How do you plan, carry out and communicate a complete statistical investigation?
Conduct a statistical investigation that draws together the skills of the course: pose a question, plan and collect data, select and apply appropriate analysis, and communicate justified conclusions with their limitations.
An overview of the statistical investigation in SQA Advanced Higher Statistics: how the skills of design, analysis and inference are combined to pose a question, collect and analyse data, and communicate justified conclusions with their limitations, as examined in the question papers.
Reviewed by: AI editorial process; not yet individually human-reviewed
Have a quick question? Jump to the Q&A page
Jump to a section
What this dot point is asking
A statistical investigation is where the whole course comes together. Rather than a single technique, the SQA asks you to run the full cycle: turn a real question into a statistical one, plan and collect suitable data, choose and apply the right analysis, and communicate a justified conclusion with its limitations. The investigation skill is assessed through the question papers, where you must select methods and interpret results in context rather than simply execute a named calculation.
The investigation cycle
Every investigation moves through the same four stages, and a good answer shows each one explicitly.
- Pose the question. Translate a real-world question into a statistical one with clear hypotheses or a quantity to estimate, identifying the population and the variables involved.
- Plan and collect. Decide on a sampling method (simple random, systematic or stratified) or an experimental design (with control, randomisation, replication and blocking), so the data can actually answer the question without bias.
- Analyse. Explore the data first, then select the technique that matches the question and the data type, and check that its assumptions are reasonable before applying it.
- Communicate. State the conclusion in the context of the original question, in language a non-specialist can follow, and acknowledge the limitations.
Choosing the right analysis
The single most examined skill is matching the analysis to the situation, because the question papers deliberately present unfamiliar contexts.
Communicating conclusions
Communication is explicitly examinable: the spec asks you to communicate conclusions reached on the basis of statistical analysis.
Try this
Q1. An investigator has paired before-and-after measurements on the same individuals. Name the analysis that exploits the pairing. [1 mark]
- Cue. A paired t-test (or, if normality is doubtful, a Wilcoxon signed-rank test), because the pairing removes between-individual variation.
Q2. State why a conclusion should always include the study's limitations. [1 mark]
- Cue. Because the validity of any statistical conclusion depends on the sampling and the test's assumptions, and significance does not establish importance or causation, so limitations make the conclusion honest and usable.
Exam-style practice questions
Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
AH style: choose analysis3 marksAn investigator wants to know whether a new teaching method changes mean test scores. They have scores for a group taught the new way and a separate group taught the old way. Outline the steps of the investigation and name a suitable analysis.Show worked answer →
State the question as testable hypotheses: that the two population mean scores are equal against that they differ (1 mark).
Plan and check the data: confirm the two groups are independent and consider whether the scores are approximately normal, which determines whether a parametric test is appropriate (1 mark).
Select and justify the analysis: a two-sample (independent) t-test compares the means; if normality is doubtful, a non-parametric Mann-Whitney test is the alternative. Conclude in context and note limitations such as how the groups were formed (1 mark). Markers reward the hypotheses, the planning and assumption check, and a justified choice of test.
AH style: communicate3 marksAfter a hypothesis test gives a p-value of at the level, write a conclusion in context for a non-specialist, and state one limitation that should accompany it.Show worked answer →
Since the p-value is less than the significance level , reject : there is significant evidence at the level of a real effect, stated in the context of the study (for example "the new fertiliser gives a higher mean yield") (1 mark).
Communicate it plainly for a non-specialist: the result is unlikely to be due to chance alone, though it does not prove a large or important effect, only a detectable one (1 mark).
State a limitation: for example the conclusion depends on the sample being representative and the test's assumptions holding, and statistical significance is not the same as practical importance (1 mark). Markers reward a contextual conclusion, clear communication and a sensible limitation.
Related dot points
- Describe and apply the main sampling methods, including simple random, systematic and stratified sampling, distinguish a sample from a population and a statistic from a parameter, and explain how a poor sampling method introduces bias.
A focused answer to the SQA Advanced Higher Statistics sampling content: the difference between a population and a sample and a parameter and a statistic, simple random, systematic and stratified sampling, how to carry each out, and how a poor sampling frame or method introduces bias.
- Calculate point estimates of a population mean and variance, construct and interpret confidence intervals for a population mean using the normal and Student's t-distributions, and construct a confidence interval for a population proportion.
A focused answer to the SQA Advanced Higher Statistics estimation content: point estimates of the population mean and variance, confidence intervals for a mean using the normal distribution and Student's t-distribution, the role of degrees of freedom, and confidence intervals for a population proportion.
- Set up null and alternative hypotheses, choose a significance level, compute and use a test statistic and p-value, decide between one- and two-tailed tests, identify the critical region, and distinguish Type I and Type II errors.
A focused answer to the SQA Advanced Higher Statistics hypothesis testing framework: forming null and alternative hypotheses, the significance level, the test statistic, the p-value and critical region, one- and two-tailed tests, and Type I and Type II errors.
- Describe the principles of experimental design, distinguish observational studies from designed experiments, identify sources of bias, and explain control, randomisation, replication and blocking when planning data collection.
A focused answer to the SQA Advanced Higher Statistics experimental design content: the difference between observational studies and designed experiments, control, randomisation, replication and blocking, the types of variable, and the common sources of bias that invalidate conclusions.