50 participants:

0.60×50=30

Therefore, 30 participants should come from that stratum.

This calculation draws on working with percentages, proportions and ratios.

Worked calculation 1: two year groups

A sixth form contains:

• 720 Year 12 students.

• 480 Year 13 students.

The total population is:

720+480=1200

The researcher requires a sample of 100 students.

Year 12 calculation

(720÷ 1200)×100=60

Year 13 calculation

(480÷ 1200)×100=40

The sample should contain:

Stratum	Population size	Number required
Year 12	720	60
Year 13	480	40
Total	1,200	100

Final check

60+40=100

The group totals match the required sample size.

Worked calculation 2: three departments

A company employs:

• 400 people in Operations.

• 250 people in Sales.

• 150 people in Finance.

The total population is:

400+250+150=800

The researcher requires a sample of 80 employees.

Operations

(400÷ 800)×80=40

Sales

(250÷ 800)×80=25

Finance

(150÷ 800)×80=15

The sample should contain:

Department	Population size	Population proportion	Number required
Operations	400	50%	40
Sales	250	31.25%	25
Finance	150	18.75%	15
Total	800	100%	80

Final check

40+25+15=80

Worked calculation 3: percentages are provided

A college population consists of:

• 45% science students.

• 35% humanities students.

• 20% creative-subject students.

The researcher needs a sample of 60 students.

Science students

0.45×60=27

Humanities students

0.35×60=21

Creative-subject students

0.20×60=12

The sample should contain:

Stratum	Population percentage	Number required
Science	45%	27
Humanities	35%	21
Creative subjects	20%	12
Total	100%	60

Worked calculation 4: calculating the percentage first

A school employs 240 members of staff.

Of these:

• 54 are teaching assistants.

• 186 are teachers.

The researcher needs a sample of 40 staff.

Teaching assistants

First calculate the population proportion:

54÷ 240=0.225

Convert to a percentage:

0.225×100=22.5%

Apply the proportion to the sample:

0.225×40=9

Teachers

186÷ 240=0.775

0.775×40=31

The sample should contain:

• 9 teaching assistants.

• 31 teachers.

Check

9+31=40

Worked calculation 5: rounding

A college has:

• 472 Year 12 students.

• 378 Year 13 students.

The total population is 850.

The researcher requires a sample of 60.

Year 12

(472÷ 850)×60=33.3176

This is approximately 33 participants.

Year 13

(378÷ 850)×60=26.6824

This is approximately 27 participants.

The final sample should contain:

• 33 Year 12 students.

• 27 Year 13 students.

Check

33+27=60

The rounded totals match the required sample size.

Why participants must be whole numbers

A researcher cannot recruit:

• 33.3 students.

• 26.7 employees.

Calculated values must therefore be converted into whole participants.

The researcher should:

1. Calculate every group before rounding.

2. Round sensibly.

3. Check that the final total is correct.

4. Adjust carefully where rounding produces too many or too few participants.

Managing rounding across several strata

Suppose calculations produce:

• Group A: 18.4.

• Group B: 15.3.

• Group C: 6.3.

The required sample size is 40.

Rounding to the nearest whole number gives:

• Group A: 18.

• Group B: 15.

• Group C: 6.

This totals only 39.

One extra participant must be allocated.

A sensible method is to allocate the remaining place to the group with the largest decimal remainder.

The decimal remainders are:

• Group A: 0.4.

• Group B: 0.3.

• Group C: 0.3.

The final sample could therefore contain:

• Group A: 19.

• Group B: 15.

• Group C: 6.

Total:

19+15+6=40

The procedure should be applied consistently rather than according to researcher preference.

Selecting participants within each stratum

Stratification identifies how many, not necessarily who

The calculation tells the researcher how many participants are required from each group.

It does not automatically determine which individuals should participate.

For example, a researcher may know that the sample needs:

• 30 Year 12 students.

• 20 Year 13 students.

They must still select the specific students.

Random selection within strata

A strong procedure is to randomly select the required number from each stratum.

For example:

1. Obtain a list of all Year 12 students.

2. Assign each a number.

3. Use a random-number generator to select 30.

4. Repeat the process to select 20 Year 13 students.

This combines:

• Proportional representation.

