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E-raamat: Simple Statistical Tests for Geography

(Swansea University, UK.)
  • Formaat: 360 pages
  • Ilmumisaeg: 03-Nov-2016
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781498758895
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  • Formaat: 360 pages
  • Ilmumisaeg: 03-Nov-2016
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781498758895
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This book is aimed directly at students of geography, particularly those who lack confidence in manipulating numbers. The aim is not to teach the mathematics behind statistical tests, but to focus on the logic, so that students can choose the most appropriate tests, apply them in the most convenient way and make sense of the results. Introductory chapters explain how to use statistical methods and then the tests are arranged according to the type of data that they require. Diagrams are used to guide students toward the most appropriate tests. The focus is on nonparametric methods that make very few assumptions and are appropriate for the kinds of data that many students will collect. Parametric methods, including Students t-tests, correlation and regression are also covered.

Although aimed directly at geography students at senior undergraduate and graduate level, this book provides an accessible introduction to a wide range of statistical methods and will be of value to students and researchers in allied disciplines including Earth and environmental science, and the social sciences.

Arvustused

"This is an unusual and exceptional book! It is designed for geography students who want to carry out statistical tests. It is not for teachers or lecturers, and certainly not for practising statisticians. It is for budding geographers who have interesting data, collected as part of, say, an undergraduate (or even postgraduate) project, who need to derive wider meaning from their results and give their study its due significance. In order to achieve this aim it is written in a most engaging fashion, directed at the student colleague, and is designed around the experiments that the students are likely to encounter in their undergraduate course. The book is functional throughout. It starts with the geographical question (i.e. when is the statistical test useful?), and then takes the student through the rationale, and the process of how to carry out the test. Functionality persists, and the student is directed how to carry out the test in a variety of ways: manually, with a range of calculators, or with the appropriate or convenient statistical package such as SPSS. To wrap up each method, the book gives worked examples, of interest to both physical and human Geographers.

Because Geographers deal with complex problems that are unlikely to yield appropriate distributions with sound, probabilistic assumptions, this book is focussed on non-parametric tests and concentrates on issues such as the inevitably unsuitable sample size, or complex and maybe extreme distributions. With this in mind, Professor Danny McCarroll takes his student colleagues through the basics and reality of what is needed to do their work. In so doing, the book introduces them to hypotheses, probability, data and distributions that underpin their experiment and leads them through the practicalities of deriving their statistical implications. The book has even included a series of spreadsheets, accessible through a hyperlink that can be used to input data and carry out the statistical test without need to use the usual specialised software. With this structure, the book takes the user through, for instance: Chi-Square Tests, Kolmogorov-Smirnov Tests, Mann-Whitney U-Test, Siegel-Tukey Test and correlation with, for instance, Spearmans Rank and Regression Analysis. Retaining its practicality to the end, the book concludes with tables of Critical Values for the various tests explained in the preceding text. This is an outstanding book that will not only bring satisfaction for coming generations of students, but is likely to greatly increase the value of early research carried out by geography undergraduates, wherever they may be." Emeritus Professor Jim Rose, Department of Geography, Royal Holloway, University of London, Visiting Research Associate, British Geological Survey

"Prof. Danny McCarroll is an excellent geographer with a lot of experience in teaching statistical methods for geographers. In this book, Prof. McCarroll aims to overcome the fear of numbers; instead encouraging students to focus on the geographical problems that interest them and use whatever statistical tools they need in order to tackle such problems. In comparison to traditional statistics books, the author focuses mainly on nonparametric (distribution-free) methods, which are the most appropriate for geography students to work with due to the scale of study and the type of data that they encounter. However, the last chapters do also introduce widely-used parametric methods such as correlation and regression. Each technique taught in this book can be adopted and utilized quickly and easily using a range of tools including free online calculators, free add-ins or using specialist software (SPSS, R). This is a fantastic book for students, who can design the sampling scheme to fit the desired test before collecting data and look for clear guidance on how to analyse collected data." Prof. Jürg Luterbacher, Director Department of Geography, Justus Liebig University of Giessen, Germany "This is an unusual and exceptional book! It is designed for geography students who want to carry out statistical tests. It is not for teachers or lecturers, and certainly not for practising statisticians. It is for budding geographers who have interesting data, collected as part of, say, an undergraduate (or even postgraduate) project, who need to derive wider meaning from their results and give their study its due significance. In order to achieve this aim it is written in a most engaging fashion, directed at the student colleague, and is designed around the experiments that the students are likely to encounter in their undergraduate course. The book is functional throughout. It starts with the geographical question (i.e. when is the statistical test useful?), and then takes the student through the rationale, and the process of how to carry out the test. Functionality persists, and the student is directed how to carry out the test in a variety of ways: manually, with a range of calculators, or with the appropriate or convenient statistical package such as SPSS. To wrap up each method, the book gives worked examples, of interest to both physical and human Geographers.

