argue about which road to take. The Humbug thinks miles are shorter, Milo thinks half‐inches are quicker, and Tock is convinced that whichever road they take it will make a difference. Suddenly, from behind the sign appears an odd creature, the Dodecahedron, with a different face for each emotion for, as he says, ‘here in Digitopolis everything is quite precise’. Milo asks the Dodecahedron if he can help them decide which road to take, and the Dodecahedron promptly sets them a hideous problem, the type that makes maths pupils have nightmares and makes grown men weep:
If a small car carrying three people at thirty miles an hour for ten minutes along a road five miles long at 11.35 in the morning starts at the same time as three people who have been travelling in a little automobile at twenty miles an hour for fifteen minutes on another road and exactly twice as long as one half the distance of the other, while a dog, a bug, and a boy travel an equal distance in the same time or the same distance in an equal time along a third road in mid‐October, then which one arrives first and which is the best way to go?
They each struggle to solve the problem.
‘I’m not very good at problems’,
admitted Milo.
‘What a shame’, sighed the Dodecahedron. ‘They’re so very useful. Why, did you know that if a beaver two feet long with a tail a foot and half long can build a dam twelve feet high and six feet wide in two days, all you would need to build the Kariba Dam is a beaver sixty‐eight feet long with a fifty‐one foot tail?’
‘Where would you find a beaver as big as that?’ grumbled the Humbug as his pencil snapped.
‘I’m sure I don’t know’, he replied, ‘but if you did, you’d certainly know what to do with him’.
‘That’s absurd’, objected Milo, whose head was spinning from all the numbers and questions.
‘That may be true’, he acknowledged, ‘but it’s completely accurate, and as long as the answer is right, who cares if the question is wrong? If you want sense, you’ll have to make it yourself’.
‘All three roads arrive at the same place at the same time’, interrupted Tock, who had patiently been doing the first problem.
‘Correct!’ shouted the Dodecahedron. ‘Now you can see how important problems are. If you hadn’t done this one properly, you might have gone the wrong way’.
‘But if all the roads arrive at the same place at the same time, then aren’t they all the right way?’ asked Milo.
‘Certainly not’, he shouted, glaring from his most upset face. ‘They’re all the wrong way. Just because you have a choice, it doesn’t mean that any of them has to be right’.
That is research design and statistics in a nutshell. Let me elaborate.
1.4 THE BASICS OF RESEARCH DESIGN
According to the Dodecahedron, the basic elements of research are as shown in Box 1.1:
He may be a little confused, but trust me, all the elements are there.
1.4.1 Developing the Hypothesis
The Dodecahedron: ‘As long as the answer is right, who cares if the question is wrong?’
The Dodecahedron has clearly lost the plot here. Formulating the question correctly is the key starting point. If the question is wrong, no amount of experimentation or measuring will provide you with an answer.
The purpose of most research is to try and provide evidence in support of a general statement of what one believes to be true. The first step in this process is to establish a hypothesis. A hypothesis is a clear statement of what one believes to be true. The way in which the hypothesis is stated will also have an impact on which measurements are needed. The formulation of a clear hypothesis is the critical first step in the development of research. Even if we can’t make measurements that reflect the truth, the hypothesis should always be a statement of what you believe to be true. Coping with the difference between what the hypothesis says is true and what we can measure is at the heart of research design and statistics.
BOX 1.1 The four key elements of research
| Hypothesis | ||
| Design | Statistics | |
| Interpretation |
TIP
Your first attempts at formulating hypotheses may not be very good. Always discuss your ideas with fellow students or researchers, or your tutor, or your friendly neighbourhood statistician. Then be prepared to make changes until your hypothesis is a clear statement of what you believe to be true. It takes practice – and don’t think you should be able to do it on your own, or get it right first time. The best research is collaborative, and developing a clear hypothesis is a group activity.
We can test a hypothesis using both inductive and deductive logic. Inductive logic says that if we can demonstrate that something is true in a particular individual or group, we might argue that it is true generally in the population from which the individual or group was drawn. The evidence will always be relatively weak, however, and the truth of the hypothesis hard to test. Because we started with the individual or group, rather than the population, we are less certain that the person or group that we studied is representative of the population with similar characteristics. Generalizability remains an issue.
Deductive logic requires us to draw a sample from a defined population. It argues that if the sample in which we carry out our measurements can be shown to be representative of the population, then we can generalize our findings from our sample to the population as a whole. This is a much more powerful model for testing hypotheses.
As we shall see, these distinctions become important when we consider the generalizability of our findings and how we go about testing our hypothesis.
1.4.2 Developing the ‘Null’ Hypothesis
In thinking about how to establish the ‘truth’6 of a hypothesis, Ronald Fisher considered a series of statements:
No amount of experimentation can ‘prove’ an inexact hypothesis.
The first task is to get the question right! Formulating a hypothesis takes time. It needs to be a clear, concise statement of what we believe to be true,
