AQA GCSE Statistics

The five stages of the cycle

Statistics is the practice of answering a question with data, and the statistical enquiry cycle is the order in which that work is done. It runs through five stages: the work is planned first, the data is collected, it is processed and presented, the results are interpreted, and the whole enquiry is then evaluated and reviewed. The last stage feeds back into the first, because what is learned from one enquiry usually sharpens the question for the next, which is why it is drawn as a cycle and not as a line.

Every technique in the course sits inside one of these stages. Choosing a sampling method belongs to planning and collection, drawing a histogram or finding a standard deviation belongs to processing, and saying what a correlation coefficient means belongs to interpretation. A piece of statistical work is judged on how well the stages fit together as much as on any single calculation.

Questions and hypotheses

An enquiry begins with a question or a hypothesis. A hypothesis is a statement that can be checked against data, for example "pupils in Year 11 spend more time on homework than pupils in Year 8" or "the price of a used car falls as its age increases". A question such as "how do pupils spend their evenings?" is also a valid start, but it does not say what result would count as an answer, so it is usually turned into one or more hypotheses.

A hypothesis can only be tested by collecting and analysing suitable data. Opinion, anecdote and a single striking example do not test it, because they say nothing about how typical the example is. A good hypothesis also names the variables involved and the group it applies to, since "pupils do more homework" cannot be checked until it is clear which pupils are meant and who they are compared with. A formal null hypothesis is not used at this level; the hypothesis is stated plainly and the data either supports it, contradicts it or is inconclusive.

Deciding what to collect

Once the hypothesis is fixed, the planner decides what data is needed and how it will be recorded. This means answering a short series of practical questions.

1. Which variables are needed, and are they categorical or numerical, discrete or continuous?
2. Who or what is being measured, and how many items are needed?
3. Will the data be collected first-hand (primary) or taken from an existing source (secondary)?
4. How will it be recorded, for instance on a tally sheet, in a questionnaire or straight into a spreadsheet?
5. How will it be processed and displayed, and will that method suit the type of data?

A plan for the processing stage is made before collecting anything. If the hypothesis compares two groups, the data must be recorded in a form that allows the groups to be separated later, and if a scatter graph is intended, both variables must be measured on the same individuals. Collecting data and then discovering that it cannot answer the question is one of the commonest ways for an investigation to fail, and it cannot be put right afterwards.

Reasons should be given for each choice. "A questionnaire" is a method; "a questionnaire because the information is about opinions that cannot be observed" is a justification.

Constraints on an investigation

Real investigations are limited, and a plan has to be realistic about those limits. The main constraints are:

• time, which restricts how much data can be collected and how often it can be collected;
• cost, such as printing, travel, equipment or paying for access to a published dataset;
• ethical issues, such as whether the people involved have agreed to take part, whether they are vulnerable, and whether any harm or embarrassment could follow;
• confidentiality, which covers who will see individual responses and how personal details are stored or removed;
• convenience, which includes who can realistically be reached and what equipment is available.

The constraints often force a compromise. A survey of every household in a town is too costly, so a sample is used. An experiment that would be the best test of a hypothesis may be unethical, so an observational study is used and its weaker conclusions have to be accepted. Naming the constraint and saying how it affects the quality of the results is part of a good plan.

Dealing with problems before they arise

A sound plan expects difficulties and prepares for them in advance, which is called a proactive strategy, so that the investigation is not derailed midway.

Difficulty in identifying the population is one example. If there is no complete list of the people of interest, such as all the customers of a shop, the planner chooses a workable alternative, such as the shop's loyalty card register, and notes that some customers will be missing from it. Non-response is another. People refuse, forget or are absent, so the planner can invite more people than the target sample size, follow up once with a reminder, keep the questionnaire short, and record who did not respond so that the effect on the results can be discussed. An unexpected outcome, such as a result that contradicts the hypothesis or a measuring instrument that fails, is handled by keeping a record of how the data was obtained and by running a pilot study, a small trial that reveals confusing questions or impractical methods before the full collection begins.

Sources of data and sensitivity

When a plan uses secondary data, where it comes from must be acknowledged. Reference publications, official statistics, the internet and the media are all possible sources, and each differs in how far it can be trusted. A government dataset comes with a stated method; a figure quoted on a website without a source may be out of date, selective or wrong. The origin, the date and the method of collection are recorded so that the reader can judge the evidence.

Sensitivity also affects what data is available. People are reluctant to answer honestly about income, health, illegal behaviour or private relationships, and some data is withheld altogether because it could identify individuals. When the content is sensitive the planner may choose an anonymous questionnaire, broader answer bands instead of exact figures, or a different variable that stands in for the one wanted, and then accepts that the data may still be less complete or less honest than data on a neutral subject.

Technology

Technology is used at every stage. Spreadsheets and databases store and organise large data sets, statistical software and calculators produce summary measures and graphs in seconds, and online forms collect responses directly into a table. The advantage of automating processing is speed and freedom from arithmetic slips; the disadvantage is that software produces an output whatever the data is like, so the person using it still has to choose an appropriate diagram or measure and check that the result is sensible.