Because Geographers deal with complex problems that are unlikely to yield appropriate distributions with sound, probabilistic assumptions, this book is focussed on non-parametric tests and concentrates on issues such as the inevitably unsuitable sample size, or complex and maybe extreme distributions. With this in mind, Professor Danny McCarroll takes his student colleagues through the basics and reality of what is needed to do their work. In so doing, the book introduces them to hypotheses, probability, data and distributions that underpin their experiment and leads them through the practicalities of deriving their statistical implications. The book has even included a series of spreadsheets, accessible through a hyperlink that can be used to input data and carry out the statistical test without need to use the usual specialised software. With this structure, the book takes the user through, for instance: Chi-Square Tests, Kolmogorov-Smirnov Tests, Mann-Whitney U-Test, Siegel-Tukey Test and correlation with, for instance, Spearmans Rank and Regression Analysis. Retaining its practicality to the end, the book concludes with tables of Critical Values for the various tests explained in the preceding text. This is an outstanding book that will not only bring satisfaction for coming generations of students, but is likely to greatly increase the value of early research carried out by geography undergraduates, wherever they may be." Emeritus Professor Jim Rose, Department of Geography, Royal Holloway, University of London, Visiting Research Associate, British Geological Survey

"Prof. Danny McCarroll is an excellent geographer with a lot of experience in teaching statistical methods for geographers. In this book, Prof. McCarroll aims to overcome the fear of numbers; instead encouraging students to focus on the geographical problems that interest them and use whatever statistical tools they need in order to tackle such problems. In comparison to traditional statistics books, the author focuses mainly on nonparametric (distribution-free) methods, which are the most appropriate for geography students to work with due to the scale of study and the type of data that they encounter. However, the last chapters do also introduce widely-used parametric methods such as correlation and regression. Each technique taught in this book can be adopted and utilized quickly and easily using a range of tools including free online calculators, free add-ins or using specialist software (SPSS, R). This is a fantastic book for students, who can design the sampling scheme to fit the desired test before collecting data and look for clear guidance on how to analyse collected data." Prof. Jürg Luterbacher, Director Department of Geography, Justus Liebig University of Giessen, Germany

Preface xix
Acknowledgements xxi
Author xxiii
1 Introduction 1(8)
1.1 Is This the Book for You?
1(1)
1.2 How to Use This Book
2(1)
1.3 Why Bother with Statistics?
3(3)
1.4 A Note for Lecturers and Teachers
6(2)
References
8(1)
2 How to Use Statistics 9(16)
2.1 Hypotheses
9(1)
2.2 The Null Hypothesis
10(1)
2.3 Bad Hypotheses
11(1)
2.4 Multiple Working Hypotheses
12(1)
2.5 Unbiased Sampling
12(2)
2.6 Probability: Is It Just Luck?
14(4)
2.7 One or Two-Tail Testing
18(1)
2.8 Effect Size
19(4)
References
23(2)
3 Different Kinds of Data 25(16)
3.1 Kinds of Data
25(4)
3.1.1 Nominal
25(1)
3.1.2 Ordinal
25(3)
3.1.3 Individual Measurements
28(1)
