Preface |
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xiii | |
Acknowledgments |
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xv | |
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1 | (17) |
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1.1 Structure of this book |
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3 | (2) |
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1.1.1 Introductory sections |
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4 | (1) |
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1.1.2 Approaches to consider when setting up a new animal model |
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4 | (1) |
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1.1.3 Approaches to consider when generating hypotheses |
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5 | (1) |
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1.1.4 Approaches to consider when testing hypotheses |
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5 | (1) |
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1.2 Statistical problems faced by animal researchers |
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5 | (1) |
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1.3 Pitfalls encountered when applying statistics in practice |
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6 | (9) |
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1.3.1 Pitfalls with experimental design |
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6 | (3) |
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1.3.2 Pitfalls with randomisation |
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9 | (1) |
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1.3.3 Pitfalls with statistical analysis |
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10 | (3) |
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1.3.4 Pitfalls when reporting animal experiments |
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13 | (2) |
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1.4 So where does statistics fit in? |
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15 | (1) |
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1.5 The ARRIVE guidelines |
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15 | (3) |
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18 | (12) |
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2.1 Decision-making: the signal-to-noise ratio |
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18 | (1) |
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2.2 Probability distributions |
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19 | (4) |
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2.2.1 The frequency distribution |
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20 | (1) |
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2.2.2 The density distribution |
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20 | (1) |
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2.2.3 The probability distribution |
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21 | (1) |
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2.2.4 The normal distribution |
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21 | (1) |
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2.2.5 The chi-squared distribution |
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22 | (1) |
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22 | (1) |
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23 | (1) |
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2.3 The hypothesis testing procedure |
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23 | (5) |
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2.3.1 The null and alternative hypotheses |
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23 | (2) |
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25 | (1) |
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2.3.3 The significance level |
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25 | (1) |
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26 | (1) |
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2.3.5 Type I and Type II errors |
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26 | (2) |
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2.4 Exploratory vs. confirmatory experiments |
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28 | (1) |
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2.5 The estimation process |
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29 | (1) |
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30 | (92) |
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3.1 Why design experiments? |
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30 | (2) |
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30 | (1) |
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3.1.2 Statistical reasons: variability, the signal and bias |
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31 | (1) |
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3.2 What does an experimental design involve? |
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32 | (14) |
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3.2.1 Variables to be recorded |
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32 | (1) |
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3.2.1.1 Types of response |
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32 | (2) |
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3.2.1.2 Reporting responses |
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34 | (1) |
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3.2.1.3 Baseline responses |
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34 | (1) |
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3.2.1.4 Recording conditions during the experiment |
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35 | (1) |
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35 | (1) |
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3.2.3 The experimental unit and the observational unit |
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36 | (1) |
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3.2.4 Effects and factors |
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37 | (2) |
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3.2.4.1 Defining factor level labels |
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39 | (1) |
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3.2.4.2 Defining the factors in an experimental design |
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39 | (1) |
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3.2.5 Fixed and random factors |
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39 | (1) |
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40 | (1) |
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40 | (1) |
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41 | (1) |
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3.2.6 Categorical factors and continuous factors |
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42 | (1) |
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3.2.7 Crossed factors and nested factors |
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42 | (1) |
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42 | (1) |
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43 | (2) |
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3.2.7.3 Partially crossed factors |
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45 | (1) |
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3.2.7.4 Designs containing nested and crossed factors |
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45 | (1) |
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3.2.8 Repeatedly measuring the animal |
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45 | (1) |
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3.3 Summary of design types |
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46 | (3) |
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46 | (1) |
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47 | (1) |
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3.3.3 Dose-response designs |
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47 | (1) |
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47 | (1) |
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48 | (1) |
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3.3.6 Repeated measures and dose-escalation designs |
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48 | (1) |
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3.3.7 Designs applied in practice |
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48 | (1) |
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49 | (14) |
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3.4.1 Practical reasons to block |
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49 | (1) |
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3.4.2 Statistical reasons to block |
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49 | (1) |
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3.4.2.1 Variance reduction |
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49 | (2) |
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51 | (1) |
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51 | (2) |
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3.4.4 Complete block designs |
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53 | (1) |
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53 | (1) |
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53 | (1) |
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3.4.4.3 Statistical analysis of block designs |
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54 | (1) |
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3.4.5 Incomplete block designs |
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54 | (1) |
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3.4.6 Balanced incomplete block design |
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55 | (1) |
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55 | (1) |
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55 | (1) |
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3.4.6.3 Statistical analysis |
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55 | (1) |
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3.4.7 More than one block: the row-column block design |
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56 | (1) |
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56 | (1) |
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56 | (1) |
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3.4.7.3 Statistical analysis |
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56 | (1) |
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3.4.8 Row-column block designs based on Latin squares |
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57 | (1) |
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58 | (1) |