• Reduced researcher selection bias.

Systematic selection within strata

A researcher could also apply a systematic procedure within each stratum.

For example:

• Select every tenth eligible Year 12 student.

• Select every tenth eligible Year 13 student.

The correct interval may differ between strata depending on:

• Group size.

• Number required.

The strengths and limitations of these procedures are examined in Random and systematic sampling.

Opportunity selection within strata

A researcher might calculate the correct proportions but then choose convenient people from each group.

For example:

• Recruit 30 available Year 12 students.

• Recruit 20 available Year 13 students.

The proportions are stratified, but the individuals may still be biased because only convenient people were selected.

The sample may match the population by year group while differing in:

• Motivation.

• Availability.

• Attendance.

• Interest in psychology.

Volunteer selection within strata

A researcher might request volunteers separately from each group until each quota is filled.

Again, the final sample may match the population proportions but contain volunteer bias.

Participants may be more:

• Interested in the topic.

• Available.

• Confident.

• Motivated by a reward.

A sample can therefore be proportionately stratified while remaining biased within each stratum.

Stratified sampling and quotas

Stratified sampling may be confused with filling a set number of places from each group.

The important issue is how people are selected within the strata.

In a strong stratified procedure:

• Population proportions are calculated.

• Individuals are selected objectively within each group.

Simply approaching convenient people until each group total is reached retains opportunity-selection bias.

When evaluating a scenario, examine both:

1. How the group numbers were calculated.

2. How individuals within each group were chosen.

Strengths of stratified sampling

Strength: proportionate representation

The main strength is that relevant population groups are represented in the same proportions as in the target population.

For example, if Year 13 students form 40% of a college population, they also form approximately 40% of the sample.

This reduces the likelihood that a large group is overrepresented simply through chance.

Strength: smaller groups are included

A simple random sample may fail to include members of a small but relevant population group, particularly when the sample is small.

Stratified sampling deliberately reserves places for each identified stratum.

For example, suppose a company contains:

• 90% office-based employees.

• 10% field-based employees.

A small random sample could contain no field-based employees.

A stratified sample ensures that they are represented proportionately.

Strength: may reduce sampling bias

Stratification can reduce bias linked to the chosen population characteristic.

For example, stratifying by year group prevents a sample from containing an excessive number of Year 12 students simply because they were easier to contact.

This may provide a more balanced picture of the target population.

Strength: may improve generalisability

A sample that reflects relevant population characteristics may provide a stronger basis for generalisation.

Suppose examination anxiety differs between Year 12 and Year 13 students.

A proportionate sample containing both groups appropriately is more likely to produce a valid estimate for the whole sixth form.

The conclusion remains limited to the defined target population.

Strength: useful for diverse populations

Stratified sampling is valuable when the population contains distinct groups that may respond differently.

Examples include populations containing:

• Several year groups.

• Different departments.

• Different occupational roles.

• Different educational courses.

• Different locations.

The method prevents the largest or easiest-to-access group from dominating the sample.

Strength: population comparisons may be possible

Because several groups are represented, researchers may be able to examine patterns across strata.

For example, they might compare:

• Year 12 and Year 13.

• Different departments.

• Different types of course.

However, each subgroup must contain enough participants to support a meaningful comparison.

A proportionately represented small group may still contain very few people.

Strength: transparent calculation

Researchers can show:

• The size of each population group.

• The proportion each group forms.

• The number selected.

• The method used within each stratum.

This makes the selection process easier to inspect and replicate.

Strength: researcher choice may be reduced

When random selection is used within strata, the researcher has limited control over which specific people are selected.

This reduces the possibility of choosing participants who:

• Appear cooperative.

• Are personally known.

• Seem likely to support the hypothesis.

• Are easiest to reach.

Limitations of stratified sampling

Limitation: detailed population information is required

The researcher needs accurate information about:

• Population membership.

• Stratum membership.

• Group sizes.

• Contact details.

This information may not be available.

For example, an organisation may not hold complete or current information about all relevant participant characteristics.