3.2 Independent or Linked Data?
29(1)
3.3 Assumptions
30(4)
3.3.1 Checking for a 'Normal' or Gaussian Distribution
31(3)
3.4 Choosing the Right Test
34(4)
References
38(3)
4 Tools of the Trade 41(18)
4.1 Introduction
41(1)
4.2 Arithmetic
41(2)
4.3 Using a Calculator
43(1)
4.4 Spreadsheets
43(7)
4.4.1 Assigning Ranks in a Spreadsheet
47(3)
4.5 SPSS
50(1)
4.6 R Commander
50(2)
4.7 Descriptive Statistics
52(5)
4.7.1 Measures of the Middle: Mean, Median and Mode
52(2)
4.7.2 Measures of Spread or Dispersion: Range, Variance and Standard Deviation
54(1)
4.7.3 Confidence Limits around the Mean
54(1)
4.7.4 Measures of the Shape of a Distribution: Skewness and Kurtosis
55(2)
References
57(2)
5 Single Sample Tests 59(22)
5.1 Introduction
59(1)
5.2 Binomial Test
60(5)
5.2.1 When It Is Useful
60(1)
5.2.2 What It Is Based On
60(1)
5.2.3 How to Do It
61(2)
5.2.3.1 Online Calculators
61(1)
5.2.3.2 In a Spreadsheet
61(1)
5.2.3.3 Companion Site Calculator
62(1)
5.2.3.4 In SPSS
63(1)
5.2.3.5 In R Commander
63(1)
5.2.3.6 By Hand
63(1)
5.2.4 Examples
63(2)
5.2.4.1 Example: Yes or No Questionnaire Answers
63(1)
5.2.4.2 Example: Is There a Gender Bias in My Sample?
64(1)
5.2.4.3 Example: Have the Limestones Been Removed by Weathering?
64(1)
5.2.4.4 Example: Are There Too Few Black Managers in English Football?
65(1)
5.3 One-Sample Chi-Square (x2) Test
65(5)
5.3.1 Introduction
65(1)
5.3.2 When It Is Useful
65(1)
5.3.3 What It Is Based On
66(1)
5.3.4 How to Do It
66(3)
5.3.4.1 Companion Site Calculator
67(1)
5.3.4.2 In a Spreadsheet
67(1)
5.3.4.3 In R Commander
68(1)
5.3.4.4 In SPSS
68(1)
5.3.5 Examples
69(1)
5.3.5.1 Example: Beautiful Beaches
69(1)
5.3.5.2 Example: Ethnic Groups
69(1)
5.3.5.3 Example: Dolphin Sightings
69(1)
5.4 Kolmogorov-Smirnov One-Sample Test
70(3)
5.4.1 When It Is Useful
70(1)
5.4.2 What It Is Based On
70(1)
5.4.3 How to Do It
71(1)
5.4.4 Examples
71(2)
5.4.4.1 Example: Are Levels of Agreement Equal?
71(1)
5.4.4.2 Example: Is My Sample Representative?
72(1)
5.5 One Sample Runs Test for Randomness
73(6)
5.5.1 When It Is Useful
73(1)
5.5.2 What It Is Based On
73(1)
5.5.3 How to Do It
74(1)
5.5.3.1 Companion Site Calculators
74(1)
5.5.3.2 In SPSS
74(1)
5.5.3.3 In R Commander
75(1)
5.5.4 Examples
75(6)
5.5.4.1 Example: Nominal Data and Small Sample Sizes
75(2)
5.5.4.2 Example: Large Sample of Individual Numbers
77(2)
References
79(2)
6 Two-Sample Tests for Counts in Two Categories 81(30)
6.1 Introduction
81(1)
6.2 Sign Test
81(3)
6.2.1 When It Is Useful
81(1)
6.2.2 What It Is Based On
82(1)
6.2.3 How to Do It
82(1)
6.2.4 Effect Size
82(1)
6.2.5 Examples
83(1)
6.2.5.1 Example: Checking Exam Improvement
83(1)
6.2.5.2 Example: Crystal Healing
83(1)
6.2.5.3 Example: Footpath Erosion
84(1)
6.3 McNemar's Test for Significance of Changes
84(7)
6.3.1 When It Is Useful
85(1)
6.3.2 What It Is Based On
85(1)
6.3.3 How to Do It
86(1)
6.3.4 Effect Size
86(1)
6.3.5 Small Samples
86(1)
6.3.6 Correction for Continuity
87(1)
6.3.7 How to Do It
87(1)
6.3.7.1 Companion Site Calculator
87(1)
6.3.7.2 Online Calculators
87(1)
6.3.7.3 In R Commander
87(1)
6.3.7.4 In SPSS
87(1)
6.3.8 Examples
