Simple Statistical Tests for Geography (100 Cases)

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Acknowledgements
Author
1. Introduction
1.1 Is This the Book for You?
1.2 How to Use This Book
1.3 Why Bother with Statistics?
1.4 A Note for Lecturers and Teachers
References
2. How to Use Statistics
2.1 Hypotheses
2.2 The Null Hypothesis
2.3 Bad Hypotheses
2.4 Multiple Working Hypotheses
2.5 Unbiased Sampling
2.6 Probability: Is It Just Luck?
2.7 One or Two-Tail Testing
2.8 Effect Size
References
3. Different Kinds of Data
3.1 Kinds of Data
3.1.1 Nominal
3.1.2 Ordinal
3.1.3 Individual Measurements
3.2 Independent or Linked Data?
3.3 Assumptions
3.3.1 Checking for a 'Normal' or Gaussian Distribution
3.4 Choosing the Right Test
References
4. Tools of the Trade
4.1 Introduction
4.2 Arithmetic
4.3 Using a Calculator
4.4 Spreadsheets
4.4.1 Assigning Ranks in a Spreadsheet
4.5 SPSS
4.6 R Commander
4.7 Descriptive Statistics
4.7.1 Measures of the Middle: Mean, Median and Mode
4.7.2 Measures of Spread or Dispersion: Range, Variance and Standard Deviation
4.7.3 Confidence Limits around the Mean
4.7.4 Measures of the Shape of a Distribution: Skewness and Kurtosis
References
5. Single Sample Tests
5.1 Introduction
5.2 Binomial Test
5.2.1 When It Is Useful
5.2.2 What It Is Based On
5.2.3 How to Do It
5.2.3.1 Online Calculators
5.2.3.2 In a Spreadsheet
5.2.3.3 Companion Site Calculator
5.2.3.4 In SPSS
5.2.3.5 In R Commander
5.2.3.6 By Hand
5.2.4 Examples
5.2.4.1 Example: Yes or No Questionnaire Answers
5.2.4.2 Example: Is There a Gender Bias in My Sample?
5.2.4.3 Example: Have the Limestones Been Removed by Weathering?
5.2.4.4 Example: Are There Too Few Black Managers in English Football?
5.3 One-Sample Chi-Square (?2) Test
5.3.1 Introduction
5.3.2 When It Is Useful
5.3.3 What It Is Based On
5.3.4 How to Do It
5.3.4.1 Companion Site Calculator
5.3.4.2 In a Spreadsheet
5.3.4.3 In R Commander
5.3.4.4 In SPSS
5.3.5 Examples
5.3.5.1 Example: Beautiful Beaches
5.3.5.2 Example: Ethnic Groups
5.3.5.3 Example: Dolphin Sightings
5.4 Kolmogorov-Smirnov One-Sample Test
5.4.1 When It Is Useful
5.4.2 What It Is Based On
5.4.3 How to Do It
5.4.4 Examples
5.4.4.1 Example: Are Levels of Agreement Equal?
5.4.4.2 Example: Is My Sample Representative?
5.5 One Sample Runs Test for Randomness
5.5.1 When It Is Useful
5.5.2 What It Is Based On
5.5.3 How to Do It
5.5.3.1 Companion Site Calculators
5.5.3.2 In SPSS
5.5.3.3 In R Commander
5.5.4 Examples
5.5.4.1 Example: Nominal Data and Small Sample Sizes
5.5.4.2 Example: Large Sample of Individual Numbers
References
6. Two-Sample Tests for Counts in Two Categories
6.1 Introduction
6.2 Sign Test
6.2.1 When It Is Useful
6.2.2 What It Is Based On
6.2.3 How to Do It
6.2.4 Effect Size
6.2.5 Examples
6.2.5.1 Example: Checking Exam Improvement
6.2.5.2 Example: Crystal Healing
6.2.5.3 Example: Footpath Erosion
6.3 McNemar's Test for Significance of Changes
6.3.1 When It Is Useful
6.3.2 What It Is Based On
6.3.3 How to Do It
6.3.4 Effect Size
6.3.5 Small Samples
6.3.6 Correction for Continuity
6.3.7 How to Do It
