Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Variability and frequency distributions
- 3 Estimation, standard errors and confidence limits
- 4 The basic idea of a significance test
- 5 Simple significance tests based on the normal distribution
- 6 The use of t-tests for small samples
- 7 Contingency tables and χ2
- 8 χ2-tests of goodness-of-fit and homogeneity
- 9 The correlation of measurements
- 10 Regression analysis
- 11 Simple experimental design and the analysis of variance
- 12 Introduction to factorial experiments
- 13 Random samples and random numbers
- 14 Partial correlation and multiple regression
- 15 Non-parametric and distribution-free tests
- 16 Notes on numerical calculation, calculators and computers
- Suggestions for more advanced reading
- Summary of statistical formulae
- Appendix tables
- Index
2 - Variability and frequency distributions
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Variability and frequency distributions
- 3 Estimation, standard errors and confidence limits
- 4 The basic idea of a significance test
- 5 Simple significance tests based on the normal distribution
- 6 The use of t-tests for small samples
- 7 Contingency tables and χ2
- 8 χ2-tests of goodness-of-fit and homogeneity
- 9 The correlation of measurements
- 10 Regression analysis
- 11 Simple experimental design and the analysis of variance
- 12 Introduction to factorial experiments
- 13 Random samples and random numbers
- 14 Partial correlation and multiple regression
- 15 Non-parametric and distribution-free tests
- 16 Notes on numerical calculation, calculators and computers
- Suggestions for more advanced reading
- Summary of statistical formulae
- Appendix tables
- Index
Summary
We have seen in Chapter 1 how considerable natural variation is inherent in the subject-matter of practically all biological and medical work. It cannot be effectively disposed of by taking a few averages and then regarding these as more-or-less precise measurements. We must learn to handle the whole pattern of variation as such. The present chapter introduces some of the more common patterns, and shows how these can be described in fairly simple numerical terms. A clear idea of the basic attitude involved in looking at one's data from this point of view is essential to a proper understanding of the elementary statistical methods recommended in later chapters.
THE NORMAL DISTRIBUTION
We shall begin by considering a simple continuously variable quantity such as stature. We know this varies greatly from one individual to another, and may also expect to find certain average differences between people drawn from different social classes or living in different geographical areas, etc. Let us suppose that a socio-medical survey of a particular community has provided us with a representative sample of 117 males whose heights are distributed as shown in the first and third columns of Table 1.
We shall assume that the original measurements were made as accurately as possible, but that they are given here only to the nearest 0.02 m (i.e. 2 cm). Thus the group labelled ‘1.66’ contains all those men whose true measurements were between 1.65 and 1.67 m. One is liable to run into trouble if the exact methods of recording the measurements and grouping them are not specified exactly.
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- Statistical Methods in Biology , pp. 7 - 23Publisher: Cambridge University PressPrint publication year: 1995