88(5)
6.3.8.1 Example: Opinions on Fracking
88(1)
6.3.8.2 Example: Land Management
89(1)
6.3.8.3 Example: Golf Green Hydrophobicity (Bad Test)
89(2)
6.4 Tests for Independent Samples Arranged as 2 x 2 Contingency Tables
91(2)
6.5 Risk Ratio and Odds Ratio
93(1)
6.5.1 Risk Ratio
93(1)
6.5.2 Odds Ratio
93(1)
6.6 Confidence Limits of the Odds Ratio and Risk Ratio
94(2)
6.6.1 How to Do It
95(1)
6.6.1.1 Companion Site Calculator
95(1)
6.6.1.2 Using an Online Calculator
95(1)
6.6.1.3 In R Commander
96(1)
6.6.1.4 In SPSS
96(1)
6.7 Sample Size Assumptions
96(2)
6.7.1 Calculating Expected Values
96(2)
6.8 Chi-Square Test for a 2 x 2 Contingency Table
98(4)
6.8.1 When It Is Useful
98(1)
6.8.2 What It Is Based On
99(1)
6.8.3 Calculating Chi-Square
99(2)
6.8.4 Continuity Correction (Yates's Correction)
101(1)
6.8.5 Effect Size: Cramer's V
101(1)
6.9 Conducting the Chi-Square Test
102(5)
6.9.1 Companion Site Calculator
102(1)
6.9.2 Online Calculators
102(1)
6.9.3 In R Commander
102(1)
6.9.4 In SPSS
103(1)
6.9.5 Examples
104(3)
6.9.5.1 Example: Organic Produce
104(1)
6.9.5.2 Example: Erratic Content
104(1)
6.9.5.3 Example: Large Sample Parametric Approach
105(1)
6.9.5.4 Example: Common Error with a Solution
106(1)
6.10 Fisher's Exact Test
107(3)
6.10.1 When It Is Useful
107(1)
6.10.2 What It Is Based On
108(1)
6.10.3 How to Do It
108(1)
6.10.3.1 Real Statistics Resource Pack for Excel
108(1)
6.10.3.2 Online Calculators
108(1)
6.10.3.3 In R Commander
109(1)
6.10.3.4 In SPSS
109(1)
6.10.4 Examples
109(3)
6.10.4.1 Example: Small Sample of Snails
109(1)
6.10.4.2 Example: Start-Up Companies
110(1)
References
110(1)
7 Two-Sample Tests for Counts in Several Categories 111(38)
7.1 Introduction
111(1)
7.2 Two-Sample Chi-Square Test
112(15)
7.2.1 When It Is Useful
112(1)
7.2.2 What It Is Based On
113(1)
7.2.3 Expected Frequencies
113(4)
7.2.4 Sample Size Assumptions
117(2)
7.2.5 Strength of the Relationship (Cramer's V)
119(3)
7.2.5.1 Calculating Cramer's V
120(1)
7.2.5.2 Where Are the Differences?
120(2)
7.2.6 How to Conduct a Two-Sample Chi-Square Test
122(1)
7.2.6.1 Companion Site Calculators
122(1)
7.2.6.2 Online Calculators
122(1)
7.2.6.3 R Commander
122(1)
7.2.6.4 In SPSS
123(1)
7.2.7 Examples
123(4)
7.2.7.1 Example: Garden Visitors
123(1)
7.2.7.2 Example: Snails (Small Sample)
124(1)
7.2.7.3 Example: Misuse of Chi-Square
125(1)
7.2.7.4 Example: Common Mistake and a Solution
126(1)
7.3 Fisher's Exact Test for More Than Two Categories
127(5)
7.3.1 When It Is Useful
127(1)
7.3.2 How to Do It
128(1)
7.3.2.1 In R Commander
128(1)
7.3.2.2 In SPSS
129(1)
7.3.3 Examples
129(3)
7.3.3.1 Example: Snails (Small Sample)
129(1)
7.3.3.2 Example: Small Questionnaire
129(1)
7.3.3.3 Example: Failed Test and a Solution
130(2)
7.4 Two-Sample Tests for Counts in Ordered Categories
132(1)
7.5 Kolmogorov-Smirnov Two-Sample Test
132(11)
7.5.1 When It Is Useful
133(1)
7.5.2 How to Perform the Kolmogorov-Smirnov Two-Sample Test with Counts in Categories
134(2)
7.5.2.1 Equal Sample Sizes
134(1)
7.5.2.2 Unequal Sample Sizes
135(1)
7.5.3 One Tail Testing
136(2)
7.5.4 Effect Size
138(1)
7.5.5 How to Do It