6.3.7.1 Companion Site Calculator
6.3.7.2 Online Calculators
6.3.7.3 In R Commander
6.3.7.4 In SPSS
6.3.8 Examples
6.3.8.1 Example: Opinions on Fracking
6.3.8.2 Example: Land Management
6.3.8.3 Example: Golf Green Hydrophobicity (Bad Test)
6.4 Tests for Independent Samples Arranged as 2 × 2 Contingency Tables
6.5 Risk Ratio and Odds Ratio
6.5.1 Risk Ratio
6.5.2 Odds Ratio
6.6 Confidence Limits of the Odds Ratio and Risk Ratio
6.6.1 How to Do It
6.6.1.1 Companion Site Calculator
6.6.1.2 Using an Online Calculator
6.6.1.3 In R Commander
6.6.1.4 In SPSS
6.7 Sample Size Assumptions
6.7.1 Calculating Expected Values
6.8 Chi-Square Test for a 2 × 2 Contingency Table
6.8.1 When It Is Useful
6.8.2 What It Is Based On
6.8.3 Calculating Chi-Square
6.8.4 Continuity Correction (Yates's Correction)
6.8.5 Effect Size: Cramer's V
6.9 Conducting the Chi-Square Test
6.9.1 Companion Site Calculator
6.9.2 Online Calculators
6.9.3 In R Commander
6.9.4 In SPSS
6.9.5 Examples
6.9.5.1 Example: Organic Produce
6.9.5.2 Example: Erratic Content
6.9.5.3 Example: Large Sample Parametric Approach
6.9.5.4 Example: Common Error with a Solution
6.10 Fisher's Exact Test
6.10.1 When It Is Useful
6.10.2 What It Is Based On
6.10.3 How to Do It
6.10.3.1 Real Statistics Resource Pack for Excel
6.10.3.2 Online Calculators
6.10.3.3 In R Commander
6.10.3.4 In SPSS
6.10.4 Examples
6.10.4.1 Example: Small Sample of Snails
6.10.4.2 Example: Start-Up Companies
References
7. Two-Sample Tests for Counts in Several Categories
7.1 Introduction
7.2 Two-Sample Chi-Square Test
7.2.1 When It Is Useful
7.2.2 What It Is Based On
7.2.3 Expected Frequencies
7.2.4 Sample Size Assumptions
7.2.5 Strength of the Relationship (Cramer's V)
7.2.5.1 Calculating Cramer's V
7.2.5.2 Where Are the Differences?
7.2.6 How to Conduct a Two-Sample Chi-Square Test
7.2.6.1 Companion Site Calculators
7.2.6.2 Online Calculators
7.2.6.3 R Commander
7.2.6.4 In SPSS
7.2.7 Examples
7.2.7.1 Example: Garden Visitors
7.2.7.2 Example: Snails (Small Sample)
7.2.7.3 Example: Misuse of Chi-Square
7.2.7.4 Example: Common Mistake and a Solution
7.3 Fisher's Exact Test for More Than Two Categories
7.3.1 When It Is Useful
7.3.2 How to Do It
7.3.2.1 In R Commander
7.3.2.2 In SPSS
7.3.3 Examples
7.3.3.1 Example: Snails (Small Sample)
7.3.3.2 Example: Small Questionnaire
7.3.3.3 Example: Failed Test and a Solution
7.4 Two-Sample Tests for Counts in Ordered Categories
7.5 Kolmogorov-Smirnov Two-Sample Test
7.5.1 When It Is Useful
7.5.2 How to Perform the Kolmogorov-Smirnov Two-Sample Test with Counts in Categories
7.5.2.1 Equal Sample Sizes
7.5.2.2 Unequal Sample Sizes
7.5.3 One-Tail Testing
7.5.4 Effect Size
7.5.5 How to Do It
7.5.5.1 Companion Site Calculators
7.5.5.2 Real Statistics Resource Pack
7.5.5.3 In SPSS
7.5.6 Examples
7.5.6.1 Example: Different Shaped Distributions
7.5.6.2 Example: Likert Scale, Small Samples
7.5.6.3 Example: Likert Scale, Large Samples
7.5.6.4 Example: Odd Case with a Bimodal Distribution
7.6 Scoring Categorical Data for Parametric Tests
7.6.1 How to Code Categorical Data