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58 | (1) |
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3.4.8.3 Statistical analysis |
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58 | (1) |
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59 | (1) |
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3.4.9.1 Complete crossover designs |
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59 | (1) |
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3.4.9.2 Incomplete crossover designs |
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60 | (1) |
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3.4.9.3 The benefits of crossover designs |
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61 | (1) |
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3.4.9.4 The issues with crossover designs |
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62 | (1) |
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3.4.9.5 Treatment carry-over effects |
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62 | (1) |
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63 | (21) |
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64 | (1) |
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3.5.2 Categorical factors and interactions |
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64 | (2) |
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3.5.3 Small factorial designs |
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66 | (2) |
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3.5.4 Large factorial designs |
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68 | (1) |
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3.5.4.1 Strategies when setting up a new animal model |
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68 | (2) |
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3.5.4.2 Graphical representation of large factorial designs |
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70 | (1) |
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3.5.4.3 Hidden replication |
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70 | (2) |
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3.5.4.4 Fractional factorial designs to reduce animal use |
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72 | (3) |
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3.5.4.5 Two-stage procedure to reduce animal use |
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75 | (2) |
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3.5.5 Factorial designs with continuous factors |
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77 | (1) |
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3.5.5.1 Strategies for setting up a new animal model |
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78 | (3) |
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3.5.5.2 Drug combination studies |
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81 | (2) |
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3.5.5.3 Continuous vs. categorical factors |
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83 | (1) |
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3.5.6 Final thoughts on factorial designs |
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83 | (1) |
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3.6 Dose-response designs |
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84 | (6) |
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3.6.1 The four- and five-parameter logistic curves |
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84 | (1) |
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3.6.2 Experimental design considerations |
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85 | (1) |
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3.6.2.1 Increasing the number of doses |
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86 | (1) |
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3.6.2.2 Decreasing the number of animals |
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86 | (1) |
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3.6.3 Including the control group |
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87 | (1) |
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3.6.3.1 Analysing a change from the control response |
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87 | (1) |
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3.6.3.2 Using a dual statistical model |
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88 | (1) |
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3.6.3.3 Adding an offset to the dose |
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88 | (2) |
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90 | (20) |
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3.7.1 Types of nested design |
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91 | (1) |
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3.7.1.1 Single-order nested design |
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91 | (1) |
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3.7.1.2 Higher-order nested design |
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91 | (2) |
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3.7.2 Sample size and power |
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93 | (1) |
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3.7.2.1 Factors that influence sample size |
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93 | (2) |
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3.7.2.2 Calculating sample sizes |
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95 | (2) |
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3.7.2.3 When not to calculate the statistical power |
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97 | (2) |
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3.7.3 Higher-order nested designs |
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99 | (1) |
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3.7.3.1 Identifying nested factors |
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99 | (2) |
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3.7.3.2 Investigating the sources of variability in higher-order nested designs |
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101 | (1) |
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3.7.3.3 Variance components: estimating the observational unit variability |
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102 | (1) |
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3.7.3.4 Predicting the experimental unit variability |
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103 | (2) |
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3.7.3.5 Investigating alternative nested designs |
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105 | (1) |
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3.7.3.6 Pseudo-replication |
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106 | (4) |
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3.8 Repeated measures and dose-escalation designs |
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110 | (7) |
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3.8.1 Repeated measures designs |
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110 | (1) |
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3.8.1.1 The repeated factor |
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110 | (2) |
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3.8.1.2 The core experimental design |
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112 | (1) |
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3.8.1.3 Nested repeated measures designs |
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112 | (2) |
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3.8.1.4 More complex repeated measures designs |
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114 | (2) |
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3.8.2 Dose-escalation designs |
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116 | (1) |
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3.8.2.1 More complex dose-escalation designs |
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117 | (1) |
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117 | (2) |
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3.9.1 Animals as whole plots |
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117 | (1) |
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3.9.2 Animals as subplots |
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118 | (1) |
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3.10 Experimental designs in practice |
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119 | (1) |
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3.11 A good design should result in... |
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120 | (2) |
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122 | (10) |
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4.1 Practical reasons to randomise |
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122 | (2) |
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122 | (1) |
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4.1.1.1 Removing unforeseen trends |
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123 | (1) |
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4.1.1.2 Humans are systematic |
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123 | (1) |
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124 | (1) |
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4.2 Statistical reasons to randomise |
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124 | (5) |
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4.2.1 Estimating the variability |
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125 | (1) |
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4.2.2 Deciding upon the statistical analysis strategy |
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125 | (1) |
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4.2.2.1 Including interactions in the statistical model |
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126 | (1) |
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4.2.2.2 Including blocking factors |
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127 | (1) |
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4.2.3 Repeatedly measured responses |
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127 | (1) |
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4.2.3.1 Repeated factors and randomised factors |
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127 | (1) |
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4.2.3.2 Block and dose-escalation designs |
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127 | (1) |
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4.2.3.3 Crossover and dose-escalation designs |
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128 | (1) |
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4.2.3.4 Including interactions involving the repeated factor |