139(1)
7.5.5.1 Companion Site Calculators
139(1)
7.5.5.2 Real Statistics Resource Pack
140(1)
7.5.5.3 In SPSS
140(1)
7.5.6 Examples
140(3)
7.5.6.1 Example: Different Shaped Distributions
140(1)
7.5.6.2 Example: Likert Scale, Small Samples
141(1)
7.5.6.3 Example: Likert Scale, Large Samples
141(1)
7.5.6.4 Example: Odd Case with a Bimodal Distribution
142(1)
7.6 Scoring Categorical Data for Parametric Tests
143(4)
7.6.1 How to Code Categorical Data
146(1)
References
147(2)
8 Two-Sample Tests for Individual Measurements 149(42)
8.1 Introduction
149(1)
8.2 Wilcoxon's Matched-Pairs Signed-Ranks Test
150(9)
8.2.1 When It Is Useful
150(1)
8.2.2 What It Is Based On
150(2)
8.2.3 Tied Ranks
152(1)
8.2.4 Effect Size
152(1)
8.2.5 How to Do It
153(2)
8.2.5.1 In a Spreadsheet
153(1)
8.2.5.2 Real Statistics Resource Pack
153(1)
8.2.5.3 Companion Site Calculator
153(1)
8.2.5.4 Online Calculators
154(1)
8.2.5.5 In R Commander
154(1)
8.2.5.6 In SPSS
155(1)
8.2.6 Examples
155(4)
8.2.6.1 Example: Attitudes to Recycling
155(1)
8.2.6.2 Example: Grazing and Plant Diversity
155(4)
8.3 Paired-Samples Student's t-Test
159(3)
8.3.1 When It Is Useful
159(1)
8.3.2 Effect Size
159(1)
8.3.3 How to Do It
159(2)
8.3.3.1 In a Spreadsheet
159(1)
8.3.3.2 Companion Site Calculator
159(1)
8.3.3.3 In R Commander
160(1)
8.3.3.4 In SPSS
160(1)
8.3.3.5 Using a Calculator
160(1)
8.3.3.6 Online Calculators
160(1)
8.3.4 Examples
161(3)
8.3.4.1 Example: Examination Marks
161(1)
8.4 Two-Sample Tests for Independent Data with Individual Measurements
162(2)
8.5 Mann-Whitney U-Test
164(10)
8.5.1 When It Is Useful
164(1)
8.5.2 What It Is Based On
165(1)
8.5.3 Dealing with Tied Ranks
165(1)
8.5.4 Effect Size
166(1)
8.5.5 How to Do It
166(4)
8.5.5.1 Online Calculators
166(1)
8.5.5.2 Real Statistics Resource Pack
166(2)
8.5.5.3 In a Spreadsheet
168(1)
8.5.5.4 Companion Site Calculator
169(1)
8.5.5.5 Using R Commander
169(1)
8.5.5.6 In SPSS
170(1)
8.5.6 Examples
170(4)
8.5.6.1 Example: Exam Performance and Gender
170(1)
8.5.6.2 Example: Biochar
170(1)
8.5.6.3 Example: Schmidt Hammer and Glacial Moraines
171(3)
8.6 Student's t-Test for Two Independent Samples
174(7)
8.6.1 When It Is Useful
174(1)
8.6.2 What It Is Based On
174(1)
8.6.3 Effect Size
175(1)
8.6.4 How to Do It
175(3)
8.6.4.1 In a Spreadsheet
175(1)
8.6.4.2 Online Calculators
176(1)
8.6.4.3 Companion Site Calculator
176(1)
8.6.4.4 In R Commander
177(1)
8.6.4.5 In SPSS
177(1)
8.6.5 Examples
178(3)
8.6.5.1 Example: Male Underperformance
178(3)
8.7 Two Independent Samples: Tests for Difference in Variability
181(1)
8.8 The F-Test for Equality of Variance
181(3)
8.8.1 When It Is Useful
181(1)
8.8.2 What It Is Based On
182(1)
8.8.3 How to Do It
182(1)
8.8.3.1 In a Spreadsheet or Companion Site Calculator
182(1)
8.8.3.2 In R Commander
182(1)
8.8.3.3 In SPSS
183(1)
8.8.3.4 Online Calculators
183(1)
8.8.4 Examples
183(1)
8.8.4.1 Example: Organic Strawberries
183(1)
8.9 Non-Parametric Tests for Equality of Variance
184(1)
8.10 Siegel-Tukey Test
184(3)
8.10.1 When It Is Useful
184(1)
8.10.2 What It Is Based On
184(1)
8.10.3 How to Do It
185(1)
8.10.3.1 Online Calculators and Spreadsheets
