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Deductive logic argues from the general to the particular. This type of logic involves a priori reasoning. This means that we think we know the outcome of our observations or experiment even before we start. What is true generally for the population⁴ will be true for each individual within the population. Here is a simple example:

All animals die.

My dog is an animal.

My dog will die.

This type of logic is very powerful for testing to see if our ideas are ‘true’. The logic is: if ‘a’ is true, then ‘b’ will be the outcome. If the evidence is robust (i.e. as good a measure as we can get, given the limitations of our measuring instruments) and shows a clear relationship, it should stand up to criticism. And as we shall see, it provides the basis for the statistical inferences based on the tests described in later chapters.

There is a problem, however. The example above about my dog is relatively simple and straightforward. We can define and measure what we mean by an ‘animal’, and we can define and measure what we mean by ‘death’. But suppose we want to understand the impact of vitamin A supplementation on risk of morbidity and blindness from measles in children aged 1 to 5 years living in areas where vitamin A deficiency is endemic. Defining and measuring variables in complex biological systems is much harder (particularly in the field of nutrition and dietetics). It becomes harder to argue that what is true generally for the population will necessarily be true for each individual within the population. This is for two reasons. First, we cannot measure all the factors that link ‘a’ (vitamin A deficiency) and ‘b’ (morbidity and blindness from measles) with perfect accuracy. Second, individuals within a population will vary from one to the next in terms of their susceptibility to infection (for a wide range of reasons) and the consequent impact of vitamin A supplementation.

For deductive logic to operate, we have to assume that the group of subjects in whom we are conducting our study is representative of the population in which we are interested. (The group is usually referred to as a ‘sample’. Ideas about populations and samples are discussed in detail in Chapter 2.) If the group is representative, then we may reasonably assume that what is true in the population should be evident in the group we are studying. There are caveats to this around the size of the sample and the accuracy of our measurements, which will be covered in Chapters 2 and 12.