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Preface | |

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How to use this book | |

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Introduction | |

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The text of the chapters | |

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What should you do if you run into trouble? | |

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Elephants | |

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The numerical examples in the text | |

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Boxes | |

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Spare-time activities | |

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Executive summaries | |

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Why go to all that bother? | |

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The bibliography | |

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Introduction | |

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What are statistics? | |

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Notation | |

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Notation for calculating the mean | |

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Summarizing variation | |

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Introduction | |

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Different summaries of variation | |

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Range | |

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Total deviation | |

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Mean deviation | |

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Variance | |

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Why n - 1? | |

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Why the squared deviations? | |

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The standard deviation | |

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The next chapter | |

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Spare-time activities | |

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When are sums of squares NOT sums of squares? | |

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Introduction | |

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Calculating machines offer a quicker method of calculating sums of squares | |

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Added squares | |

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The correction factor | |

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Avoid being confused by the term "sum of squares" | |

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Summary of the calculator method of calculating down to standard deviation | |

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Spare-time activities | |

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The normal distribution | |

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Introduction | |

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Frequency distributions | |

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The normal distribution | |

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What per cent is a standard deviation worth? | |

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Are the percentages always the same as these? | |

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Other similar scales in everyday life | |

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The standard deviation as an estimate of the frequency of a number occurring in a sample | |

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From per cent to probability | |

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Executive summary 1 - The standard deviation | |

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The relevance of the normal distribution to biological data | |

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To recap | |

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Is our observed distribution normal? | |

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Checking for normality | |

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What can we do about a distribution that clearly is not normal? | |

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Transformation | |

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Grouping samples | |

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Doing nothing! | |

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How many samples are needed? | |

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Factors affecting how many samples we should take | |

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Calculating how many samples are needed | |

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Further calculations from the normal distribution | |

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Introduction | |

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Is "A" bigger than "B"? | |

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The yardstick for deciding | |

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Derivation of the standard error of a difference between two means | |

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from variance of single data to variance of means | |

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from variance of single data to "variance of differences" | |

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The combination of Steps 1 and 2; the standard error of difference between means (s.e.d.m.) | |

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Recap of the calculation of s.e.d.m. from the variance calculated from the individual values | |

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The importance of the standard error of differences between means | |

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Summary of this chapter | |

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Executive summary 2 - Standard error of a difference between two means | |

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Spare-time activities | |

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The t-test | |

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Introduction | |

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The principle of the t-test | |

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The t-test in statistical terms | |

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Why t? | |

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Tables of the t-distribution | |

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The standard t-test | |

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The procedure | |

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The actual t-test | |

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t-test for means associated with unequal variances | |

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The s.e.d.m. when variances are unequal | |

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A worked example of the t-test for means associated with unequal variances | |

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The paired t-test | |

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Pair when possible | |

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Executive summary 3 - The t-test | |

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Spare-time activities | |

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One tail or two? | |

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Introduction | |

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Why is the analysis of variance F-test one-tailed? | |

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The two-tailed F-test | |

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How many tails has the t-test? | |

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The final conclusion on number of tails | |

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Analysis of variance - What is it? How does it work? | |

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Introduction | |

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Sums of squares in the analysis of variance | |

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Some "made-up" variation to analyze by Anova | |

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The sum of squares table | |

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Using Anova to sort out the variation in Table C | |

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Phase 1 | |

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Phase 2 | |

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SqADS - an important acronym | |

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Back to the sum of squares table | |

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How well does the analysis reflect the input? | |

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End Phase | |

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Degrees of freedom in Anova | |

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The completion of the End Phase | |

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The variance ratio | |

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The relationship between "t" and "F" | |

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Constraints on the analysis of variance | |

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Adequate size of experiment | |

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Equality of variance between treatments | |

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Testing the homogeneity of variance | |

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The element of chance: randomization | |

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Comparison between treatment means in the analysis of variance | |

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The least significant difference | |

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A caveat about using the LSD | |

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Executive summary 4 - The principle of the analysis of variance | |

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Experimental designs for analysis of variance | |

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Introduction | |

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Fully randomized | |

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Data for analysis of a fully randomized experiment | |

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Prelims | |

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Phase 1 | |

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Phase 2 | |

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End Phase | |

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Randomized blocks | |

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Data for analysis of a randomized block experiment | |

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Prelims | |

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Phase 1 | |

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Phase 2 | |

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End Phase | |

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Incomplete blocks | |

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Latin square | |

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Data for the analysis of a Latin square | |

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Prelims | |

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Phase 1 | |

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Phase 2 | |

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End Phase | |

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Further comments on the Latin square design | |