185(1)
8.10.3.2 In R Commander
186(1)
8.10.3.3 In SPSS
186(1)
8.10.4 Examples
186(1)
8.10.4.1 Example: Extremity of Opinion
186(1)
8.10.5 'Measuring from the Middle' Approach
187(1)
8.11 Kolmogorov-Smirnov Two-Sample Test for Continuous Data
187(3)
8.11.1 When It Is Useful
187(1)
8.11.2 How to Do It
188(6)
8.11.2.1 Companion Site Calculator
189(1)
8.11.2.2 In SPSS and R Commander
189(1)
References
190(1)
9 Comparing More Than Two Samples 191(44)
9.1 Introduction
191(1)
9.2 'Family-Wise' Error and the Bonferroni Correction
191(3)
9.3 K-Sample Tests
194(2)
9.3.1 Introduction
194(2)
9.4 Complex Chi-Square
196(7)
9.4.1 When It Is Useful
196(1)
9.4.2 What It Is Based On
196(1)
9.4.2.1 The Data are Counts, Not Percentages or Proportions
196(1)
9.4.2.2 The Data Must Be Independent
196(1)
9.4.2.3 Adequate Sample Size
197(1)
9.4.3 Effect Size
197(1)
9.4.4 How to Do It
197(2)
9.4.4.1 In R Commander
198(1)
9.4.4.2 In SPSS
198(1)
9.4.4.3 Online Calculators
199(1)
9.4.5 Examples
199(4)
9.4.5.1 Example: Typical Act of Desperation
199(3)
9.4.5.2 Example: Glacial Deposits
202(1)
9.5 Fisher's Exact Calculation for Small Samples
203(2)
9.5.1 When It Is Useful
203(1)
9.5.2 How to Do It
203(1)
9.5.2.1 In SPSS
203(1)
9.5.2.2 In R Commander
203(1)
9.5.2.3 Online Calculators
203(1)
9.5.3 Examples
203(2)
9.5.3.1 Example: Snails
203(1)
9.5.3.2 Example: Use of Space
204(1)
9.6 Kruskal-Wallis H-Test
205(7)
9.6.1 When It Is Useful
205(1)
9.6.2 What It Is Based On
206(1)
9.6.3 Obtaining a Probability Value
206(1)
9.6.4 Effect Size
207(1)
9.6.5 Post Hoc Tests
207(1)
9.6.6 How to Do It
207(5)
9.6.6.1 Real Statistics Resource Pack for Excel
207(1)
9.6.6.2 Companion Site Calculator
208(1)
9.6.6.3 Online Calculators
209(1)
9.6.6.4 In R Commander
209(1)
9.6.6.5 In SPSS
209(3)
9.7 Dunn's Test (Post Hoc Tests for Kruskal-Wallis Test)
212(4)
9.7.1 Effect Size
213(1)
9.7.2 Examples
213(3)
9.7.2.1 Example: Soil Compaction
213(2)
9.7.2.2 Example: Tourist Spending
215(1)
9.8 Jonckheere-Terpstra Trend Test
216(5)
9.8.1 When It Is Useful
216(1)
9.8.2 How It Works
217(1)
9.8.3 One- and Two-Tail Testing, Post Hoc Tests and Effect Size
218(1)
9.8.4 How to Do It
218(1)
9.8.4.1 In SPSS
218(1)
9.8.4.2 Companion Site Calculator
219(1)
9.8.5 Examples
219(2)
9.8.5.1 Example: Age Group Opinions
219(2)
9.9 Friedman's Test
221(7)
9.9.1 When It Is Useful
221(1)
9.9.2 What It Is Based On
221(1)
9.9.3 One- and Two-Tail Testing, Post Hoc Tests and Effect Size
222(1)
9.9.4 How to Do It
222(2)
9.9.4.1 Real Statistics Resource Pack for Excel
223(1)
9.9.4.2 Companion Site Calculator
223(1)
9.9.4.3 In SPSS
223(1)
9.9.4.4 R Commander
224(1)
9.9.5 Examples
224(4)
9.9.5.1 Example: Exam Performance
224(1)
9.9.5.2 Example: Icons of Nationalism
225(3)
9.10 Page's Trend Test
228(7)
9.10.1 When It Is Useful
228(1)
9.10.2 What It Is Based On
228(1)
9.10.3 One- and Two-Tail Testing, Post Hoc Tests and Effect Size
229(1)
9.10.4 How to Do It
229(1)
9.10.5 Examples
230(3)
9.10.5.1 Example: Metal Pollution in a River
230(1)
9.10.5.2 Example: Rental Prices with Distance from City Centre
231(2)
References
233(2)
