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Table of contents
Foreward 4
1 Introduction 6
2 So, what are data? 8
3 Numbers; counting and measuring, precision and accuracy 9
4 Data collection: Sampling and populations, different types of data, data distributions 12
5 Descriptive statistics: measures to describe and summarize data sets. 16
6 Testing for Normality and transforming skewed data sets 22
7 The Standard Normal Distribution 28
8 Non-Parametric Descriptive statistics 30
9 Summary of descriptive statistics; so, what values may I use to describe my data? 34
Decision Flowchart 1: Descriptive Statistics – Parametric v Non-parametric data 43
10 Introduction to Inferential statistics 44
11 Comparing 2 sets of data – Independent t-test 50
12 Comparing 2 sets of data – Paired t-test 55
13 Comparing 2 sets of data – Independent non-parametric data 58
14 Comparing 2 sets of data – Paired non-parametric data 62
15 Parametric 1-way Analysis of Variance 66
16 Repeated Measures Analysis of Variance 78
17 Complex Analysis of Variance models 86
18 Non-parametric ANOVA 102
Decision Flowchart 2: Inferential Statistics – Single and multiple pairwise comparisons 115
19 Correlation Analysis 116
20 Regression Analysis 126
21 Chi-Square Analysis 136
Decision Flowchart 3: Inferential Statistics –Tests of Association 145
22 Confidence Intervals 146
23 Permutation Test of Exact Inference 150
24 General Linear Model 152
Appendices Introduction to Appendices 155
A Data distribution: probability mass function and probability density functions
A.1 Binomial Distribution 156
A.2 Exponential Distribution 157
A.3 Normal Distribution 158
A.4 Chi-square Distribution 159
A.5 Student t-Distribution 160
A.6 F Distribution 161
B Standard Normal Probabilities
B.1 AUC values for z values below the mean (i.e. -z) 162
B.2 AUC values for z values above the mean (i.e. +z) 163
C Critical values of the t-distribution 164
D Critical values of the Mann-Whitney U statistic
D.1 Critical values for U; One-tailed test, p = 0.05 165
D.2 Critical values for U; One-tailed test, p = 0.01 166
D.3 Critical values for U; Two-tailed test, p = 0.05 167
D.4 Critical values for U; Two-tailed test, p = 0.01 168
E Critical values of the F distribution
E.1 Critical values of F, p = 0.05 169
E.2 Critical values of F, p = 0.01 170
E.3 Critical values of F, p = 0.001 171
F Critical values of the Chi-square distribution 172
G Critical z values for multiple non-parametric pairwise comparisons
G.1 Critical values of z according to the number of comparisons 173
G.2 Alternative critical values of z according to the number of comparisons when all groups have an equal number of subjects 173
H Critical values of correlation coefficients
H.1 Pearson Product Moment Correlation 174
H.2 Spearman Rank Correlation 174
H.3 Kendall’s Rank Correlation (Kendall’s tau) 175
Overall Decision Flowchart: Descriptive and Inferential Statistics 176
Index