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Random numbers

Introduction

There are many occasions when you need to select objects, study plots or just numbers at random. A common misconception among students is that 'haphazard' selection is the same as random selection, when in fact if is liable to all kinds of biases. For example, students doing a visitor satisfaction survey at a national park are likely to approach people who look happy rather than grumpy - and the happy ones all turn out to be satisfied!

Random number tables and software that generates random numbers (or usually pseudo-random numbers) don't quite catch the intuitive concept of randomness. Here are some techniques which do.

Lucky draw

Chips with the weights of a population of squirrels, which are drawn at random from a bag.

If your sampling universe is reasonably small, create a card for each, shuffle and draw. In the picture, I've written the weights of 100 squirrels on plastic chips and students each draw a sample of 5 'squirrels' and calculate the mean of their sample. We then compare the sample means with the 'real' mean of all 100 squirrels. You might be able to do the same with, say, the heights of all the first-year engineering students in your school.

These samples are obviously random. But the method becomes unworkable if the sampling universe is big. It's better to number each item and then draw random numbers.

Lottery balls

Numbered ping-pong balls in a black bag A good way to get numbers which are intuitively random is to draw numbered balls from a bag. This is a familiar and accepted way of selecting lottery winners! For big numbers, it's better to have a bag of balls for each digit:
   1 bag with 0, 1, 2, 3, ...9
   a 2nd bag with 00, 10, 20, ... 90
   a 3rd bag with 000, 100, 200, ... 900 and so on.
(If you use just one set of 10 balls and draw several times to get a series of digits, remember to replace the balls between each draw, otherwise you'll miss 11, 22, 33, etc!)

Rolling dice

Bags of numbered balls get a bit bulky and aren't really suitable for use by the students. Numbered dice are a much neater solution - provided you use 10-sided dice in place of the usual 6-sided variety! A possible snag here is that fair polyhedral dice are not easy to make; so we'll all have to buy! Koplow Games make 10-sided dice showing 0-9, 00-90, 000-900 and 0000-9000. Koplow don't retail, but I got mine by mail order from the GameStation in the USA.

A few polyhedral pice Once you start thinking out of the cube, other possibilities arise - the picture shows a 30-sided die, ideal for selecting which day of the month to do a survey.

(I got the idea of using dice from Gelman and Nolan, 2002, Teaching statistics, OUP (page 103), but they use 20-sided dice with each digit, 0-9, marked twice. Koplow also make those, but I prefer the 10-sided dice.)