10 Correlation 235(26)
10.1 Introduction
235(2)
10.2 Assumptions of Correlation Analysis
237(5)
10.2.1 Assumption 1: Data Are Continuous
238(1)
10.2.2 Assumption 2: Most of the Data Are Near the Middle, or They Are Evenly Distributed
239(1)
10.2.3 Assumption 3: The Relationship Forms a Straight Line Rather Than a Curve
240(1)
10.2.4 Assumption 4: No Outliers or Extreme Values
240(2)
10.2.5 Assumption 5: Sample Size Is Large Enough
242(1)
10.3 Pearson's Correlation Coefficient
242(6)
10.3.1 R-Squared, r-Values and the Effect Size
243(1)
10.3.2 How to Do It
243(3)
10.3.2.1 Companion Site Calculator
243(1)
10.3.2.2 In a Spreadsheet
244(1)
10.3.2.3 Real Statistics Resource Pack for Excel
245(1)
10.3.2.4 Online Calculators
245(1)
10.3.2.5 In R Commander
246(1)
10.3.2.6 In SPSS
246(1)
10.3.3 Examples
246(3)
10.3.3.1 Example: Tree Growth and Summer Temperature
246(1)
10.3.3.2 Example: Opinions on Global Issues
247(1)
10.4 Point-Biserial Correlation
248(1)
10.5 Spearman's Rank Correlation or Spearman's Rho
249(5)
10.5.1 When It Is Useful
249(1)
10.5.2 What It Is based On
249(1)
10.5.3 How to Do It
249(1)
10.5.4 Examples
249(5)
10.5.4.1 Example: As-Used for Pearson's Correlation
249(1)
10.5.4.2 Example: Coastal Zone Vegetation
250(1)
10.5.4.3 Example: Use of Space
251(1)
10.5.4.4 Example: Using Rank Order Rather Than Numbers
252(1)
10.5.4.5 Example: Grumpy Old Men
253(1)
10.6 Tests for Comparing Two Correlation Coefficients
254(4)
10.6.1 Independent Correlation Coefficients
254(1)
10.6.1.1 How to Do It
254(1)
10.6.1.2 Worked Example: Incompetent Marking
255(1)
10.6.2 Linked Correlation Coefficients
255(3)
10.7 Kendall's Tau and Other Approaches to Correlation
258(1)
References
259(2)
11 Regression Analysis 261(36)
11.1 Simple Linear Regression
261(1)
11.2 The Straight Line Equation
261(4)
11.3 Best-Fit Regression Lines
265(3)
11.4 Assumptions of Simple Linear Regression
268(4)
11.4.1 Homoscedasticity
269(1)
11.4.2 Independence of Residuals
270(1)
11.4.3 Outliers and Extreme Values
271(1)
11.5 Conflating Variables
272(1)
11.6 Interpreting Regression Results
272(5)
11.6.1 Statistical Significance
272(2)
11.6.2 Effect Sizes in Regression: r, R2 and Slope
274(1)
11.6.3 Uncertainty of the Slope Parameter
275(1)
11.6.4 Estimating Goodness of Fit and Uncertainty
275(2)
11.7 Performing Simple Linear Regression Analysis
277(4)
11.7.1 In a Spreadsheet
277(1)
11.7.2 Companion Site Calculators
278(1)
11.7.3 In SPSS
278(1)
11.7.4 R Commander
278(1)
11.7.5 Examples
279(10)
11.7.5.1 Example: Predicting the Weather
279(1)
11.7.5.2 Example: Predicting Degree Outcomes
280(1)
11.8 Tests for Comparing Two Regression Analyses
281(3)
11.9 Standardising (z-Scoring) and Variance Scaling
284(3)
11.10 Reduced Major Axis Regression
287(2)
11.11 The Durbin-Watson Test for Autocorrelation of Residuals
289(2)
11.11.1 How To Do It
291(1)
11.12 Tests for Validation or Verification
291(3)
11.13 More Complicated Regression Models
294(2)
11.13.1 Non-Linear Regression
294(1)
11.13.2 Multiple Linear Regression
294(2)
References
296(1)
12 Tables of Critical Values 297(30)
12.1 Sign Test
297(1)
12.2 Chi-Square Distribution
