Investigating the OCR Large Data Set

The four data sets concern travel to work and age structure, each in 2001 and 2011. Read the workbook information sheet for category definitions, the population covered and the geographical units. The travel population is not automatically the whole resident population.

A row summarises an area. A count in an age band or travel category is aggregated information, not one person’s measurement. Treating rows as individuals changes the question completely.

Travel mode is recorded for the longest part of the usual journey to work by distance. Someone who drives to a station and then takes a much longer train journey is not counted once under each mode. Distinguish a person’s usual main mode from every mode used.

For comparisons across years, check that geography, categories and eligibility definitions are comparable. A change in a raw count may reflect population size or classification, as well as a change in behaviour.

To compare the prevalence of cycling in two authorities, divide each cycle count by the matching eligible travel total. Comparing counts alone favours larger areas.

A proportion is $\dfrac{\text{category count}}{\text{relevant total}}$. Multiply by 100 for a percentage. Keep the numerator and denominator from the same year, area and population definition.

The unweighted mean of authority percentages describes a typical authority. Combining all category counts and dividing by all eligible totals describes a typical person in the combined population. Those are different summaries.

Percentage change in a count is $100\dfrac{\text{new}-\text{old}}{\text{old}}$. A change from 10% to 15% is 5 percentage points, and a 50% relative increase in the percentage. State which quantity you calculated.

Do not interpret a change in an authority total as a change in every resident’s behaviour. The people in the area can change between censuses. These are snapshots, not a tracked panel of the same individuals.

Age is recorded at last birthday. A band labelled 20–24 represents ages from 20 up to, but not including, 25 when treated as a continuous class; its width is 5 years. Always inspect the actual band definitions.

For a histogram use $\text{frequency density}=\dfrac{\text{frequency}}{\text{class width}}$. Unequal widths mean bar height cannot simply equal the count. Area represents frequency.

Grouped means use class midpoints and are estimates because the individual ages are unknown. An open-ended oldest-age band needs special care: it has no finite width or midpoint unless a modelling assumption is supplied.

Travel modes are categories. Use a bar chart or a comparison of proportions for them, rather than a histogram with invented numerical widths.

Start with a specific question, such as whether authorities with higher public-transport shares have lower car shares. Define the year, eligible population, included categories and any exclusions before calculating.

Keep an untouched copy of the source data. In a working sheet, retain area identifiers, create category totals and proportions in new columns, and check that valid mutually exclusive category shares sum to about 1. Investigate discrepancies rather than deleting rows silently.

Draw a scatter diagram, identify unusual points and possible subgroups, and use appropriate summaries. A negative association between shares that are parts of the same total may partly arise from the shared denominator. It does not establish that changing one causes the other.

For sampling authorities, assign each eligible row a unique identifier. Generate random identifiers without replacement and record the sample and method. Repeated samples show how conclusions vary. Sampling equal numbers of authorities does not make every person equally likely to be selected.

Finish with a conclusion at the right level: describe the areas and years analysed, state a limitation, and suggest what additional information would test your explanation. Historical census associations alone do not establish present-day commuting patterns.