Mr Kidman's Classroom
Revise the key ideas
Enquiry cycle
- Question and hypothesis — Start with a question about a defined population and measurable variables. A hypothesis predicts a relationship that appropriate data can support or challenge; a personal opinion alone cannot test it. For example, investigate whether older bicycles tend to sell for less.
- Plan before collecting — Decide the source, sample, recording method, diagrams and calculations before gathering observations. Explain why each choice answers the question. A plan that collects only favourite colours cannot test a claim about journey duration.
- Constraints and safeguards — Time, cost, access, sensitive information and confidentiality can restrict a study. Use informed participation, collect only necessary information, anonymise records and secure them. Plan alternative sources and follow-up for non-response before difficulties arise.
Confidential means restricting who can see private information. Anonymising means removing details that could identify someone. Tell participants what the study involves and how their data will be used before they agree.
- Process and represent — Clean records (check for errors and inconsistent formats), organise tables, draw appropriate graphs and calculate suitable summaries. A spreadsheet automates arithmetic but cannot decide whether a sample or chart is suitable; check formulas, ranges, labels and outputs yourself.
- Interpret in context — Explain what the evidence suggests about the original hypothesis, with numbers, units and any limits on the conclusion. Describe uncertainty, unusual observations and the population to which the result can reasonably apply; a sample result is not a universal proof.
- Evaluate and refine — Identify limitations, explain their likely effect and propose a specific improvement. Communicate for the intended audience with labelled displays and concise conclusions. Retest or refine the question when evidence reveals a weakness: the cycle is iterative: stages are repeated to improve the investigation.
An iterative statistical enquiry. Original illustrative diagram; numerical datasets are fictional worked examples. Enlarge diagram - Authentic enquiry — For a full investigation choose a real sourced dataset or ethical primary collection with your teacher. Record the source, date, population and methods. Worked examples here illustrate techniques; they do not represent your own collected evidence.
Data and variables
- Qualitative and ordinal — Qualitative data describe categories, such as travel mode. Ordinal categories have a meaningful order, such as poor, fair and good, but equal gaps are not implied. Assigning category codes 1, 2 and 3 does not make their differences measured quantities.
- Discrete and continuous — Quantitative data are numerical. Discrete data have separate possible values, such as a count of customers; continuous data are measurements, such as mass, that can take any value in an interval. Rounding a mass to whole grams does not change the underlying variable to discrete.
- Raw and grouped — Raw data are individual recorded values. Grouping values into classes makes patterns easier to see but loses exact observations. Use non-overlapping classes covering the possible range: 10 ≤ x < 20 includes 10 but excludes 20; its width is 10.
- Bivariate roles — Bivariate data record two variables for the same item, such as age and sale price for each bicycle. Put the explanatory variable on the horizontal x-axis and response on the vertical y-axis. Their roles express the investigation, not automatic proof of causation.
The explanatory variable is used to help explain changes, here bicycle age. The response is the outcome measured, here sale price. Causation means one variable causing a change in another.
- Primary and secondary — Primary data are collected for the current investigation; secondary data were already collected for another purpose. Primary collection can fit the question but costs time. Secondary data can be extensive but may use different definitions, dates, sampling or precision; acknowledge the source.
- Merging categories — Combining rare travel modes as other simplifies a display but hides distinctions. Preserve relevant categories for the hypothesis, explain regrouping and check that totals are unchanged. Use original data when an exact value is needed rather than trying to reconstruct exact observations from a grouped estimate.
Higher — multivariate data
- Several variables — Multivariate records contain more than two variables for each item, such as age, price, condition and brand of a bicycle. Extra variables can help explore confounding explanations; inspecting pairwise plots still does not establish a causal effect.
A confounding variable is related to both variables under study and can give an alternative explanation for their apparent relationship. Pairwise plots show just two variables at a time.
