Sampling and Data Interpretation

This lesson covers the second part of AQA A-Level Business topic 3.3.2, focusing on sampling methods, correlation, confidence intervals, and extrapolation. Understanding these concepts is essential for interpreting market research data and evaluating the reliability of business decisions based on that data.

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Sampling

Key Definition: Sampling is the process of selecting a subset of individuals from a larger population in order to make inferences about the whole population. A sample is a group chosen to represent the target population.

Businesses cannot survey every potential customer (a census would be too expensive and time-consuming), so they select a sample. The quality of the research depends critically on the sampling method used.

Why Sample?

Reason	Explanation
Cost	Surveying the entire population is prohibitively expensive
Time	A sample can be researched much faster than the whole population
Practicality	It may be impossible to identify or contact every member of the population
Sufficiency	A well-chosen sample can provide reliable results — it does not need to include everyone

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Sampling Methods

1. Random Sampling

Key Definition: Random sampling is a method where every member of the target population has an equal chance of being selected.

How it works: Each member of the population is assigned a number, and a random number generator (or random number table) is used to select the sample.

Strengths:

• Eliminates selection bias — every individual has an equal probability of selection
• Results can be generalised to the whole population with known confidence levels
• Statistical tests (e.g., confidence intervals) are valid

Weaknesses:

• Requires a complete and accurate list of the population (a sampling frame), which may not exist
• May produce an unrepresentative sample by chance (e.g., all respondents may happen to be from one demographic group)
• Can be expensive if the population is geographically dispersed

Example: A national retailer wanting to survey its loyalty card holders could use random sampling by randomly selecting 2,000 card numbers from its database of 5 million members.

2. Stratified Sampling

Key Definition: Stratified sampling involves dividing the population into distinct subgroups (strata) based on a shared characteristic (e.g., age, gender, income, region) and then randomly sampling from each stratum in proportion to its size in the population.

How it works:

1. Identify the relevant strata (e.g., age groups: 18-24, 25-34, 35-44, 45-54, 55+)
2. Determine the proportion of the population in each stratum
3. Randomly sample from each stratum in the same proportion

Age Group	% of Population	Sample Size (from 1,000)
18-24	15%	150
25-34	22%	220
35-44	20%	200
45-54	23%	230
55+	20%	200

Strengths:

• Ensures representation of key subgroups — more representative than simple random sampling
• Reduces sampling error compared to random sampling (especially when strata differ significantly)
• Allows analysis of subgroups (e.g., comparing attitudes of 18-24 year olds with those of 55+)

Weaknesses:

• Requires prior knowledge of the population structure (which strata exist and their proportions)
• More complex and time-consuming to organise than random sampling
• If the wrong strata are chosen, the benefits are lost

Real-World Example: Ipsos and YouGov (major UK polling firms) use stratified sampling in political and consumer opinion polls. They stratify by age, gender, region, and social class to ensure their samples mirror the UK population. This is why their polls of 1,500-2,000 people can reasonably predict the behaviour of 48 million voters.

3. Quota Sampling

Key Definition: Quota sampling involves setting quotas for specific subgroups (e.g., "interview 50 males aged 18-30 and 50 females aged 18-30") and then using non-random methods to fill the quotas.

How it works: The researcher is given targets (quotas) for each subgroup and selects respondents who meet the criteria until the quota is filled. The selection within each quota is not random — the researcher chooses who to approach.

Strengths:

• Cheaper and quicker than random or stratified sampling — no sampling frame needed
• Ensures representation of key groups (like stratified sampling)
• Widely used in commercial market research because of its practicality

Weaknesses:

• Selection bias — the researcher chooses who to approach, so the sample may not be truly representative. Interviewers on a high street tend to approach people who look approachable, excluding those in a hurry, those with disabilities, or those who look unfriendly.
• Not a probability sample — statistical tests (confidence intervals, significance tests) are technically not valid
• Results may not be generalisable to the wider population

Real-World Example: A cosmetics company conducting high-street research might set quotas of 100 women aged 18-30, 100 women aged 31-50, and 100 women aged 51+. Interviewers would approach women in each age group until the quotas were filled. This is quick and practical but introduces bias — women shopping on a Tuesday afternoon may differ systematically from those who shop on a Saturday evening.

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Comparison of Sampling Methods

Criterion	Random	Stratified	Quota
Representativeness	Moderate (may be unrepresentative by chance)	High (ensures subgroup representation)	Moderate (quotas ensure group coverage but selection is biased)
Cost	High	High	Low
Speed	Slow	Slow	Fast
Bias risk	Low (if sampling frame is complete)	Low	High (interviewer selection bias)
Requires sampling frame	Yes	Yes	No
Statistical validity	High	High	Low (not a probability sample)

Exam Tip: When evaluating research findings, always consider the sampling method. If a business claims "80% of customers prefer our product," ask: How were respondents selected? Was the sample random or quota-based? How large was the sample? Could selection bias have influenced the result?

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Correlation

Key Definition: Correlation measures the strength and direction of the relationship between two variables. It does not prove that one variable causes the other.