Limitation: requires an appropriate sampling frame

A sampling frame must identify every eligible person and the group to which they belong.

If the frame is incomplete, people absent from it have no chance of selection.

If group information is inaccurate, the calculated proportions may also be wrong.

Limitation: time-consuming

Stratified sampling requires several stages:

1. Define the population.

2. Decide which strata matter.

3. Obtain group information.

4. Calculate proportions.

5. Calculate sample numbers.

6. Create separate sampling frames.

7. Select participants from each stratum.

8. Manage non-response in each group.

This is more demanding than selecting people who are immediately available.

Limitation: potentially expensive

Researchers may need to:

• Access several institutions.

• Contact separate population groups.

• Travel to different locations.

• Translate materials.

• Provide different arrangements for different groups.

• Maintain several recruitment lists.

These requirements may increase research costs.

Limitation: only selected characteristics are represented

A stratified sample is proportionately representative only for the characteristics used to create the strata.

Suppose a college sample is stratified by year group.

It may accurately reflect:

• The proportion of Year 12 and Year 13 students.

It may still be unrepresentative in terms of:

• Subject studied.

• Prior attainment.

• Cultural background.

• Revision habits.

• Willingness to participate.

Stratifying by one variable does not create perfect representation on every other characteristic.

Limitation: researcher judgement affects the chosen strata

Researchers decide which population characteristics are important.

They may:

• Select irrelevant strata.

• Ignore an important subgroup.

• Use broad categories that hide meaningful differences.

• Base the choice on unsupported assumptions.

For example, stratifying by department may be less useful than stratifying by working arrangement in research on remote working.

The choice should be justified by the research aim.

Limitation: complex populations create many strata

Using several characteristics at once can create a large number of combined groups.

Suppose researchers stratify by:

• Year group: two categories.

• Course type: three categories.

• Location: four categories.

This produces:

2×3×4=24

combined strata.

A moderate sample divided across 24 groups may contain very few participants in each.

Limitation: very small strata

A small population group may produce a calculated sample contribution below one participant.

For example:

• Group contains 4 of 1,000 population members.

• Required sample is 100.

(4÷ 1000)×100=0.4

Rounding may produce zero participants.

The group is proportionately tiny, but excluding it means its experiences are not represented.

Researchers must decide whether:

• Proportionate sampling is sufficient.

• A larger sample is required.

• The group should be deliberately oversampled for a separate purpose.

For standard A-Level calculations, follow the instructions and maintain the required total.

Limitation: rounding may alter exact proportions

Calculations do not always produce whole numbers.

Rounding can create small differences between:

• Population proportions.

• Sample proportions.

The researcher must ensure that:

• The final sample size is correct.

• Rounding is applied consistently.

• One group is not favoured arbitrarily.

Limitation: non-response can disrupt the sample

Some selected people may refuse or fail to participate.

Suppose the researcher requires:

• 40 Year 12 students.

• 30 Year 13 students.

If many selected Year 13 students refuse, the final sample may no longer contain the correct proportions.

Limitation: replacements can introduce bias

The researcher should not replace a non-responder with the easiest available member of the same stratum.

Although the group proportion would be restored, the individual-selection process would become biased.

A better procedure would use the same objective selection method within the stratum.

Limitation: participation is still voluntary

Stratified sampling identifies people to invite.

It does not guarantee that they will agree.

If the people who participate differ from those who refuse, volunteer or non-response bias may remain.

Limitation: classification may be difficult

Some population members may not fit easily into the selected categories.

For example:

• An employee works across two departments.

• A student studies subjects from several course areas.

• A participant changes group during the research period.

The researcher needs clear classification rules.

Limitation: personal information may be sensitive

Creating strata may require information about personal characteristics.

Researchers should consider:

• Whether the information is necessary.

• Whether access is permitted.

• How confidentiality will be protected.

• Whether category labels could be intrusive or stigmatising.

• How the sampling records will be stored.

Stratified sampling and representativeness

Representation is the central purpose

The aim of stratified sampling is to improve representation of identified population groups.

A representative sample should resemble the target population in characteristics likely to influence the findings.

