Statistical terms, types of data and surveys

Last time

Before we start: last time, in Sampling methods, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Where statistics begins

Every statistical study starts by deciding what to measure and whom to ask. This lesson covers the key terms, the types of data, and how surveys and questionnaires are designed, and how to improve a sample so that its results can be trusted.

Statistical terms

The population is every member of the group being studied; a census collects data from all of them. A sample is part of the population; a survey collects data from a sample. A sampling frame is the list the sample is chosen from. Bias is a systematic error that pushes results one way, such as asking only the people who are easiest to reach.

Types of data

Qualitative, or categorical, data are descriptions, such as colour or mode of transport. Quantitative data are numbers. Discrete data take separate values, such as the number of children; continuous data are measured, such as height or time. Primary data are collected by the researcher; secondary data were collected by someone else, such as government statistics.

Census or sample?

A census gives complete information, but it is expensive and slow, and impossible when testing destroys the item. A sample is cheaper and quicker, but its results may differ from the population's: sampling error. For a large population, a well-chosen sample is usually the sensible choice.

Designing a questionnaire

Questions should be clear, short and relevant, and not personal or embarrassing. An open question lets people answer in their own words: rich answers, but hard to analyse. A closed question gives options: easy to analyse, but it may miss views. A leading question pushes people towards an answer, such as: do you agree the new hours are better? That creates bias. Answer boxes must not overlap and should cover every possible answer.

Carrying out a survey

A pilot survey tests the questionnaire on a few people first, to find unclear questions. Interviews get a high response and allow questions to be explained, but they cost more and the interviewer may influence the answers. Postal and online surveys are cheap and reach many people, but response rates are low and those who reply may not be typical.

Improving a sample

Use a larger sample: its results vary less from one sample to another. Choose at random, from a complete sampling frame, so that no group is left out. Spread the sample across the whole population, its places and times, or stratify it so that each group is represented.

Which type of data?

Examples of each type of data.

Mistakes that lose marks

Mistake one: calling a count, such as the number of people, continuous. Mistake two: writing a leading question, or answer boxes that overlap. Mistake three: saying a larger sample removes bias. It reduces random variation, but a biased method stays biased. The fix: the exact term, a fair question, and a reason.

The full-marks tip

The full-marks tip: use the exact terms: population, sampling frame, census, bias. When asked to improve a survey, name the problem and say how your change fixes it.

On one card

So, on one card: data and surveys. Keep it for revision.