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Preface | |

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Introduction | |

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Why do life scientists need to know about experimental design and statistics? | |

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What is this book designed to do? | |

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'Doing science' - hypotheses, experiments, and disproof | |

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Introduction | |

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Basic scientific method | |

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Making a decision about an hypothesis | |

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Why can't an hypothesis or theory ever be proven? | |

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'Negative' outcomes | |

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Null and alternate hypotheses | |

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Conclusion | |

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Collecting and displaying data | |

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Introduction | |

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Variables, experimental units, and types of data | |

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Displaying data | |

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Displaying ordinal or nominal scale data | |

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Bivariate data | |

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Multivariate data | |

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Summary and conclusion | |

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Introductory concepts of experimental design | |

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Introduction | |

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Sampling - mensurative experiments | |

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Manipulative experiments | |

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Sometimes you can only do an unreplicated experiment | |

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Realism | |

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A bit of common sense | |

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Designing a 'good' experiment | |

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Conclusion | |

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Probability helps you make a decision about your results | |

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Introduction | |

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Statistical tests and significance levels | |

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What has this got to do with making a decision or statistical testing? | |

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Making the wrong decision | |

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Other probability levels | |

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How are probability values reported? | |

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All statistical tests do the same basic thing | |

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A very simple example - the chi-square test for goodness of fit | |

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What if you get a statistic with a probability of exactly 0.05? | |

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Statistical significance and biological significance | |

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Summary and conclusion | |

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Working from samples - data, populations, and statistics | |

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Using a sample to infer the characteristics of a population | |

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Statistical tests | |

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The normal distribution | |

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Samples and populations | |

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Your sample mean may not be an accurate estimate of the population mean | |

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What do you do when you only have data from one sample? | |

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Why are the statistics that describe the normal distribution so important? | |

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Distributions that are not normal | |

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Other distributions | |

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Other statistics that describe a distribution | |

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Conclusion | |

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Normal distributions - tests for comparing the means of one and two samples | |

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Introduction | |

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The 95% confidence interval and 95% confidence limits | |

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Using the Z statistic to compare a sample mean and population mean when population statistics are known | |

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Comparing a sample mean with an expected value | |

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Comparing the means of two related samples | |

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Comparing the means of two independent samples | |

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Are your data appropriate for a t test? | |

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Distinguishing between data that should be analysed by a paired sample test or a test for two independent samples | |

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Conclusion | |

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Type 1 and Type 2 errors, power, and sample size | |

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Introduction | |

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Type 1 error | |

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Type 2 error | |

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The power of a test | |

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What sample size do you need to ensure the risk of Type 2 error is not too high? | |

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Type 1 error, Type 2 error, and the concept of biological risk | |

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Conclusion | |

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Single factor analysis of variance | |

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Introduction | |

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Single factor analysis of variance | |

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An arithmetic/pictorial example | |

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Unequal sample sizes (unbalanced designs) | |

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An ANOVA does not tell you which particular treatments appear to be from different populations | |

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Fixed or random effects | |

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Multiple comparisons after ANOVA | |

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Introduction | |

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Multiple comparison tests after a Model I ANOVA | |

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An a-posteriori Tukey comparison following a significant result for a single factor Model I ANOVA | |

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Other a-posteriori multiple comparison tests | |

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Planned comparisons | |

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Two factor analysis of variance | |

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Introduction | |

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What does a two factor ANOVA do? | |

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How does a two factor ANOVA analyse these data? | |

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How does a two factor ANOVA separate out the effects of each factor and interaction? | |

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An example of a two factor analysis of variance | |

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Some essential cautions and important complications | |

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Unbalanced designs | |

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More complex designs | |

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Important assumptions of analysis of variance: transformations and a test for equality of variances | |

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Introduction | |

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Homogeneity of variances | |

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Normally distributed data | |

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Independence | |

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Transformations | |

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Are transformations legitimate? | |

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Tests for heteroscedasticity | |

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Two factor analysis of variance without replication, and nested analysis of variance | |

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Introduction | |

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Two factor ANOVA without replication | |

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A-posteriori comparison of means after a two factor ANOVA without replication | |

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Randomised blocks | |

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Nested ANOVA as a special case of a one factor ANOVA | |

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A pictorial explanation of a nested ANOVA | |

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A final comment on ANOVA - this book is only an introduction | |

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Relationships between variables: linear correlation and linear regression | |

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Introduction | |

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Correlation contrasted with regression | |

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Linear correlation | |

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Calculation of the Pearson r statistic | |

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Is the value of r statistically significant? | |

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Assumptions of linear correlation | |

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Summary and conclusion | |

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Simple linear regression | |

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Introduction | |

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Linear regression | |

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Calculation of the slope of the regression line | |

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Calculation of the intercept with the Y axis | |

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Testing the significance of the slope and the intercept of the regression line | |

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An example - mites that live in the your hair follicles | |

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Predicting a value of Y from a value of X | |

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Predicting a value of X from a value of Y | |

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The danger of extrapolating beyond the range of data available | |

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Assumptions of linear regression analysis | |

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Further topics in regression | |

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Non-parametric statistics | |

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Introduction | |

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The danger of assuming normality when a population is grossly non-normal | |

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The value of making a preliminary inspection of the data | |

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Non-parametric tests for nominal scale data | |

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Introduction | |

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Comparing observed and expected frequencies - the chi-square test for goodness of fit | |

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Comparing proportions among two or more independent samples | |

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Bias when there is one degree of freedom | |

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Three-dimensional contingency tables | |

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Inappropriate use of tests for goodness of fit and heterogeneity | |

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Recommended tests for categorical data | |

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Comparing proportions among two or more related samples of nominal scale data | |

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Non-parametric tests for ratio, interval, or ordinal scale data | |

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Introduction | |

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A non-parametric comparison between one sample and an expected distribution | |

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Non-parametric comparisons between two independent samples | |

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Non-parametric comparisons among more than two independent samples | |

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Non-parametric comparisons of two related samples | |

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Non-parametric comparisons among three or more related samples | |

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Analysing ratio, interval, or ordinal data that show gross differences in variance among treatments and cannot be satisfactorily transformed | |

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Non-parametric correlation analysis | |

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Other non-parametric tests | |

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Choosing a test | |

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Introduction | |

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Doing science responsibly and ethically | |

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Introduction | |

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Dealing fairly with other people's work | |

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Doing the experiment | |

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Evaluating and reporting results | |

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Quality control in science | |

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References | |

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Index | |