1
2
Elements of Experimentation.
Single-Factor Experiments.
Two-Factor Experiments.
Three-or More-Factor Experiments.
Comparison Between Treatment Means.
Analysis of Multiobservation Data.
Problem Data.
Analysis of Data from a Series of Experiments.
Regression and Correlation Analysis.
Covariance Analysis.
Chi-Square Test.
Soil Heterogeneity.
Competition Effects.
Mechanical Errors.
Sampling in Experimental Plots.
Experiments in Farmers' Fields.
Presentation of Experimental Results.
Appendices.
Index.
Single-Factor Experiments.
Two-Factor Experiments.
Three-or More-Factor Experiments.
Comparison Between Treatment Means.
Analysis of Multiobservation Data.
Problem Data.
Analysis of Data from a Series of Experiments.
Regression and Correlation Analysis.
Covariance Analysis.
Chi-Square Test.
Soil Heterogeneity.
Competition Effects.
Mechanical Errors.
Sampling in Experimental Plots.
Experiments in Farmers' Fields.
Presentation of Experimental Results.
Appendices.
Index.
3
Preface.
1 Eight steps to successful data analysis.
2 The basics.
Observations.
Hypothesis testing.
P-values.
Sampling.
Experiments.
Statistics.
3 Choosing a test: a key.
Remember: eight steps to successful data analysis.
The art of choosing a test.
A key to assist in your choice of statistical test.
4 Hypothesis testing, sampling and experimental design.
Hypothesis testing.
Acceptable errors.
P-values.
Sampling.
Experimental design.
5 Statistics, variables and distributions.
What are statistics?
Types of statistics.
What is a variable?
Types of variables or scales of measurement.
Types of distribution.
Discrete distributions.
Continuous distributions.
Non-parametric ‘distributions’.
6 Descriptive and presentational techniques.
General advice.
Displaying data: summarizing a single variable.
Displaying data: showing the distribution of a single variable.
Descriptive statistics.
Using the computer packages.
Displaying data: summarizing two or more variables.
Displaying data: comparing two variables.
Displaying data: comparing more than two variables.
7 The tests 1: tests to look at differences.
Do frequency distributions differ?
Do the observations from two groups differ?
Do the observations from more than two groups differ?
There are two independent ways of classifying the data.
More than one observation for each factor combination (with replication).
There are more than two independent ways to classify the data.
Not all classifications are independent.
Nested or hierarchical designs.
8 The tests 2: tests to look at relationships.
Is there a correlation or association between two variables?
Is there a cause-and-effect relationship between two variables?
Tests for more than two variables.
9 The tests 3: tests for data exploration.
Types of data.
Observation, inspection and plotting.
Symbols and letters used in statistics.
Greek letters.
Symbols.
Upper-case letters.
Lower-case letters.
Glossary.
Assumptions of the tests.
Hints and tips.
A table of statistical tests.
Index.
4
Preface.
1. How to Use this Book.
Introduction.
The Text of the Chapters.
What Should You Do if You Run into Trouble?
Elephants.
The Numerical Examples in the Text.
Boxes.
Spare-time Activities.
Executive Summaries.
Why Go to All that Bother?
The Bibliography.
2. Introduction.
What are Statistics?
Notation.
Notation for Calculating the Mean.
3. Summarizing Variation.
Introduction.
Different Summaries of Variation.
Why n – 1?
Why the Squared Deviations?
The Standard Deviation.
The Next Chapter.
4. When are Sums of Squares Not Sums of Squares?
Introduction.
Calculating Machines Offer a Quicker Method of Calculating Sums of Squares.
Avoid Being Confused by the Term “Sum of Squares”.
Summary of the Calculator Method of Calculating Down to Standard Deviation.
5. The Normal Distribution.
Introduction.
Frequency Distributions.
The Normal Distribution.
What Per Cent is a Standard Deviation Worth?
Are the Percentages Always the Same as These?
Other Similar Scales in Everyday Life.
The Standard Deviation as an Estimate of the Frequency of a Number Occurring in a Sample.
From Per Cent to Probability.
Executive Summary 1 –The Standard Deviation.
6. The Relevance of the Normal Distribution to Biological Data.
To Recap.
