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| Why use this book | |
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| How to use this book | |
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| How to teach this text | |
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| An introduction to analysis of variance | |
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| Model formulae and geometrical pictures | |
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| General Linear Models | |
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| The basic principles of ANOVA | |
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| An example of ANOVA | |
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| The geometrical approach for an ANOVA | |
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| Regression | |
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| What kind of data are suitable for regression? | |
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| How is the best fit line chosen? | |
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| The geometrical view of regression | |
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| Regression--an example | |
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| Confidence and prediction intervals | |
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| Conclusions from a regression analysis | |
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| Unusual observations | |
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| The role of X and Y--does it matter which is which? | |
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| Models, parameters and GLMs | |
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| Populations and parameters | |
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| Expressing all models as linear equations | |
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| Turning the tables and creating datasets | |
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| Using more than one explanatory variable | |
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| Why use more than one explanatory variable? | |
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| Elimination by considering residuals | |
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| Two types of sum of squares | |
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| Urban Foxes--an example of statistical elimination | |
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| Statistical elimination by geometrical analogy | |
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| Designing experiments--keeping it simple | |
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| Three fundamental principles of experimental design | |
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| The geometrical analogy for blocking | |
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| The concept of orthogonality | |
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| Combining continuous and categorical variables | |
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| Reprise of models fitted so far | |
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| Combining continuous and categorical variables | |
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| Orthogonality in the context of continuous and categorical variables | |
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| Treating variables as continuous or categorical | |
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| The general nature of General Linear Models | |
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| Interactions--getting more complex | |
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| The factorial principle | |
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| Analysis of factorial experiments | |
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| What do we mean by an interaction? | |
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| Presenting the results | |
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| Extending the concept of interactions to continuous variables | |
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| Uses of interactions | |
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| Checking the models I: independence | |
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| Heterogeneous data | |
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| Repeated measures | |
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| Nested data | |
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| Detecting non-independence | |
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| Checking the models II: the other three asumptions | |
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| Homogeneity of variance | |
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| Normality of error | |
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| Linearity/additivity | |
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| Model criticism and solutions | |
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| Predicting the volume of merchantable wood: an example of model criticism | |
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| Selecting a transformation | |
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| Model selection I: principles of model choice and designed experiments | |
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| The problem of model choice | |
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| Three principles of model choice | |
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| Four different types of model choice problem | |
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| Orthogonal and near orthogonal designed experiments | |
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| Looking for trends across levels of a categorical variable | |
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| Model selection II: datasets with several explanatory variables | |
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| Economy of variables in the context of multiple regression | |
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| Multiplicity of p-values in the context of multiple regression | |
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| Automated model selection procedures | |
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| Whale Watching: using the GLM approach | |
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| Random effects | |
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| What are random effects? | |
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| Four new concepts to deal with random effects | |
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| A one-way ANOVA with a random factor | |
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| A two-level nested ANOVA | |
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| Mixing random and fixed effects | |
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| Using mock analyses to plan an experiment | |
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| Categorical data | |
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| Categorical data: the basics | |
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| The Poisson distribution | |
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| The chi-squared test in contingency tables | |
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| General linear models and categorical data | |
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| What lies beyond? | |
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| Generalised Linear Models | |
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| Multiple y variables, repeated measures and within-subject factors | |
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| Conclusion | |
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| Answers to exercises | |
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| Revision section: The basics | |
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| Populations and samples | |
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| Three types of variability: of the sample, the population and the estimate | |
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| Confidence intervals: a way of precisely representing uncertainty | |
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| The null hypothesis--taking the conservative approach | |
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| Comparing two means | |
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| Conclusion | |
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| The meaning of p-values and confidence intervals | |
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| What is a p-value? | |
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| What is a confidence interval? | |
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| Analytical results about variances of sample means | |
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| Introducing the basic notation | |
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| Using the notation to define the variance of a sample | |
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| Using the notation to define the mean of a sample | |
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| Defining the variance of the sample mean | |
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| To illustrate why the sample variance must be calculated with n - 1 in its denominator (rather than n) to be an unbiased estimate of the population variance | |
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| Probability distributions | |
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| Some gentle theory | |
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| Confirming simulations | |
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| Bibliography | |
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| Index | |