The Statistical Enquiry Cycle: Reviewing the Whole Investigation
This lesson covers the general principles of the Statistical Enquiry Cycle that apply to all students. The specific investigation, data and methods your class used in your coursework or class project will be different — refer to your teacher's notes alongside this lesson.
The Statistical Enquiry Cycle
Statistics is not just a collection of techniques — it is a systematic way of answering questions about the world. The Statistical Enquiry Cycle (SEC) is the overarching framework that ties all the individual techniques together. Each of your two exam papers ends with a question that integrates all five stages of the SEC, so understanding the cycle thoroughly is essential.
The five stages are:
- Stage 1: Initial Planning — Define a question or hypothesis to investigate. Decide what data to collect, how to collect and record it, and how to process and represent it. Justify each decision.
- Stage 2: Data Collection — Collect the data using the chosen method (primary or secondary). Recognise constraints, acknowledge sources, and be aware of sensitivity issues.
- Stage 3: Data Processing and Presentation — Organise and clean the data. Choose appropriate graphs and statistical measures. Use technology to automate processing where appropriate.
- Stage 4: Interpretation of Results — Analyse diagrams and calculations. Draw conclusions that relate back to the original question or hypothesis. Make inferences or predictions and discuss reliability.
- Stage 5: Evaluation and Review — Identify weaknesses in approach or representation. Suggest improvements. Refine the process to investigate further.
The five stages of the SEC: (1) Initial Planning, (2) Data Collection, (3) Data Processing and Presentation, (4) Interpretation of Results, (5) Evaluation and Review. Both exam papers end with a SEC question that tests your ability to link all five stages.
Stage 1 in Detail: Initial Planning
Good planning makes all subsequent stages easier. At Stage 1, you must define a testable hypothesis, decide what data you need (and why), choose your sampling method (and justify it), and plan how you will process the data. Decisions made at this stage affect every other stage. A vague hypothesis leads to ambiguous data; a biased sampling method undermines any conclusion.
Stage 4 in Detail: Interpretation of Results
Interpretation is where your statistics turn into meaning. You must analyse the graphs and measures you calculated, reach conclusions that relate to your original question, and discuss the reliability of your findings. Conclusions must be in context — not “the mean is higher” but “students who revised more than five hours scored higher on average, with a mean of 72% compared to 58% for those who revised fewer than two hours.”
Reliability of findings depends on several factors: the size of the sample, how representative it is, whether the data collection method was valid, and whether there are alternative explanations for the pattern seen. Always consider: could a lurking variable explain this result? Could sampling bias have inflated or deflated the finding?
Stage 5 in Detail: Evaluation and Review
Evaluation is not about listing everything that went well — it is about identifying specific weaknesses and suggesting specific improvements. A strong answer shows that you understand why a weakness matters, not just that something could have been done differently.
The structure that scores highest in evaluation questions: (1) identify a weakness at a specific SEC stage, (2) explain why that weakness undermines the conclusion, (3) suggest a specific improvement. This three-part structure applies whether you are evaluating a fictional enquiry or your own class investigation.
The 8-mark SEC Critique question (one of the highest-mark questions in each paper) presents a fictional investigation scenario and asks you to evaluate it. The structure that scores Mastering is:
Step 1: Identify a weakness at one SEC stage (e.g. Stage 2 — Data Collection: “The investigator used opportunity sampling from one shopping centre.”)
Step 2: Explain why this weakness undermines the conclusion: “This means the sample is likely biased towards shoppers at that location, who may differ systematically in their habits from the wider population. The conclusion therefore cannot be generalised.”
Step 3: Suggest a specific improvement: “A stratified random sample drawn from a complete sample frame of the target population would reduce this bias.”
Step 4: Repeat for a second SEC stage (e.g. Stage 1 — Planning: “The hypothesis is vague and does not specify measurable variables.”)
Mastering responses identify weaknesses at TWO different SEC stages and follow the three-step structure for each. Students who describe what the investigation did rather than evaluate its limitations score Emerging or Developing only.
Target Audience and Communication
Stage 4 also involves communicating your findings clearly to a target audience. A report written for a school governor has different requirements from one written for a science journal. The specification expects you to consider: is the level of technical language appropriate? Are the graphs and tables clearly labelled? Do the conclusions use plain, accessible language?
Good communication means presenting conclusions clearly and concisely, using appropriate visualisations, and not overloading the reader with unnecessary technical detail. Poor communication — even when the statistics are correct — means the findings fail to reach the people who need to act on them.
Sample Size, Reliability and Replication
The specification makes an important point about sample size: replication — the ability of another researcher to reach a similar conclusion by repeating the study — is more likely when the sample is large and representative. A finding based on 10 participants is much less replicable than one based on 1,000.
A larger sample reduces the impact of random variation on the results. In a very small sample, one or two unusual respondents can dominate the findings. In a larger sample, their influence is diluted. This is why increasing sample size is one of the most commonly recommended improvements in evaluation questions.
Distribution of Sample Means (Higher)
When you take many different samples from the same population and calculate the mean of each, those sample means form their own distribution. The specification requires you to know, at an intuitive level, that a set of sample means is more closely distributed (less spread out) than the individual values from the same population. This means the mean of any given sample is a better estimate of the population mean than any single individual value from the population would be.
Why? Individual values in a population are spread widely by natural variability. But when you take a mean of several values, the high values and low values in the sample tend to cancel each other out, pulling the sample mean back towards the centre. The larger the sample, the more this cancellation effect reduces the spread of sample means.
You do not need to use any formal notation for this idea — a clear verbal explanation in context is sufficient. If asked in an exam: “The sample means form a tighter distribution than the individual values because extreme values within each sample cancel out when averaged.”
The most common reason for losing marks in SEC evaluation questions is describing rather than evaluating. Describing says: “The investigator used opportunity sampling.” Evaluating says: “The use of opportunity sampling means the sample over-represents people who visit shopping centres, which may differ from the wider population in their habits — so the conclusions cannot be generalised.”
Every evaluation point needs three parts: (1) what the weakness is, (2) why it matters for the conclusion, (3) what specific change would fix it. Missing any of these parts limits your mark to Developing at best.
Evaluation structure for full marks: (1) identify the weakness at a named SEC stage, (2) explain why it undermines the conclusion, (3) suggest a specific, actionable improvement. Use this structure for both weaknesses in an 8-mark question.