298(1)
12.2.1 Critical Values of x2 (Two-Tail)
298(1)
12.2.2 Critical Values of x2 for Two-Sample Chi-Square Tests
298(1)
12.3 Kolmogorov-Smirnov One-Sample Test
299(1)
12.4 One Sample Number of Runs Test for Randomness
300(4)
12.4.1 One-Tail Test, p = 0.05 Small/Unequal Sample Sizes
300(1)
12.4.2 One-Tail Test, p = 0.01 Small/Unequal Sample Sizes
300(1)
12.4.3 Two-Tail Test, p = 0.05 Small/Unequal Sample Sizes
301(1)
12.4.4 Two-Tail Test, p = 0.01 Small/Unequal Sample Sizes
301(1)
12.4.5 One-Tail Test, Equal Sample Sizes
302(1)
12.4.6 Two-Tail Test, Equal Sample Sizes
303(1)
12.5 Kolmogorov-Smirnov Two-Sample Test
304(4)
12.5.1 Two-Tail Tests, Small Unequal Sizes n = 5-20
304(1)
12.5.2 Two-Tail Tests, Small Unequal Sizes n = 15-30
304(1)
12.5.3 One-Tail Tests, Small Unequal Sizes n = 5-20
305(1)
12.5.4 One-Tail Tests, Small Unequal Sizes n = 15-30
305(1)
12.5.5 Two-Tail Tests, Equal Sample Sizes
306(1)
12.5.6 One-Tail Tests, Equal Sample Sizes
307(1)
12.6 Wilcoxon's Matched-Pairs Signed-Ranks Test
308(1)
12.7 Student's t-Tests
309(2)
12.7.1 Two-Tail t-Tests
309(1)
12.7.2 One-Tail t-Tests
310(1)
12.8 Mann-Whitney U-Test
311(5)
12.8.1 Small Samples of Equal Size: Sum or Ranks
311(1)
12.8.2 Two-Tail Tests, Small Unequal Samples
312(1)
12.8.3 One-Tail Tests, Small Unequal Samples
313(1)
12.8.4 Two Tail Tests, Equal Sample Sizes
314(1)
12.8.5 One Tail Tests, Equal Sample Sizes
315(1)
12.9 F-Test for Equality of Variance
316(2)
12.9.1 Two-Tail Tests, Equal Sample Sizes
316(1)
12.9.2 One Tail Tests, Equal Sample Sizes
317(1)
12.10 Page's Trend-Test
318(2)
12.10.1 Three to Six Categories
318(1)
12.10.2 Seven to Ten Categories
319(1)
12.11 Pearson's Correlation Coefficient (r-Value)
320(2)
12.11.1 Two-Tail Probabilities
320(1)
12.11.2 One Tail Probabilities
321(1)
12.12 Spearman's Rank Correlation Coefficient (Rho)
322(2)
12.12.1 Two-Tail Probabilities
322(1)
12.12.2 One-Tail Probabilities
323(1)
12.13 Durbin-Watson Test
324(2)
12.13.1 One-Tail Critical Values p = 0.05
324(1)
12.13.2 One-Tail Critical Values p = 0.01
325(1)
12.14 Critical Values from the Standard Normal Distribution (Significance of z-Scores)
326(1)
12.14.1 Single Test Critical Values
326(1)
12.14.2 Applying a Bonferroni Correction for Multiple Testing
326(1)
Index 327
Danny McCarroll completed a Geography degree at the University of Sheffield in 1983 and a PhD, on Little Ice Age fluctuations of Norwegian glaciers, at Swansea University in 1986. He later worked for a few years in the Universities of Cardiff and Southampton before returning to Swansea, where he has sincereceived awards for excellence in both teaching and research as well as a Personal Chair. His research interests include geomorphology, reconstructing Quaternary environments and high resolution climate reconstruction, particularly using tree rings. He coordinated the European Union funded Millennium project which brought together an interdisciplinary team of more than 100 scientists from 40 universities to reconstruct the climate of Europe over the last one thousand years. He has more than 100 publications in international journals.