Preface p. xvii
Note to Students p. xix
Conventions in Our Presentation p. xxi
How Long Is a Worm? p. 1
Introduction p. 1
Sampling a Population p. 2
Measuring Worms p. 2
Summary Measures: "Centre" p. 3
Summary Measures: "Spread" p. 3
Generalising from the Sample to the Population p. 7
How Reliable Is Our Sample Estimate? p. 8
Naming of Parts p. 8
The Normal Distribution p. 8
Probability p. 10
What Do We Mean by a Probability? p. 11
Writing Down Probabilities p. 11
Multiplication Law (Product Rule) p. 12
Addition Law (Summation Rule) p. 12
Important Restriction p. 12
An Example p. 13
Probability Density Functions p. 14
What Have We Drawn, Exactly? p. 15
Continuous Measurements - Worms Again p. 16
Standardising the Normal - An Ingenious Arithmetical Conjuring Trick p. 19
Estimating Population Parameters from Sample Statistics p. 21
Expressing Variability p. 22
The First Step - The Sum of the Differences p. 22
The Second Step - The Sum of the Squared Differences p. 22
Third Step - The Variance p. 24
Degrees of Freedom p. 25
Estimated Parameters p. 25
Bias in the Estimation p. 26
Fourth Step - The Standard Deviation p. 27
Fifth Step - The Sampling Distribution of the Mean p. 28
Sixth Step - The Standard Error of the Mean p. 30
Confidence Intervals p. 33
The Importance of Confidence Intervals p. 33
Calculating Confidence Intervals p. 34
Another Way of Looking at It p. 36
Your First Statistical Test p. 38
Develop a Research Hypothesis - Something That You Can Test p. 38
Deduce a Null Hypothesis - Something That You Can Disprove p. 39
Collect the Data p. 39
Calculate a Test Statistic p. 40
Find the Probability of the Test Statistic Value if the Null Hypothesis Was True p. 40
Finding the Probability Directly p. 40
Comparing the Test-Statistic with a Threshold p. 40
Decide Whether to Reject or Accept the Null Hypothesis p. 42
Using the Computer to Conduct the Test p. 43
One- and Two-Tailed Tests p. 44
Why Is the Two-Tailed Confidence Interval Different from the One-Tailed? p. 46
What if the New Area Turned Out to Have Smaller Fish? p. 47
Tails and Tables p. 49
When You Can and Cannot Use a One-Tailed Alternative p. 49
The Other Side of the Coin - Type II Errors p. 49
Recap - Hypothesis Testing p. 50
A Complication p. 51
Testing Fish with t p. 52
MINITAB Does a One-Sample t-Test p. 53
95% CI for Worms p. 53
Anatomy of Test Statistics p. 54
Comparing Things: Two Sample Tests p. 57
A Simple Case p. 57
Matched-Pairs t-Test p. 58
Another Example - Testing Twin Sheep p. 60
Independent Samples: Comparing Two Populations p. 63
The Two-Sample t-Test p. 63
Calculation of Independent Samples t-Test p. 64
One- and Two-Tailed Tests - A Reminder p. 69
MINITAB Carries Out a Two-Sample t-Test p. 70
Pooling the Variances? p. 71
Why Pool? p. 71
When to Pool? p. 71
What if the Variances Are Different? p. 72
Planning an Experiment p. 75
Principles of Sampling p. 75
First, Catch Your Worm! p. 75
The Concept of Random Sampling p. 76
How to Select a Random Sample p. 76
Systematic Sampling p. 77
Comparing More Than Two Groups p. 78
Principles of Experimental Design p. 79
Objectives p. 79
Replication p. 79
Randomisation p. 81
Controls p. 82
Blocking p. 83
Recording Data and Simulating an Experiment p. 86
Simulating Your Experiment p. 86
Creating the Data Set p. 87
Analysing the Simulated Data p. 89
Partitioning Variation and Constructing a Model p. 91
It's Simple... p. 91
...But Not That Simple p. 91
The Example: Field Margins in Conservation p. 92