References
8. Two-Sample Tests for Individual Measurements
8.1 Introduction
8.2 Wilcoxon's Matched-Pairs Signed-Ranks Test
8.2.1 When It Is Useful
8.2.2 What It Is Based On
8.2.3 Tied Ranks
8.2.4 Effect Size
8.2.5 How to Do It
8.2.5.1 In a Spreadsheet
8.2.5.2 Real Statistics Resource Pack
8.2.5.3 Companion Site Calculator
8.2.5.4 Online Calculators
8.2.5.5 In R Commander
8.2.5.6 In SPSS
8.2.6 Examples
8.2.6.1 Example: Attitudes to Recycling
8.2.6.2 Example: Grazing and Plant Diversity
8.3 Paired-Samples Student's t-Test
8.3.1 When It Is Useful
8.3.2 Effect Size
8.3.3 How to Do It
8.3.3.1 In a Spreadsheet
8.3.3.2 Companion Site Calculator
8.3.3.3 In R Commander
8.3.3.4 In SPSS
8.3.3.5 Using a Calculator
8.3.3.6 Online Calculators
8.3.4 Examples
8.3.4.1 Example: Examination Marks
8.4 Two-Sample Tests for Independent Data with Individual Measurements
8.5 Mann-Whitney U-Test
8.5.1 When It Is Useful
8.5.2 What It Is Based On
8.5.3 Dealing with Tied Ranks
8.5.4 Effect Size
8.5.5 How to Do It
8.5.5.1 Online Calculators
8.5.5.2 Real Statistics Resource Pack
8.5.5.3 In a Spreadsheet
8.5.5.4 Companion Site Calculator
8.5.5.5 Using R Commander
8.5.5.6 In SPSS
8.5.6 Examples
8.5.6.1 Example: Exam Performance and Gender
8.5.6.2 Example: Biochar
8.5.6.3 Example: Schmidt Hammer and Glacial Moraines
8.6 Student's t-Test for Two Independent Samples
8.6.1 When It Is Useful
8.6.2 What It Is Based On
8.6.3 Effect Size
8.6.4 How to Do It
8.6.4.1 In a Spreadsheet
8.6.4.2 Online Calculators
8.6.4.3 Companion Site Calculator
8.6.4.4 In R Commander
8.6.4.5 In SPSS
8.6.5 Examples
8.6.5.1 Example: Male Underperformance
8.7 Two Independent Samples: Tests for Difference in Variability
8.8 The F-Test for Equality of Variance
8.8.1 When It Is Useful
8.8.2 What It Is Based On
8.8.3 How to Do It
8.8.3.1 In a Spreadsheet or Companion Site Calculator
8.8.3.2 In R Commander
8.8.3.3 In SPSS
8.8.3.4 Online Calculators
8.8.4 Examples
8.8.4.1 Example: Organic Strawberries
8.9 Non-Parametric Tests for Equality of Variance
8.10 Siegel-Tukey Test
8.10.1 When It Is Useful
8.10.2 What It Is Based On
8.10.3 How to Do It
8.10.3.1 Online Calculators and Spreadsheets
8.10.3.2 In R Commander
8.10.3.3 In SPSS
8.10.4 Examples
8.10.4.1 Example: Extremity of Opinion
8.10.5 'Measuring from the Middle' Approach
8.11 Kolmogorov-Smirnov Two-Sample Test for Continuous Data
8.11.1 When It Is Useful
8.11.2 How to Do It
8.11.2.1 Companion Site Calculator
8.11.2.2 In SPSS and R Commander
References
9. Comparing More Than Two Samples
9.1 Introduction
9.2 'Family-Wise' Error and the Bonferroni Correction
9.3 K-Sample Tests
9.3.1 Introduction
9.4 Complex Chi-Square
9.4.1 When It Is Useful
9.4.2 What It Is Based On
9.4.2.1 The Data are Counts, Not Percentages or Proportions
9.4.2.2 The Data Must Be Independent
9.4.2.3 Adequate Sample Size
9.4.3 Effect Size
9.4.4 How to Do It
9.4.4.1 In R Commander
9.4.4.2 In SPSS
9.4.4.3 Online Calculators
9.4.5 Examples
9.4.5.1 Example: Typical Act of Desperation
9.4.5.2 Example: Glacial Deposits
9.5 Fisher's Exact Calculation for Small Samples