For example, in research on workplace satisfaction, occupational role may be relevant because:

• Managers.

• Office staff.

• Field workers.

may have different experiences.

A sample drawn almost entirely from office staff could provide a misleading estimate for the whole company.

Representativeness is not guaranteed

A sample may match population proportions but still be biased.

Consider a sample that accurately represents departments but includes only employees who:

• Work daytime hours.

• Are present at one location.

• Agree to take part.

• Have easy access to the researcher.

The sample is representative by department but not necessarily by:

• Shift.

• Location.

• Availability.

• Willingness to participate.

Representativeness depends on relevant characteristics

Researchers should explain why the selected strata might affect the findings.

Weak claim:

The sample is representative because it includes different departments.

Developed claim:

The sample includes each department in its population proportion. This may improve representativeness because employees in different departments have different working conditions that could affect job-satisfaction scores.

The developed claim links the strata to the measured outcome.

Stratified sampling and generalisation

Why stratification may improve generalisation

If relevant population groups are represented proportionately, the results may provide a more accurate estimate of the wider target population.

For example, suppose anxiety differs by year group.

A sample containing:

• Too many Year 12 students.

could overestimate or underestimate anxiety across the whole sixth form.

Matching the year-group proportions reduces this source of sampling bias.

Generalisation remains limited to the population

A stratified sample from one college does not automatically represent:

• Every sixth-form college.

• All A-Level students.

• All young people.

• Students in different countries.

Stratification improves representation within the defined population.

It does not expand the target population.

Other features of the study still matter

A representative sample does not guarantee that the research findings are valid.

The study may still contain:

• Poorly operationalised variables.

• Leading questionnaire items.

• Demand characteristics.

• Investigator effects.

• Unreliable measurements.

• Artificial procedures.

Sampling quality affects generalisation, but it is only one aspect of research quality.

Replication across populations

Broader generalisation may be supported by repeating the research with stratified samples from:

• Different schools.

• Different workplaces.

• Different locations.

• Different cultural contexts.

• Different time periods.

Similar findings across populations provide stronger support than one sample alone.

Stratified sampling compared with random sampling

Feature	Stratified sampling	Random sampling
Population division	Divided into relevant strata	Treated as one complete group
Proportions	Important groups represented proportionately	Proportions left to chance
Selection	Usually selected separately within each stratum	Selected from the whole population
Main advantage	Ensures identified groups are represented	Gives each listed member an equal chance
Main limitation	Requires detailed group information	Chance may produce an imbalanced sample
Complexity	More complex	Usually simpler
Researcher decisions	Must choose relevant strata	Must define the frame and chance procedure
Representativeness	Improved for selected characteristics	Possible but not guaranteed

Direct comparison

A strong comparison might state:

Random sampling selects participants by chance from the whole target population, so subgroup proportions may vary. Stratified sampling first divides the population into relevant subgroups and selects participants from each in proportion to its population size.

Stratified selection may include random selection

The methods are not always completely separate stages.

A stratified sample may use random sampling within each stratum.

For example:

• Calculate that 30 science students are required.

• Randomly select those 30 from the science-student register.

The overall method remains stratified because the group numbers were calculated proportionately.

Stratified sampling compared with systematic sampling

Systematic sampling selects every nth person from an ordered list.

Stratified sampling ensures proportionate representation of population groups.

A systematic procedure might accidentally overrepresent one group if:

• The list has a pattern.

• Group members are clustered in particular positions.

• The interval repeatedly selects the same category.

A stratified procedure prevents this for the characteristics used to create the strata.

However, stratified sampling takes longer to organise.

Stratified sampling compared with opportunity sampling

Opportunity sampling recruits people who are available.

It may be:

• Fast.

• Inexpensive.

• Easy to arrange.

However, it can overrepresent people who are:

• Present at a particular time.

• Easy to approach.

• Located near the researcher.

• Willing to stop.

Stratified sampling is generally more representative of identified population groups, but requires more planning and population information.

Stratified sampling compared with volunteer sampling

Volunteer sampling recruits people who respond to an invitation.

Volunteers may differ from non-volunteers.

