Essential Statistics (3rd): Rees, D. G.: 9780412612800: Book: : eCampus.com

Preface

Preface to the second edition

xii

Preface to the first edition

xiii

Acknowledgements

What is statistics?

(4)

Statistics as a science

(1)

Types of statistical data

(3)

Worksheet 1

(2)

Some statistical notation

(5)

(1)

Factorials

(1)

Decimal places and significant figures

(3)

Worksheet 2

(2)

Summarizing data by tables and by graphical methods

(14)

Tables and graphs for one continuous variable

(4)

Tables and graphs for one discrete variable

(3)

Tables and graphs for one categorical variable

(1)

Tables and graphs for two-variable data

(3)

Summary

(4)

Worksheet 3

(4)

Summarizing data by numerical measures

(14)

Averages

(1)

Sample mean (x)

(1)

Sample median

(1)

Sample mode

(2)

When to use the mean, median and mode

(2)

Measures of variation

(1)

Sample standard deviation (s)

(2)

Sample inter-quartile range

(1)

When to use standard deviation and inter-quartile range

(1)

Box and whisker plots

(1)

Other measures of variation

(1)

A measure of skewness

(1)

Summary

(3)

Worksheet 4

(2)

Probability

(17)

Introduction

(1)

Basic ideas of probability

(1)

The a priori definition of probability for equally likely outcomes

(1)

The relative frequency definition of probability, based on experimental data

(1)

The range of possible values for a probability value

(1)

Probability, percentage, proportion and odds

(1)

Subjective probability

(1)

Probabilities involving more than one event

(1)

Multiplication law (the `and' law)

(2)

Addition law (the `or' law)

(2)

Mutually exclusive and exhaustive events

(1)

Complementary events and the calculation of P (at least 1...)

(1)

Probability trees

(2)

Venn diagrams and Rees diagrams

(1)

Summary

(4)

Worksheet 5

(3)

Discrete probability distributions

(16)

Introduction

(1)

Binomial distribution, an example

(1)

The general binomial distribution

(1)

Calculating binomial probabilities, an example

(1)

The mean and standard deviation of the binomial distribution

(1)

Binomial probabilities using tables

(1)

Binomial probabilities using Minitab

(1)

Simulation of binomial distributions using Minitab

(1)

Poisson distribution, an introduction

(1)

Some examples of Poisson variables

(1)

The general Poisson distribution

(1)

Calculating Poisson probabilities, an example

(1)

The mean and standard deviation of the Poisson distribution

(1)

Poisson probabilities using tables

(1)

Poisson probabilities using Minitab

(1)

Simulation of Poisson distributions using Minitab

(1)

Poisson approximation to the binomial distribution

(1)

Summary

(4)

Worksheet 6

(3)

Continuous probability distributions

(13)

Introduction

(2)

The normal distribution

(1)

An example of a normal distribution

(2)

Normal probabilities using Minitab

(1)

Simulation of the normal distribution using Minitab

(1)

Rectangular distribution

(1)

The normal approximation to the binomial distribution

(1)

Summary

(4)

Worksheet 7

(4)

Samples and populations

(9)

Introduction

(1)

Reasons for sampling

(1)

Sampling methods

(2)

Sample size

(1)

Sampling distribution of the sample mean

(2)

Simulation of the sampling distribution of the sample mean using Minitab

(1)

Summary

(3)

Worksheet 8

(2)

Confidence interval estimation

(19)

Introduction

(1)

95% confidence intervals

(1)

Calculating a 95% confidence interval for the mean, μ, of a population: large sample size, n

(2)

Calculating a 95% confidence interval for the mean, μ, of a population: small sample size, n

(3)

The t distribution

(1)

The choice of sample size when estimating the mean of a population

(1)

Degrees of freedom

100

(1)

95% confidence interval for a binomial probability

101

(1)

The choice of sample size when estimating a binomial probability

102

(1)

95% confidence interval for the mean of a population of differences, `paired' samples data

102

(2)

95% confidence interval for the difference in the means of two populations, `unpaired' samples data

104

(3)

Summary

107

(5)

Worksheet 9

107

(5)

Hypothesis testing

112

(18)

Introduction

112

(1)

What is a hypothesis?