9.5.1 When It Is Useful
9.5.2 How to Do It
9.5.2.1 In SPSS
9.5.2.2 In R Commander
9.5.2.3 Online Calculators
9.5.3 Examples
9.5.3.1 Example: Snails
9.5.3.2 Example: Use of Space
9.6 Kruskal-Wallis H-Test
9.6.1 When It Is Useful
9.6.2 What It Is Based On
9.6.3 Obtaining a Probability Value
9.6.4 Effect Size
9.6.5 Post Hoc Tests
9.6.6 How to Do It
9.6.6.1 Real Statistics Resource Pack for Excel
9.6.6.2 Companion Site Calculator
9.6.6.3 Online Calculators
9.6.6.4 In R Commander
9.6.6.5 In SPSS
9.7 Dunn's Test (Post Hoc Tests for Kruskal-Wallis Test)
9.7.1 Effect Size
9.7.2 Examples
9.7.2.1 Example: Soil Compaction
9.7.2.2 Example: Tourist Spending
9.8 Jonckheere-Terpstra Trend Test
9.8.1 When It Is Useful
9.8.2 How It Works
9.8.3 One- and Two-Tail Testing, Post Hoc Tests and Effect Size
9.8.4 How to Do It
9.8.4.1 In SPSS
9.8.4.2 Companion Site Calculator
9.8.5 Examples
9.8.5.1 Example: Age Group Opinions
9.9 Friedman's Test
9.9.1 When It Is Useful
9.9.2 What It Is Based On
9.9.3 One- and Two-Tail Testing, Post Hoc Tests and Effect Size
9.9.4 How to Do It
9.9.4.1 Real Statistics Resource Pack for Excel
9.9.4.2 Companion Site Calculator
9.9.4.3 In SPSS
9.9.4.4 R Commander
9.9.5 Examples
9.9.5.1 Example: Exam Performance
9.9.5.2 Example: Icons of Nationalism
9.10 Page's Trend Test
9.10.1 When It Is Useful
9.10.2 What It Is Based On
9.10.3 One- and Two-Tail Testing, Post Hoc Tests and Effect Size
9.10.4 How to Do It
9.10.5 Examples
9.10.5.1 Example: Metal Pollution in a River
9.10.5.2 Example: Rental Prices with Distance from City Centre
References
10. Correlation
10.1 Introduction
10.2 Assumptions of Correlation Analysis
10.2.1 Assumption 1: Data Are Continuous
10.2.2 Assumption 2: Most of the Data Are Near the Middle, or They Are Evenly Distributed
10.2.3 Assumption 3: The Relationship Forms a Straight Line Rather Than a Curve
10.2.4 Assumption 4: No Outliers or Extreme Values
10.2.5 Assumption 5: Sample Size Is Large Enough
10.3 Pearson's Correlation Coefficient
10.3.1 R-Squared, r-Values and the Effect Size
10.3.2 How to Do It
10.3.2.1 Companion Site Calculator
10.3.2.2 In a Spreadsheet
10.3.2.3 Real Statistics Resource Pack for Excel
10.3.2.4 Online Calculators
10.3.2.5 In R Commander
10.3.2.6 In SPSS
10.3.3 Examples
10.3.3.1 Example: Tree Growth and Summer Temperature
10.3.3.2 Example: Opinions on Global Issues
10.4 Point-Biserial Correlation
10.5 Spearman's Rank Correlation or Spearman's Rho
10.5.1 When It Is Useful
10.5.2 What It Is based On
10.5.3 How to Do It
10.5.4 Examples
10.5.4.1 Example: As Used for Pearson's Correlation
10.5.4.2 Example: Coastal Zone Vegetation
10.5.4.3 Example: Use of Space
10.5.4.4 Example: Using Rank Order Rather Than Numbers
10.5.4.5 Example: Grumpy Old Men
10.6 Tests for Comparing Two Correlation Coefficients
10.6.1 Independent Correlation Coefficients
10.6.1.1 How to Do It
10.6.1.2 Worked Example: Incompetent Marking
10.6.2 Linked Correlation Coefficients
10.7 Kendall's Tau and Other Approaches to Correlation
References
11. Regression Analysis
11.1 Simple Linear Regression
