Читать книгу Statistics in Nutrition and Dietetics - Michael Nelson - Страница 28

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,⁷ with no ambiguity. If our aim is to evaluate the effect of a new diet on reducing cholesterol levels in serum, we need to say specifically that the new diet will ‘lower’ cholesterol, not simply that it will ‘affect’ or ‘change’ it. If we are comparing growth in two groups of children living in different circumstances, we need to say in which group we think growth will be better, not simply that it will be ‘different’ between the two groups.

The hypothesis that we formulate will determine what we choose to measure. If we take the time to discuss the formulation of our hypothesis with colleagues, we are more likely to develop a robust hypothesis and to choose the appropriate measurements. Failure to get the hypothesis right may result in the wrong measurements being taken, in which case all your efforts will be wasted. For example, if the hypothesis relates to the effect of diet on serum cholesterol, there may be a particular cholesterol fraction that is altered. If this is stated clearly in the hypothesis, then we must measure the relevant cholesterol fraction in order to provide appropriate evidence to test the hypothesis.

No finite amount of experimentation can ‘prove’ an exact hypothesis.

Suppose that we carry out a series of four studies with different samples, and we find that in each case our hypothesis is ‘proven’ (our findings are consistent with our beliefs). But what do we do if in a fifth study we get a different result which does not support the hypothesis? Do we ignore the unusual finding? Do we say, ‘It is the exception that proves the rule?’ Do we abandon the hypothesis? What would we have done if the first study which was carried out appeared not to support our hypothesis? Would we have abandoned the hypothesis, when all the subsequent studies would have suggested that it was true?

There are no simple answers to these questions. We can conclude that any system that we use to evaluate a hypothesis must take into account the possibility that there may be times when our hypothesis appears to be false when in fact it is true (and conversely, that it may appear to be true when in fact it is false). These potentially contradictory results may arise because of sampling variations (every sample drawn from the population will be different from the next, and because of sampling variation, not every set of observations will necessarily support a true hypothesis), and because our measurements can never be 100% accurate.

A finite amount of experimentation can disprove an exact hypothesis.

It is easier to disprove something than prove it. If we can devise a hypothesis which is the negation of what we believe to be true (rather than its opposite), and then disprove it, we could reasonably conclude that our hypothesis was true (that what we observe, for the moment, seems to be consistent with what we believe).

This negation of the hypothesis is called the ‘null’ hypothesis. The ability to refute the null hypothesis lies at the heart of our ability to develop knowledge. A good null hypothesis, therefore, is one which can be tested and refuted. If I can refute (disprove) my null hypothesis, then I will accept my hypothesis.

A theory which is not refutable by any conceivable event is non‐scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice. [1, p. 36]

Let us take an example. Suppose we want to know whether giving a mixture of three anti‐oxidant vitamins (β‐carotene, vitamin C, and vitamin E) will improve walking distance in patients with Peripheral Artery Disease (PAD), an atherosclerotic disease of the lower limbs. The hypothesis (which we denote by the symbol H₁) would be:

H₁: Giving anti‐oxidant vitamins A, C, and E as a dietary supplement will improve walking distance in patients with PAD.⁸

The null hypothesis (denoted by the symbol H₀) would be:

H₀: Giving anti‐oxidant vitamins A, C, and E as a dietary supplement will not improve walking distance in patients with PAD.

H₀ is the negation of H₁, suggesting that the vitamin supplements will make no difference. It is not the opposite, which would state that giving supplements reduces walking distance.

It is easier, in statistical terms, to set about disproving H₀. If we can show that H₀ is probably not true, there is a reasonable chance that our hypothesis is true. Box 1.2 summarizes the necessary steps. The statistical basis for taking this apparently convoluted approach will become apparent in Chapter 5.