Random Samples

The condition is about the method

You cannot look at a finished sample and tell whether it is random. Sixty pupils drawn properly at random might, by chance, contain forty boys; sixty chosen by a teacher who deliberately balanced the sexes would look tidier and would not be random at all. The word describes how the selection was made, not how the selection turned out.

That is why exam questions describe a procedure and ask you to judge it. The test to apply is always the same: did every member of the population have the same chance of being chosen? If some group was harder to reach, less likely to reply, or simply not on the list used, the answer is no, and the sample is biased towards whoever was easy to reach.

A method that passes

Number every member of the population, generate random numbers with a calculator, a spreadsheet or a table, and take the members whose numbers come up, discarding repeats. Written as an exam answer it should include all three steps — the numbering, the random generation, and what happens on a repeat — because that is where the marks sit.

The step people skip is the first one, and it is the one that carries the condition. You need a complete list of the population before you can number it: the full register, not the pupils present today. Sampling from an incomplete list produces a perfectly random sample of the wrong population, which is a subtler error than an obviously lazy method and just as wrong.

Methods that fail, and the exact reason

Naming a method as "not random" earns nothing on its own; the mark is for saying who gets left out. Each of these is a real school-survey method with a specific group it under-represents.

Methods like these have a collective name — convenience sampling — and the reason they persist is that their results look perfectly reasonable. Nothing in a set of sixty replies announces that the people who would have answered differently were never asked. The flaw is in the procedure and nowhere in the data, which is why the procedure has to be described honestly in the write-up.

• Asking your friends — people you know are like you in age, subjects and interests, so their answers are not the school's
• Standing at the gate at 08:00 — misses everyone who arrives by late bus, and over-samples pupils who live nearby
• Putting the survey online and taking the first 60 replies — over-samples pupils who check messages often and those who feel strongly about the topic
• Taking the first 60 names on an alphabetical register — surnames cluster by family and by community, so siblings and some groups are over-represented
• Asking every pupil in one class — a class shares a timetable, a set option and often an ability band, so it is not a miniature of the school