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Preface | |

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Basic Principles of Experimentation | |

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Introduction | |

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Field and glasshouse experiments | |

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Choice of site | |

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Soil testing | |

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Satellite mapping | |

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Sampling | |

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Basic Statistical Calculations | |

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Introduction | |

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Measurements and type of variable | |

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Samples and populations | |

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Basic Data Summary | |

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Introduction | |

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Frequency distributions (discrete data) | |

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Frequency distributions (continuous data) | |

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Descriptive statistics | |

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The Normal Distribution, the t-Distribution and Confidence Intervals | |

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Introduction to the normal distribution | |

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The standard normal distribution | |

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Further use of the normal tables | |

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Use of the percentage points table (Appendix 2) | |

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The normal distribution in practice | |

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Introduction to confidence intervals | |

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Estimation of the population mean, [mu] | |

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The sampling distribution of the mean | |

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Confidence limits for [mu] when [sigma] is known | |

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Confidence limits for [mu] when [sigma] is unknown--use of the t-distribution | |

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Determination of sample size | |

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Estimation of total crop yield | |

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Introduction to Hypothesis Testing | |

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The standard normal distribution and the t-distribution | |

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The single sample t-test | |

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The P-value | |

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Type I and Type II errors | |

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Choice of level of significance | |

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The usefulness of a test | |

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Estimation versus hypothesis testing | |

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The paired samples t-test | |

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Comparison of Two Independent Sample Means | |

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Introduction | |

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The Independent Samples t-test | |

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Confidence intervals | |

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The theory behind the t-test | |

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The F-test | |

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Unequal sample variances | |

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Determination of sample size for a given precision | |

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Linear Regression and Correlation | |

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Basic principles of Simple Linear Regression (SLR) | |

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Experimental versus observational studies | |

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The correlation coefficient | |

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The least squares regression line and its estimation | |

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Calculation of residuals | |

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The goodness of fit | |

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Calculation of the correlation coefficient | |

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Assumptions, hypothesis tests and confidence intervals for simple linear regression | |

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Testing the significance of a correlation coefficient | |

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Curve Fitting | |

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Introduction | |

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Polynomial fitting | |

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Quadratic regression | |

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Other types of curve | |

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Multiple linear regression | |

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The Completely Randomised Design | |

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Introduction | |

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Design construction | |

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Preliminary analysis | |

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The one-way analysis of variance model | |

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Analysis of variance | |

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After ANOVA | |

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Reporting results | |

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The completely randomised design--unequal replication | |

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Determination of number of replicates per treatment | |

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The Randomised Block Design | |

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Introduction | |

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The analysis ignoring blocks | |

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The analysis including blocks | |

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Using the computer | |

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The effect of blocking | |

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The randomised blocks model | |

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Using a hand calculator to find the sums of squares | |

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Comparison of treatment means | |

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Reporting the results | |

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Deciding how many blocks to use | |

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Plot sampling | |

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The Latin Square Design | |

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Introduction | |

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Randomisation | |

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Interpretation of computer output | |

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The Latin square model | |

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Using your calculator | |

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Factorial Experiments | |

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Introduction | |

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Advantages of factorial experiments | |

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Main effects and interactions | |

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Varieties as factors | |

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Analysis of a randomised blocks factorial experiment with two factors | |

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General advice on presentation | |

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Experiments with more than two factors | |

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Confounding | |

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Fractional replication | |

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Comparison of Treatment Means | |

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Introduction | |

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Treatments with no structure | |

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Treatments with structure (factorial structure) | |

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Treatments with structure (levels of a quantitative factor) | |

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Treatments with structure (contrasts) | |

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Checking the Assumptions and Transformation of Data | |

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The assumptions | |

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Transformations | |

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Missing Values and Incomplete Blocks | |

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Introduction | |

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Missing values in a completely randomised design | |

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Missing values in a randomised block design | |

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Other types of experiment | |

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Incomplete block designs | |

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Split Plot Designs | |

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Introduction | |

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Uses of this design | |

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The skeleton analysis of variance tables | |

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An example with interpretation of computer output | |

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The growth cabinet problem | |

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Other types of split plot experiment | |

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Repeated measures | |

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Comparison of Regression Lines and Analysis of Covariance | |

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Introduction | |

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Comparison of two regression lines | |

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Analysis of covariance | |

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Analysis of covariance applied to a completely randomised design | |

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Comparing several regression lines | |

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Conclusion | |

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Analysis of Counts | |

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Introduction | |

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The binomial distribution | |

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Confidence intervals for a proportion | |

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Hypothesis test of a proportion | |

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Comparing two proportions | |

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The chi-square goodness of fit test | |

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r [times] c contingency tables | |

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2 [times] c contingency tables: comparison of several proportions | |

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2 [times] 2 contingency tables: comparison of two proportions | |

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Association of plant species | |

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Heterogeneity chi-square | |

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Some Non-parametric Methods | |

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Introduction | |

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The Sign test | |

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The Wilcoxon single-sample test | |

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The Wilcoxon matched pairs test | |

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The Mann-Whitney U test | |

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The Kruskal-Wallis test | |

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Friedman's test | |

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The normal distribution function | |

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Percentage points of the normal distribution | |

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Percentage points of the t-distribution | |

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5 per cent points of the F-distribution | |

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2.5 per cent points of the F-distribution | |

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1 per cent points of the F-distribution | |

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0.1 per cent points of the F-distribution | |

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Percentage points of the sample correlation coefficient (r) when the population correlation coefficient is 0 and n is the number of X, Y pairs | |

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5 per cent points of the Studentised range, for use in Tukey and SNK tests | |

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Percentage points of the chi-square distribution | |

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Probabilities of S or fewer successes in the binomial distribution with n 'trials' and p = 0.5 | |

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Critical values of T in the Wilcoxon signed rank or matched pairs test | |

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Critical values of U in the Mann-Whitney test | |

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References | |

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Further reading | |

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Index | |