FS1–FS2, FS5, HS1–HS2, HS6 - Populations, samples and questionnaires
Choose people fairly, ask clear questions and use their answers to draw appropriately limited conclusions. FS1–FS2 and HS1–HS2 cover sampling and questionnaires; FS5 and HS6 connect the evidence to the population being described.
Population and sampling
Can a survey of hundreds of people still give a misleading answer? Yes: who gets asked matters as well as how many answer.
Population, sample and census
The population is the whole group about which a question is being asked. A sample is a subset investigated to learn about that population. A census attempts to collect information from every member of the population.
Define the population before choosing the sample. “Pupils at this school” and “pupils who use the library” are different populations. A census may take too much time or money, and some people may not respond even when everyone is contacted.
A biased method systematically favours some members or answers over others. A representative sample should reflect the population relevant to the question. A simple random sample, selected from a complete list with each member having the same chance of selection, helps avoid selection bias. It does not guarantee that every small sample matches the population perfectly.
Worked example 1: choosing from the population
Question. A school with pupils wants to know whether pupils support a new lunchtime club. Describe a way to choose a random sample of pupils.
Plan. Give every pupil a chance by starting with the complete school roll.
Number all pupils to . Use a random number generator to select different numbers in this range, ignoring repeats. Ask the corresponding pupils the same question. Arrange to contact selected pupils who are absent rather than automatically replacing them with nearby friends.
Answer. Select distinct pupils randomly from the complete roll.
Check. Every pupil appears once on the list and can be selected. The sample is of the population, but the fairness comes from the selection method, not the percentage alone.
Keep the population and sample size fixed, but change how the pupils are chosen.
Worked example 2: a large sample can be biased
Question. Instead, the school asks the first volunteers at its existing lunchtime sports club. Is this a reliable way to find the whole school's opinion about the new lunchtime club?
Plan. Compare who can enter the sample with the population in the question.
Pupils already attending a lunchtime club may be more interested in another club. Pupils who go home at lunchtime or prefer other activities are less likely to be included. Volunteering may also favour pupils with strong opinions.
Answer. The sample is liable to bias; randomly selecting from the complete roll would be more suitable.
Check. Both methods ask people. Increasing the number of existing club volunteers would still leave the same selection problem.
Random sampling can produce different results by chance: this is sampling variation, not automatically evidence of bias. Non-response can introduce bias if people who answer differ systematically from those who do not.
Make a criticism specific
“The sample is biased” names a problem but does not explain it. Identify the group favoured or missing, and connect that group to the question being investigated.
Apply that reasoning to a different school survey.
Questionnaire design
Fair selection cannot repair an unclear question. Respondents should understand the same question and be able to give their actual answer.
A fair question
A useful questionnaire question is neutral, clear and about one idea at a time. State any necessary time period and units. Response options should not overlap and should cover the possible answers.
Avoid leading language such as “excellent” or “surely”. Avoid asking two things at once: someone may like the food but dislike the prices. Test the questionnaire on a small pilot group to find confusing wording before collecting the main data.
Worked example 3: removing a leading question
Question. Criticise and improve: “Don't you agree that our excellent library should open on Saturdays? Yes / No.”
Plan. Remove words that encourage agreement and allow an uncertain opinion.
“Don't you agree” pushes towards “Yes”, and “excellent” promotes a favourable view of the library. A neutral replacement is:
“Should the school library open on Saturdays? Yes / No / Not sure.”
Answer. Use the neutral replacement with the three response options.
Check. A pupil can disagree or be unsure without contradicting the wording of the question. Only one issue, Saturday opening, is being asked about.
Continue this lesson.
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