Statistics in Nutrition and Dietetics. Michael Nelson

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СКАЧАТЬ an influence produces consistent effects in a chosen group of subjects, we are tempted to conclude that the same influences would have similar effects in all subjects with similar characteristics. When we evaluated the results from our observations, we would try to ensure that other factors which might affect the outcome (age, sex, dietary iron intake, dietary inhibitors of iron absorption, etc.) were taken into account.

      1.2.2 Deductive Logic

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.

      Examples of Research Designs that Depend on Deductive Logic

      Intervention trials are designed to prove that phenomena which are true in the population are also true in a representative sample drawn from that population.

      Compare the relative impact of two iron preparations in the treatment of anaemia.

      This may sound similar to the statement that was made under ‘Experimental Studies’. The two statements are different, however. In the intervention trial, we would try to ensure that the two groups in which we were comparing treatments were similar to each other and similar to the population from which they were drawn. In the experimental study, we chose a group of subjects, measured the exposure and outcome and other characteristics of the group, and assumed that if the outcome was true in that group, it would be true in the population with similar characteristics. These differences in approach and logic are subtle but important.

      In practice, the aim of most studies is to find evidence which is generalizable to the population (or a clearly defined subgroup). The relationship between the type of logic used and the generalizability of the findings is discussed below. The limitations of inductive logic and their resolution are discussed lucidly by Popper [1, pp. 54–55].

1.3 EXPERIMENTATION AND RESEARCH DESIGN

      Here is a quote from ‘The Design of Experiments’ by Sir Ronald Fisher [2]:

       Men5 have always been capable of some mental processes of the kind we call ‘learning by experience’. Doubtless this experience was often a very imperfect basis, and the reasoning processes used in interpreting it were very insecure; but there must have been in these processes a sort of embryology of knowledge, by which new knowledge was gradually produced.

       Experimental observations are only experience carefully planned in advance, and designed to form a secure basis of new knowledge; that is, they are systematically related to the body of knowledge already acquired, and the results are deliberately observed, and put on record accurately.

      Research usually has one of two main purposes: either to describe in as accurate and reliable a way as possible what one observes, or to test an idea about what one believes to be true. To undertake research, be it quantitative or qualitative, a systematic process of investigation is needed. This involves formulating clear ideas about the nature of the problem to be investigated, designing methods for collecting information, analyzing the data in an appropriate way, and interpreting the results.

      1.3.1 A Children’s Story

      One of my favourite children’s stories is The Phantom Tollbooth by Norton Juster [3], in which he brilliantly summarizes the purpose of research and statistics. This may seem unlikely, but read on.

      The book tells the story of Milo, a young boy living in an apartment in New York. He is endlessly bored and someone for whom everything is a waste of time. He arrives home after school one day to find a large package sitting in the middle of the living room. (I don’t know where his parents are.) He unpacks and assembles a tollbooth (he lives in America, don’t forget), gets in his electric car, deposits his coin, and drives through the tollbooth into a land of fanciful characters and logical challenges.

      The story is this. The princesses Rhyme and Reason have been banished, and it is his job to rescue them and restore prosperity to the Kingdom of Wisdom. He drives from Dictionopolis (where only words are important) to Digitopolis (where – you guessed it – only numbers are important) to reach the Castle in the Air, where the princesses are held captive. He shares his journey with two companions: a Watchdog named Tock who is very vigilant about paying attention to everything (provided he keeps himself wound up); and the Humbug, ‘a large beetle‐like insect dressed in a lavish coat, striped trousers, checked waistcoat, spats and a derby hat’, whose favourite word is BALDERDASH – the great sceptic.

      On the way to Digitopolis, the road divides into three, with an enormous sign pointing in all three directions stating clearly:

      DIGITOPOLIS

      5 miles

      1 600 rods

      8 800 Yards

      26 400 ft

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