The Idea of a Statistical Model p. 93
Laying Out the Experiment p. 94
Replication p. 94
Randomisation and Blocking p. 95
Practical Considerations p. 96
Sources of Variation: Random Variation p. 97
The Model p. 98
Blocking p. 99
Analysing Your Results: Is There Anything There? p. 105
Is Spider Abundance Affected by Treatment? p. 105
Why Not Use Multiple t-Tests? p. 105
ANOVA for a Wholly Randomised Design p. 106
Calculating the Total Sum-of-Squares p. 107
Calculating the Error (Residual) Sum-of-Squares p. 110
Calculating the Treatment Sum-of-Squares p. 110
Comparing the Sources of Variation p. 111
The Two Extremes of Explanation: All or Nothing p. 111
Treatments Explain Nothing p. 111
Treatments Explain Everything p. 112
The ANOVA Table p. 112
Sources of Variation and Degrees of Freedom p. 112
Comparing the Sums of Squares p. 113
The Mean Square p. 114
Testing Our Hypothesis p. 115
Including Blocks: Randomised Complete Block Designs p. 116
Analysing the Spider Data Set in MINITAB p. 119
One-Way ANOVA p. 119
Two-Way ANOVA p. 120
Box Plots for Treatments p. 121
The Assumptions Behind ANOVA and How to Test Them p. 122
Independence p. 122
Normality of Error p. 122
Homogeneity of Variance p. 124
Additivity p. 124
Another Use for the F-Test: Testing Homogeneity of Variance p. 125
Interpreting Your Analysis: From Hypothesis Testing to Biological Meaning p. 127
Treatment Means and Confidence Intervals p. 127
Calculating the 95% Confidence Interval for the Treatment Mean p. 128
Difference Between Two Treatment Means p. 129
Getting More Out of an Experiment: Factorial Designs and Interactions p. 130
What Is "Hidden Replication"? p. 131
Getting More Out of the Analysis: Using the Factorial Design to Ask More Relevant Questions p. 131
Interactions p. 134
Where Does the Interaction Term Come from? p. 134
Testing the Interaction: Is It Significant? p. 135
Degrees of Freedom for an Interaction Term p. 135
Adding Blocking to the Factorial Analysis p. 137
How to Interpret Interaction Plots: The Plant Hormone Experiment p. 138
Loss of Data and Unbalanced Experiments p. 142
An Example of Loss of Data: The Plant Hormone Experiment p. 143
Calculating Standard Errors Where You Have Missing Observations p. 144
Limitations of ANOVA and the General Linear Model (GLM) p. 145
Relating One Variable to Another p. 147
Correlation p. 147
Calculating the Correlation Coefficient, and a New Idea: Covariance p. 151
Regression p. 152
Linear Regression p. 154
The Model p. 155
Interpreting Hypothesis Tests in Regression p. 160
Fitting Data to Hypotheses p. 160
A Further Example of Linear Regression p. 161
Assumptions p. 164
Independence p. 164
Normal Distribution of Error p. 165
Homogeneity of Variance p. 165
Linearity p. 165
Continuity p. 165
Absence of "Errors" in x-Values p. 167
The Importance of Plotting Observations p. 168
Same Equation from Different Patterns? p. 168
Plot the Data and the Fitted Line p. 170
Plot the Histogram of the Standardised Residuals p. 170
Plot the Residuals against the Fitted Values p. 170
Conclusion p. 174
Confidence Intervals p. 174
C.I. for the Slope of the Line p. 175
C.I. for the Regression Line p. 175
Standard Error of Prediction (Prediction Interval) p. 176
Caution in the Interpretation of Regression and Correlation p. 178
Correlation Is Not Causation p. 178
Extrapolation Is Dangerous! p. 178
Categorical Data p. 179
The Chi-Squared Goodness-of-Fit Test p. 180