113

(1)

Which is the null hypothesis and which is the alternative hypothesis?

113

(1)

What is a significance level?

114

(1)

What is a test statistic, and how do we calculate it?

114

(1)

How do we find the tabulated test statistic?

115

(1)

How do we compare the calculated and tabulated test statistics?

115

(1)

What is our conclusion, and what assumptions have we made?

116

(1)

Hypothesis test for the mean, μ, of a population

116

(1)

Two examples of hypothesis tests with one-sided alternative hypotheses

117

(1)

Hypothesis test for a binomial probability

118

(2)

Hypothesis test for the mean of a population of differences, `paired' samples data

120

(1)

Hypothesis test for the difference in the means of two populations, `unpaired' samples data

121

(2)

Hypothesis test for the equality of the variances of two normally distributed populations

123

(1)

The effect of choosing significance levels other than 5%

123

(1)

What if the assumptions of a hypothesis test are not valid?

124

(1)

The connection between confidence interval estimation and hypothesis testing

124

(1)

Summary

125

(5)

Worksheet 10

125

(5)

Non-parametric hypothesis tests

130

(16)

Introduction

130

(1)

Sign test for the median of a population

130

(2)

Sign test for the median of a population of differences, `paired' samples data

132

(1)

Sign test for large samples (n > 10)

133

(2)

Sign test using Minitab

135

(1)

Wilcoxon signed rank test for the median of a population of differences, `paired' samples data

135

(2)

Wilcoxon signed rank test for large samples (n > 25)

137

(1)

Wilcoxon signed rank test using Minitab

138

(1)

Mann-Whitney U test for the difference in the medians of two populations, `unpaired' samples data

139

(2)

Mann-Whitney U test for large samples

141

(1)

Mann-Whitney U test using Minitab

142

(1)

Summary

142

(4)

Worksheet 11

142

(4)

Association of categorical variables

146

(13)

Introduction

146

(1)

Contingency tables

146

(1)

x2 test for independence, 2 x 2 contingency table data

147

(2)

x2 test for independence, 3 x 3 table

149

(2)

x2 test for independence using Minitab

151

(1)

Fisher exact test

152

(2)

x2 trend test

154

(1)

Summary

155

(4)

Worksheet 12

155

(4)

Correlation of quantitative variables

159

(15)

Introduction

159

(1)

Pearson's correlation coefficient

159

(3)

Hypothesis test for Pearson's population correlation coefficient, ρ

162

(1)

The interpretation of significant and non-significant correlation coefficients

163

(2)

Spearman's rank correlation coefficient

165

(2)

Hypothesis test for Spearman's rank correlation coefficient

167

(1)

Spearman's rank correlation coefficient in the case of ties

167

(2)

Correlation coefficients using Minitab

169

(1)

Summary

170

(4)

Worksheet 13

170

(4)

Regression analysis

174

(15)

Introduction

174

(1)

Determining the regression equation from sample data

175

(1)

Plotting the regression line on the scatter diagram

176

(1)

Predicting values of y

177

(1)

Confidence intervals for predicted values of y

178

(2)

Hypothesis test for the slope of the regression line

180

(1)

The connection between regression and correlation

181

(1)

Regression analysis using Minitab

181

(1)

Transformations to produce linear relationships

182

(2)

Summary

184

(5)

Worksheet 14

185

(4)

Goodness-of-fit tests

189

(12)

Introduction

189

(1)

Goodness-of-fit for a `simple proportion' distribution

189

(2)

Goodness-of-fit for a binomial distribution

191

(2)

The Goodness-of-fit for a Poisson distribution

193

(2)

The Shapiro-Wilk test for normality

195

(2)

Summary

197

(4)

Worksheet 15

197

(4)

Appendix A Data set for a random sample of 40 students

201

(2)

Appendix B Multiple-choice test

203

(6)

Appendix C Solutions to Worksheets and multiple-choice test

209

(20)

Appendix D Statistical tables

229

(23)

Appendix E Glossary of symbols

252

(3)

Appendix F Introduction to Minitab data entry and list of Minitab commands

255

(5)

Index

260


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