Stratified sampling can calculate how many people are needed from each group, but volunteer bias may remain if individuals within the strata self-select.

The strengths and weaknesses of these convenient methods are developed in Opportunity and volunteer sampling.

Selecting stratified sampling for a research scenario

Appropriate scenario: diverse college population

A researcher wants to estimate examination anxiety across a college containing:

• Year 12 and Year 13 students.

• Several course types.

• Different examination schedules.

Stratified sampling may be appropriate because relevant groups may experience different levels of anxiety.

The researcher could stratify by year group if that characteristic is most relevant to the aim.

Appropriate scenario: workplace investigation

A psychologist investigates job satisfaction in a company containing:

• Office staff.

• Managers.

• Field workers.

• Technical staff.

Stratification by role may ensure that the large office-based workforce does not completely dominate the sample.

Less appropriate scenario: no population information

A researcher wants to study people attending an unregistered public event.

There is no complete list and no reliable information about population group sizes.

Accurate stratified sampling may be impossible because:

• The population is not clearly defined.

• Stratum proportions are unknown.

• No appropriate sampling frame exists.

Less appropriate scenario: highly specialised rare population

A researcher investigates an extremely rare psychological condition.

The population may be:

• Very small.

• Difficult to identify.

• Spread across many locations.

The researcher may need to recruit every accessible eligible person rather than construct a proportionate stratified sample.

Worked scenario: employee wellbeing

A company employs:

• 360 office employees.

• 180 technical employees.

• 60 managers.

The total population is:

360+180+60=600

The researcher needs 50 participants.

Office employees

(360÷ 600)×50=30

Technical employees

(180÷ 600)×50=15

Managers

(60÷ 600)×50=5

The sample should contain:

• 30 office employees.

• 15 technical employees.

• 5 managers.

Evaluation

The sample represents job roles proportionately.

However, five managers may be too few for a detailed statistical comparison between managers and other groups.

Proportionate representation and subgroup sample size are separate issues.

Worked scenario: inappropriate conclusion

A researcher obtains a stratified sample of 100 students from one college and concludes:

These findings show how all UK A-Level students revise.

This conclusion is too broad.

The sample may represent the selected college by the chosen strata.

It does not necessarily represent:

• Other colleges.

• Different exam boards.

• Different geographical areas.

• Students with different resources.

• The whole UK A-Level population.

A more appropriate conclusion would refer to:

Students attending the college or students in similar educational settings.

A method for answering stratified-sampling calculations

Step 1: identify the total population

Add the strata if the total is not provided.

Step 2: identify the required sample size

Do not confuse:

• Population size.

• Sample size.

• Stratum size.

Step 3: use the formula for each group

stratum size÷ population size×sample size

Step 4: show working

Write the fraction, multiplication and result.

Step 5: round where necessary

Participants must be whole people.

Step 6: check the total

Add all calculated sample contributions.

They must equal the required sample size.

A method for evaluating stratified sampling

Step 1: identify the strata

State how the population was divided.

Step 2: explain the proportions

State whether each group is represented according to its population size.

Step 3: identify how individuals were selected

Determine whether participants were:

• Randomly selected.

• Systematically selected.

• Chosen conveniently.

• Recruited as volunteers.

Step 4: evaluate representativeness

Explain which characteristic is represented well.

Step 5: identify remaining bias

Consider:

• Missing population characteristics.

• Non-response.

• Inaccurate population records.

• Convenient selection within strata.

• Small group sizes.

Step 6: judge generalisation

State where the findings may reasonably apply.

Writing an effective definition

A strong definition might state:

Stratified sampling is a method in which the target population is divided into relevant subgroups, or strata, and participants are selected from each stratum in proportion to its size within the population.

This definition identifies:

• The target population.

• The creation of strata.

• Proportionate representation.

• Participant selection.

Writing an effective procedure

The researcher would divide the college population into Year 12 and Year 13 students. The proportion of students in each year group would be calculated and applied to the required sample size. The researcher would then randomly select the required number from each year-group register.

This answer explains:

• How the strata are formed.

• How numbers are calculated.

• How individuals are selected.

