The third edition xiv

How to use this book xiv

Packages used xv

Example data xv

Acknowledgements for the first edition xv

Acknowledgements for the second edition xv

Acknowledgements for the third edition xvi

1 Eight steps to successful data analysis 1

2 The basics 2

Observations 2

Hypothesis testing 2

P-values 3

Sampling 3

Experiments 4

Statistics 4

Descriptive statistics 5

Tests of difference 5

Tests of relationships 5

Tests for data investigation 6

3 Choosing a test: a key 7

Remember: eight steps to successful data analysis 7

The art of choosing a test 7

A key to assist in your choice of statistical test 8

4 Hypothesis testing, sampling and experimental design 23

Hypothesis testing 23

Acceptable errors 23

P-values 24

Sampling 25

Choice of sample unit 25

Number of sample units 26

Positioning of sample units to achieve a random sample 26

Timing of sampling 27

Experimental design 27

Control 28

Procedural controls 28

Temporal control 28

Experimental control 29

Statistical control 29

Some standard experimental designs 29

5 Statistics, variables and distributions 32

What are statistics? 32

Types of statistics 33

Descriptive statistics 33

Parametric statistics 33

Non-parametric statistics 33

What is a variable? 33

Types of variables or scales of measurement 34

Measurement variables 34

Continuous variables 34

Discrete variables 35

How accurate do I need to be? 35

Ranked variables 35

Attributes 35

Derived variables 36

Types of distribution 36

Discrete distributions 36

The Poisson distribution 36

The binomial distribution 37

The negative binomial distribution 39

The hypergeometric distribution 39

Continuous distributions 40

The rectangular distribution 40

The normal distribution 40

The standardized normal distribution 40

Convergence of a Poisson distribution to a normal distribution 41

Sampling distributions and the 'central limit theorem' 41

Describing the normal distribution further 41

Skewness 41

Kurtosis 43

Is a distribution normal? 43

Transformations 43

An example 44

The angular transformation 44

The logit transformation 45

The t-distribution 46

Confidence intervals 47

The chi-square distribution 47

The exponential distribution 47

Non-parametric 'distributions' 48

Ranking, quartiles and the interquartile range 48

Box and whisker plots 48

6 Descriptive and presentational techniques 49

General advice 49

Displaying data: summarizing a single variable 49

Box and whisker plot (box plot) 49

Displaying data: showing the distribution of a single variable 50

Bar chart: for discrete data 50

Histogram: for continuous data 51

Pie chart: for categorical data or attribute data 52

Descriptive statistics 52

Statistics of location or position 52

Arithmetic mean 53

Geometric mean 53

Harmonic mean 53

Median 53

Mode 53

Statistics of distribution, dispersion or spread 55

Range 55

Interquartile range 55

Variance 55

Standard deviation (SD) 55

Standard error (SE) 56

Confidence intervals (CI) or confidence limits 56

Coefficient of variation 56

Other summary statistics 56

Skewness 57

Kurtosis 57

Using the computer packages 57

General 57

Displaying data: summarizing two or more variables 62

Box and whisker plots (box plots) 62

Error b