11.2 The Straight Line Equation
11.3 Best-Fit Regression Lines
11.4 Assumptions of Simple Linear Regression
11.4.1 Homoscedasticity
11.4.2 Independence of Residuals
11.4.3 Outliers and Extreme Values
11.5 Conflating Variables
11.6 Interpreting Regression Results
11.6.1 Statistical Significance
11.6.2 Effect Sizes in Regression: r, R2 and Slope
11.6.3 Uncertainty of the Slope Parameter
11.6.4 Estimating Goodness of Fit and Uncertainty
11.7 Performing Simple Linear Regression Analysis
11.7.1 In a Spreadsheet
11.7.2 Companion Site Calculators
11.7.3 In SPSS
11.7.4 R Commander
11.7.5 Examples
11.7.5.1 Example: Predicting the Weather
11.7.5.2 Example: Predicting Degree Outcomes
11.8 Tests for Comparing Two Regression Analyses
11.9 Standardising (z-Scoring) and Variance Scaling
11.10 Reduced Major Axis Regression
11.11 The Durbin-Watson Test for Autocorrelation of Residuals
11.11.1 How To Do It
11.12 Tests for Validation or Verification
11.13 More Complicated Regression Models
11.13.1 Non-Linear Regression
11.13.2 Multiple Linear Regression
References
12. Tables of Critical Values
12.1 Sign Test
12.2 Chi-Square Distribution
12.2.1 Critical Values of ?2 (Two-Tail)
12.2.2 Critical Values of ?2 for Two-Sample Chi-Square Tests
12.3 Kolmogorov-Smirnov One-Sample Test
12.4 One Sample Number of Runs Test for Randomness
12.4.1 One-Tail Test, p = 0.05 Small/Unequal Sample Sizes
12.4.2 One-Tail Test, p = 0.01 Small/Unequal Sample Sizes
12.4.3 Two-Tail Test, p = 0.05 Small/Unequal Sample Sizes
12.4.4 Two-Tail Test, p = 0.01 Small/Unequal Sample Sizes
12.4.5 One-Tail Test, Equal Sample Sizes
12.4.6 Two-Tail Test, Equal Sample Sizes
12.5 Kolmogorov-Smirnov Two-Sample Test
12.5.1 Two-Tail Tests, Small Unequal Sizes n = 5-20
12.5.2 Two-Tail Tests, Small Unequal Sizes n = 15-30
12.5.3 One-Tail Tests, Small Unequal Sizes n = 5-20
12.5.4 One-Tail Tests, Small Unequal Sizes n = 15-30
12.5.5 Two-Tail Tests, Equal Sample Sizes
12.5.6 One-Tail Tests, Equal Sample Sizes
12.6 Wilcoxon's Matched-Pairs Signed-Ranks Test
12.7 Student's t-Tests
12.7.1 Two-Tail t-Tests
12.7.2 One-Tail t-Tests
12.8 Mann-Whitney U-Test
12.8.1 Small Samples of Equal Size: Sum or Ranks
12.8.2 Two-Tail Tests, Small Unequal Samples
12.8.3 One-Tail Tests, Small Unequal Samples
12.8.4 Two-Tail Tests, Equal Sample Sizes
12.8.5 One-Tail Tests, Equal Sample Sizes
12.9 F-Test for Equality of Variance
12.9.1 Two-Tail Tests, Equal Sample Sizes
12.9.2 One-Tail Tests, Equal Sample Sizes
12.10 Page's Trend-Test
12.10.1 Three to Six Categories
12.10.2 Seven to Ten Categories
12.11 Pearson's Correlation Coefficient (r-Value)
12.11.1 Two-Tail Probabilities
12.11.2 One-Tail Probabilities
12.12 Spearman's Rank Correlation Coefficient (Rho)
12.12.1 Two-Tail Probabilities
12.12.2 One-Tail Probabilities
12.13 Durbin-Watson Test
12.13.1 One-Tail Critical Values p = 0.05
12.13.2 One-Tail Critical Values p = 0.01
12.14 Critical Values from the Standard Normal Distribution (Significance of z-Scores)
12.14.1 Single Test Critical Values
12.14.2 Applying a Bonferroni Correction for Multiple Testing
Index