Writing an effective strength paragraph

One strength of stratified sampling is that relevant population groups are represented in their correct proportions. If Year 13 students form 40% of the college, they will also form approximately 40% of the sample. This may reduce sampling bias and improve generalisability if year group affects the behaviour being studied. However, the sample may still be unrepresentative in characteristics that were not used to form the strata.

Writing an effective limitation paragraph

One limitation is that stratified sampling requires accurate information about the size and membership of every relevant subgroup. If the college register is incomplete or students are placed in the wrong year-group category, the calculated proportions will be inaccurate. This may produce a biased sample despite the use of a systematic calculation.

Overall summary

Stratified sampling involves:

• Dividing the target population into relevant strata.

• Calculating each stratum’s population proportion.

• Applying that proportion to the required sample size.

• Selecting the required number from each stratum.

• Maintaining the proportions as far as possible during recruitment.

The calculation is:

number in stratum÷ total population×required sample size

Its main strengths are:

• Proportionate representation.

• Inclusion of smaller population groups.

• Reduced sampling bias for selected characteristics.

• Improved potential for generalisation.

• Transparent and replicable calculations.

Its main limitations are:

• Need for accurate population information.

• Time and cost.

• Complex calculations and recruitment.

• Possible rounding problems.

• Difficulty classifying some individuals.

• Non-response.

• Bias within strata.

• Representation only of the characteristics used to create the strata.

The key judgement is:

Stratified sampling can make a sample more representative of identified population groups, but it cannot guarantee that the sample is representative in every relevant way.

Key Words 🔑

Key word	Student-friendly definition	How it may be used in an exam
Stratified sampling	A method that represents relevant population groups in proportion to their size.	Define the method or describe a proportionate selection procedure.
Stratum	One subgroup within a target population.	Identify one population category used in stratification.
Strata	The plural of stratum, meaning two or more population subgroups.	Describe how a population has been divided.
Proportionate sample	A sample in which group percentages match those in the population.	Explain the purpose of stratified sampling.
Target population	The complete group about which the researcher wants to draw conclusions.	Identify the group being divided into strata.
Sample	The smaller group selected to participate in the research.	State the final number recruited from each stratum.
Sampling frame	A list identifying eligible members of the target population.	Explain how people within each stratum may be selected.
Population proportion	The fraction or percentage of the population belonging to a group.	Calculate how much of the sample should come from a stratum.
Representative sample	A sample reflecting relevant characteristics of the target population.	Evaluate the likely generalisability of findings.
Sampling bias	A systematic difference between the sample and target population.	Explain why incorrect proportions or non-response are problematic.
Generalisability	The extent to which findings can be applied beyond the sample studied.	Evaluate the effect of proportional representation.
Random selection	Using chance to select individuals from a population or stratum.	Explain how researcher choice may be reduced within strata.
Systematic selection	Selecting every nth person from an ordered list.	Describe an alternative way of selecting individuals within strata.
Non-response bias	Bias occurring when participants differ from selected people who do not respond.	Evaluate the final stratified sample.
Overrepresentation	A group forming a larger proportion of the sample than of the population.	Identify a sampling problem avoided by stratification.
Underrepresentation	A group forming a smaller proportion of the sample than of the population.	Explain why findings may not represent the population.
Opportunity sampling	Selecting participants who are available and convenient.	Evaluate biased selection within strata.
Volunteer sampling	Recruiting people who choose to respond to an invitation.	Explain why self-selection may remain after stratification.
Rounding	Converting a calculated decimal into a practical whole number.	Calculate participant numbers while maintaining the total sample size.
Inclusion criteria	Rules defining who belongs to the target population or stratum.	Explain how group membership should be determined.

Common Mistakes ⚠️

Mistake: Saying stratified sampling means selecting equal numbers from every group.

Why this is incorrect:Groups are normally represented in proportion to their size in the target population.

How to improve:Calculate the percentage or fraction of the population belonging to each stratum.

Mistake: Dividing the sample equally when the population groups are unequal.

Why this is incorrect:This would overrepresent smaller groups and underrepresent larger groups.

How to improve:Use the formula: stratum size ÷ population size × sample size.