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Split plot | |

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Executive summary 5 - Analysis of a randomized block experiment | |

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Spare-time activities | |

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Introduction to factorial experiments | |

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What is a factorial experiment? | |

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Interaction | |

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If there is no interaction | |

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What if there is interaction? | |

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How about a biological example? | |

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Measuring any interaction between factors is often the main/only purpose of an experiment | |

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How does a factorial experiment change the form of the analysis of variance? | |

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Degrees of freedom for interactions | |

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The similarity between the "residual" in Phase 2 and the "interaction" in Phase 3 | |

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Sums of squares for interactions | |

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2-Factor factorial experiments | |

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Introduction | |

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An example of a 2-factor experiment | |

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Analysis of the 2-factor experiment | |

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Prelims | |

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Phase 1 | |

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Phase 2 | |

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End Phase (of Phase 2) | |

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Phase 3 | |

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End Phase (of Phase 3) | |

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Two important things to remember about factorials before tackling the next chapter | |

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Analysis of factorial experiments with unequal replication | |

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Executive summary 6 - Analysis of a 2-factor randomized block experiment | |

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Spare-time activity | |

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Factorial experiments with more than two factors | |

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Introduction | |

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Different "orders" of interaction | |

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Example of a 4-factor experiment | |

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Prelims | |

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Phase 1 | |

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Phase 2 | |

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Phase 3 | |

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To the End Phase | |

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Addendum - Additional working of sums of squares calculations | |

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Spare-time activity | |

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Factorial experiments with split plots | |

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Introduction | |

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Deriving the split plot design from the randomized block design | |

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Degrees of freedom in a split plot analysis | |

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Main plots | |

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Sub-plots | |

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Numerical example of a split plot experiment and its analysis | |

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Calculating the sums of squares | |

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End Phase | |

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Comparison of split plot and randomized block experiment | |

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Uses of split plot designs | |

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Spare-time activity | |

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The t-test in the analysis of variance | |

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Introduction | |

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Brief recap of relevant earlier sections of this book | |

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Least significant difference test | |

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Multiple range tests | |

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Operating the multiple range test | |

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Testing differences between means | |

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Suggested "rules" for testing differences between means | |

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Presentation of the results of tests of differences between means | |

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The results of the experiments analyzed by analysis of variance in Chapters 11-15 | |

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Spare-time activities | |

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Linear regression and correlation | |

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Introduction | |

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Cause and effect | |

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Other traps waiting for you to fall into | |

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Extrapolating beyond the range of your data | |

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Is a straight line appropriate? | |

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The distribution of variability | |

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Regression | |

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Independent and dependent variables | |

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The regression coefficient (b) | |

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Calculating the regression coefficient (b) | |

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The regression equation | |

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A worked example on some real data | |

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The data (Box 17.2) | |

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Calculating the regression coefficient (b) - i.e. the slope of the regression line | |

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Calculating the intercept (a) | |

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Drawing the regression line | |

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Testing the significance of the slope (b) of the regression | |

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How well do the points fit the line? - the coefficient of determination (r[superscript 2]) | |

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Correlation | |

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Derivation of the correlation coefficient (r) | |

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An example of correlation | |

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Is there a correlation line? | |

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Extensions of regression analysis | |

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Nonlinear regression | |

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Multiple linear regression | |

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Multiple nonlinear regression | |

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Analysis of covariance | |

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Executive summary 7 - Linear regression | |

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Spare-time activities | |

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Chi-square tests | |

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Introduction | |

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When and where not to use x[superscript 2] | |

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The problem of low frequencies | |

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Yates' correction for continuity | |

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The x[superscript 2] test for "goodness of fit" | |

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The case of more than two classes | |

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x[superscript 2] with heterogeneity | |

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Heterogeneity x[superscript 2] analysis with "covariance" | |

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Association (or contingency) x[superscript 2] | |

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2 x 2 contingency table | |

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Fisher's exact test for a 2 x 2 table | |

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Larger contingency tables | |

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Interpretation of contingency tables | |

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Spare-time activities | |

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Nonparametric methods (what are they?) | |

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Disclaimer | |

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Introduction | |

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Advantages and disadvantages of the two approaches | |

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Where nonparametric methods score | |

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Where parametric methods score | |

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Some ways data are organized for nonparametric tests | |

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The sign test | |

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The Kruskal-Wallis analysis of ranks | |

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Kendall's rank correlation coefficient | |

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The main nonparametric methods that are available | |

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How many replicates | |

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Statistical tables | |

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Solutions to "Spare-time activities" | |

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Bibliography | |

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Index | |