Simple Example: Sex Ratio in an Oxford Family p. 180
A More Interesting Example: Testing Genetic Models p. 181
Expected Proportions p. 182
Expected Frequencies p. 184
Degrees of Freedom - A Catch p. 184
Hypothesis Testing in Genetics p. 185
Contingency Analysis: Chi-Squared Test of Proportions p. 185
Organizing the Data for Contingency Analysis p. 187
Some Important Requirements for Carrying Out a Valid x[superscript 2] Contingency Test p. 189
A Further Example of a Chi-Squared Contingency Test p. 191
Beyond Two-Dimensional Tables: The Likelihood Ratio Chi-Square p. 192
Nonparametric Tests p. 195
Introduction p. 195
When Are Assumptions Likely to Fail? p. 196
Basic Ideas p. 199
Ranking p. 199
Measures of Centre and Scatter p. 200
Median p. 200
Quartiles and Other Quantiles p. 201
A Taxonomy of Tests p. 202
Hypothesis Testing p. 202
Test Statistics p. 202
Single-Sample Tests p. 203
Sign Test p. 203
Wilcoxon Single-Sample Test p. 204
Matched-Pairs Tests p. 205
Sign Test and Wilcoxon on Differences p. 206
Independent Samples p. 206
Two Groups: Mann-Whitney Test p. 206
More than Two Groups: Kruskal-Wallis Test p. 208
Another Example of the Kruskal-Wallis Test p. 211
Several Groups with Blocking: Friedman's Test p. 212
Antibiotic Experiment with Blocking p. 214
Two Quantitative Variables: Spearman's Rank Correlation p. 216
Tied Observations in Spearman's Correlation p. 218
Why Bother with Parametric Tests? p. 218
Nonparametrics Have Lower Power Efficiency p. 218
Available Nonparametric Analyses Are Less Complex p. 218
Managing Your Project p. 219
Choosing a Topic and a Supervisor p. 219
Common Mistakes p. 220
General Principles of Experimental Design and Execution p. 221
What Are the Aims and Objectives of the Experiment? p. 221
What Population Are You Studying? p. 221
What Are the Experimental Units, and How Are They Grouped? p. 222
What Are the Experimental Treatments, and What Is Your Control? p. 222
Will Randomisation Be across All the Experimental Units or Constrained within Groups? p. 223
How Many Replicates Should You Have? p. 223
What Resources (and Constraints) Do You Have? p. 223
How Will You Analyse Your Data? p. 224
Recording Data p. 224
Other Considerations: Health and Safety, Ethical and Legal Issues p. 224
Fieldwork p. 225
Labwork p. 225
Analysing Your Data and Writing the Report p. 226
Are Your Data Correct? p. 226
Structure p. 227
Title p. 227
Abstract p. 227
Introduction p. 227
Materials and Methods p. 227
Results p. 228
Discussion p. 228
References p. 229
Acknowledgments p. 229
Appendices p. 229
The First Draft p. 230
Illustrating Results p. 230
Graphs p. 231
Tables p. 231
What It Is All About: Getting Through Your Project p. 232
An Introduction to MINITAB p. 237
Conventions Used in This Book p. 237
Starting Up p. 238
Help p. 238
Data Entry p. 238
Looking at the Worms Data p. 239
Display the Information in a Column p. 239
Dot Plot the Data p. 239
Produce Summary Statistics p. 239
Box Plot p. 239
Histogram p. 240
Updating Graphs p. 241
Stacking and Unstacking - A Useful Trick p. 241
Looking Up Probabilities p. 242
Probability Density p. 243
Cumulative Density p. 243
Inverse Cumulative Density p. 244
Graphical Output - New in MINITAB 15 p. 245
Report Writer p. 245
The MINITAB Command Line p. 246
Saving Your Session p. 247
Statistical Power and Sample Size p. 249
Statistical Tables p. 255
References and Further Reading p. 265
References p. 265
Further Reading p. 265
Statistical Tests p. 267
Index p. 269