Mistake: Confusing a stratum with the whole sample.

Why this is incorrect:A stratum is one subgroup, while the sample contains participants selected across all relevant strata.

How to improve:Identify each population group separately before calculating the total sample.

Mistake: Using the sample size as the denominator.

Why this is incorrect:The denominator should be the total target-population size.

How to improve:Use the structure part ÷ whole × required sample.

Mistake: Forgetting to calculate the total population.

Why this is incorrect:The population total is needed to determine each group’s proportion.

How to improve:Add all stratum sizes before beginning the calculations.

Mistake: Calculating the percentage correctly but failing to apply it to the sample size.

Why this is incorrect:The percentage alone does not show how many participants should be recruited.

How to improve:Multiply the population proportion by the required sample size.

Mistake: Reporting decimal participants.

Why this is incorrect:Researchers must recruit whole people.

How to improve:Round appropriately and check that the group totals equal the required sample.

Mistake: Rounding every value without checking the final total.

Why this is incorrect:The rounded group totals may produce too many or too few participants.

How to improve:Add the rounded values and make a consistent adjustment where necessary.

Mistake: Saying stratified sampling guarantees a representative sample.

Why this is incorrect:It ensures representation only for the characteristics used to form the strata.

How to improve:Identify which characteristic is represented and which possible sources of bias remain.

Mistake: Ignoring how people are selected within each stratum.

Why this is incorrect:Choosing only convenient or willing people can create bias even when group proportions are correct.

How to improve:Describe an objective selection procedure, such as random sampling within each stratum.

Mistake: Saying a stratified sample contains no volunteer bias.

Why this is incorrect:Selected people still decide whether to participate.

How to improve:Consider non-response and whether participants differ from those who refuse.

Mistake: Selecting irrelevant strata.

Why this is incorrect:Matching the population on an unrelated characteristic may not improve the accuracy of the findings.

How to improve:Explain why the chosen groups might differ on the behaviour being investigated.

Mistake: Assuming that one stratified sample represents every wider population.

Why this is incorrect:Stratification improves representation within the defined target population, such as one college or company.

How to improve:Restrict conclusions to the population from which the sample was selected.

Mistake: Saying stratified sampling is always quick.

Why this is incorrect:Researchers must obtain population information, calculate proportions and recruit separately from each group.

How to improve:Recognise that the method is often more time-consuming than opportunity sampling.

Mistake: Confusing stratified sampling with random sampling.

Why this is incorrect:Random sampling selects from the population as one group, while stratified sampling fixes subgroup proportions first.

How to improve:Explain that random selection may be used within each stratum after the required numbers have been calculated.

Exam-Style Questions ✍️

Question 1

Which one of the following best describes stratified sampling?

A. Selecting every tenth person from an ordered list

B. Selecting equal numbers from every population group

C. Selecting population groups in proportion to their size

D. Recruiting anyone who is available

[1 mark]

Question 2

Define stratified sampling.

[2 marks]

Question 3

A college contains 800 Year 12 students and 400 Year 13 students. A researcher requires a sample of 60 students.

Calculate the number of participants required from each year group. Show your working.

[4 marks]

Question 4

A company employs:

• 300 office staff.

• 150 technical staff.

• 50 managers.

A psychologist needs a stratified sample of 80 employees.

Calculate the number required from each group. Show your working.

[6 marks]

Question 5

Explain how a researcher could select individual participants after calculating the number required from each stratum.

[3 marks]

Question 6

Explain one strength of stratified sampling.

[3 marks]

Question 7

Explain one limitation of stratified sampling.

[3 marks]

Question 8

A researcher constructs a sample containing the correct proportions of Year 12 and Year 13 students. She recruits only volunteers within each year group.

Explain why the final sample may still be biased.

[4 marks]

Question 9

A stratified sample from one school accurately reflects the school’s year-group proportions. The researcher concludes that the findings apply to every UK secondary-school student.

Explain why this conclusion may not be justified.

[4 marks]

Question 10

Evaluate stratified sampling as a method of selecting participants for psychological research.

Refer to calculation, representativeness, sampling bias and generalisation in your answer.

[8 marks]