Is Our Observed Distribution Normal?
What Can We Do about a Distribution that Clearly is not Normal?
How Many Samples are Needed?
7. Further Calculations from the Normal Distribution.
Introduction.
Is “A” Bigger than “B”?
The Yardstick for Deciding.
Derivation of the Standard Error of a Difference Between Two Means.
The Importance of the Standard Error of Differences Between Means.
Summary of this Chapter.
Executive Summary 2 – Standard Error of a Difference Between Two Means.
8. The t-test.
Introduction.
The Principle of the t-test.
The t-test in Statistical Terms.
Why t?
Tables of the t-distribution.
The Standard t-test.
t-test for Means Associated with Unequal Variances.
The Paired t-test.
Executive Summary 3 – The t-test.
9. One Tail or Two?
Introduction.
Why is the Analysis of Variance F-test One-tailed?
The Two-tailed F-test.
How Many Tails has the t-test?
The Final Conclusion on Number of Tails.
10. Analysis of Variance – What is it? How Does it work?
Introduction.
Sums of Squares in the Analysis of Variance.
Some “Made-up” Variation to Analyze by Anova.
The Sum of Squares Table.
Using Anova to Sort Out the Variation in Table C.
The Relationship Between “t” and “F”.
Constraints on the Analysis of Variance.
Comparison Between Treatment Means in the Analysis of Variance.
The Least Significant Difference.
A Caveat About Using the LSD.
Executive Summary 4 – The Principle of the Analysis of Variance.
11. Experimental Designs for Analysis of Variance.
Introduction.
Fully Randomized.
Randomized Blocks.
Incomplete Blocks.
Latin Square.
Split Plot.
Executive Summary 5 – Analysis of a Randomized Block Experiment.
12. Introduction to Factorial Experiments.
What is a Factorial Experiment?
Interaction.
How Does a Factorial Experiment Change the Form of the Analysis of Variance?
Sums of Squares for Interactions.
13. 2-Factor Factorial Experiments.
Introduction.
An Example of a 2-Factor Experiment.
Analysis of the 2-Factor Experiment.
Two Important Things to Remember About Factorials Before Tackling the Next Chapter.
Analysis of Factorial Experiments with Unequal Replication.
Executive Summary 6 – Analysis of a 2-Factor Randomized Block Experiment.
14. Factorial Experiments with More than Two Factors.
Introduction.
Different “Orders” of Interaction.
Example of a 4-Factor Experiment.
Addendum – Additional Working of Sum of Squares Calculations.
15. Factorial Experiments with Split Plots.
Introduction.
Deriving the Split Plot Design from the Randomized Block Design.
Degrees of Freedom in a Split Plot Analysis.
Numerical Example of a Split Plot Experiment and its Analysis.
Comparison of Split Plot and Randomized Block Experiment.
Uses of Split Plot Designs.
16. The t-test in the Analysis of Variance.
Introduction.
Brief Recap of Relevant Earlier Sections of this Book.
Least Significant Difference Test.
Multiple Range Tests.
Testing Differences Between Means.
Presentation of the Results of Tests of Differences Between Means.
The Results of the Experiments Analyzed by Analysis of Variance in Chapters 11–15.
17. Linear Regression and Correlation.
Introduction.
Cause and Effect.
Other Traps Waiting for You to Fall Into.
Regression.
Independent and Dependent Variables.
The Regression Coefficient (b).
Calculating the Regression Coefficient (b).
The Regression Equation.
A Worked Example on Some Real Data.
Correlation.
Extensions of Regression Analysis.
Executive Summary 7 – Linear Regression.
18. Chi-square Tests.
Introduction.
When and Where Not to Use c2.
The Problem of Low Frequencies.
Yates' Correction for Continuity.
The c 2 Test for “Goodness of Fit”.
Association (or Contingency) c2.
19. Nonparametric Methods (What are They?).
Disclaimer.
Introduction.
Advantages and Disadvantages of the Two Approaches.
Some Ways Data are Organized for Nonparametric Tests.
The Main Nonparametric Methods that are Available.
Appendix.
A1 How Many Replicates?
A2 Statistical Tables.
A3 Solutions to “Spare-time Activities”.
A4 Bibliography.
Index.
5
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