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129 | (1) |
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129 | (1) |
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130 | (2) |
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132 | (106) |
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132 | (3) |
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133 | (1) |
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5.1.2 A recommended five-stage parametric analysis procedure |
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133 | (2) |
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135 | (5) |
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5.2.1 Parametric measures of location |
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135 | (1) |
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5.2.1.1 The true mean and the sample mean |
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135 | (1) |
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5.2.1.2 The observed mean |
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136 | (1) |
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5.2.1.3 The predicted mean |
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137 | (1) |
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5.2.1.4 The geometric mean |
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137 | (1) |
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5.2.2 Parametric measures of spread |
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138 | (1) |
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138 | (1) |
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5.2.2.2 Standard deviation |
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138 | (1) |
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5.2.2.3 Standard error of the mean |
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138 | (1) |
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5.2.2.4 Confidence intervals |
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139 | (1) |
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5.2.2.5 Coefficient of variation |
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139 | (1) |
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5.2.3 Non-parametric measures of location |
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139 | (1) |
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5.2.4 Non-parametric measures of spread |
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140 | (1) |
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140 | (11) |
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140 | (2) |
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142 | (1) |
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143 | (1) |
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5.3.4 Categorised case profiles plot |
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144 | (1) |
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5.3.5 Means with SEMs plot |
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145 | (1) |
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5.3.5.1 Problems with the means with SEMs plot |
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145 | (6) |
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5.3.5.2 Benefits of the means with SEMs plot |
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151 | (1) |
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151 | (77) |
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5.4.1 Parametric assumptions |
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152 | (1) |
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5.4.1.1 Numeric and continuous responses |
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152 | (1) |
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5.4.1.2 Normally distributed residuals |
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153 | (2) |
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5.4.1.3 Homogeneity of variance |
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155 | (3) |
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5.4.1.4 Independence of the responses |
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158 | (1) |
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5.4.1.5 Removal of outliers |
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159 | (3) |
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162 | (1) |
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163 | (1) |
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5.4.2.1 The unpaired t-test |
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163 | (2) |
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5.4.2.2 When not to use an unpaired t-test |
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165 | (2) |
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5.4.2.3 The paired t-test |
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167 | (1) |
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5.4.2.4 Randomisation and the paired t-test |
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168 | (1) |
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5.4.3 Analysis of variance (ANOVA) |
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168 | (1) |
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169 | (4) |
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5.4.3.2 Including the positive control |
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173 | (1) |
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174 | (2) |
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5.4.3.4 Two-way vs. one-way ANOVA |
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176 | (1) |
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5.4.3.5 Dealing with missing factor combinations |
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177 | (2) |
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5.4.4 Repeated measures analysis |
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179 | (2) |
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5.4.4.1 Categorised case profiles plot |
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181 | (1) |
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5.4.4.2 Analysis of summary measures |
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181 | (8) |
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5.4.4.3 Repeated measures analysis |
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189 | (2) |
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5.4.4.4 The mixed-model approach vs. the ANOVA-based approach |
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191 | (4) |
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5.4.4.5 Advantages and disadvantages of the repeated measures analysis |
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195 | (1) |
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5.4.5 Predicted means from the parametric analysis |
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196 | (1) |
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5.4.5.1 Least square (predicted) means |
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196 | (1) |
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5.4.5.2 Variability of the least square (predicted) means |
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197 | (1) |
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5.4.5.3 Geometric means and confidence intervals |
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197 | (1) |
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5.4.5.4 Reliability of the predicted means |
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198 | (1) |
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5.4.6 Analysis of covariance (ANCOVA) |
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199 | (1) |
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5.4.6.1 What is a covariate? |
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200 | (1) |
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5.4.6.2 Best-fit lines and predicted lines |
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201 | (1) |
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5.4.6.3 Categorised scatterplot |
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201 | (1) |
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5.4.6.4 Predictions from ANCOVA |
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202 | (1) |
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5.4.6.5 Predicted group means |
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203 | (1) |
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5.4.6.6 Assumptions for ANCOVA |
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204 | (3) |
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5.4.6.7 Strategy for when the independence assumption does not hold |
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207 | (1) |
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5.4.6.8 ANCOVA and stratified randomisation |
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208 | (1) |
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5.4.6.9 Change from baseline responses |
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208 | (3) |
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5.4.7 Regression analysis |
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211 | (1) |
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5.4.8 Multiple comparison procedures |
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212 | (1) |
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5.4.8.1 The risk of finding false positives and false negatives |
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212 | (2) |
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5.4.8.2 Choosing the family of tests |
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214 | (1) |
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215 | (3) |
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5.4.8.4 Stepwise multiple comparison procedures that control the FDR |
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218 | (1) |
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5.4.8.5 Simultaneous multiple comparison procedures that control the FWE |
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218 | (4) |
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5.4.8.6 Stepwise multiple comparison procedures based on group differences that control the FWE |
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222 | (1) |
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5.4.8.7 Stepwise-based multiple comparison procedures based on p-values that control the FWE |
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223 | (1) |
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5.4.8.8 The gateway ANOVA approach |
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224 | (3) |
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5.4.8.9 Multiple comparison procedures in statistical software packages |
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227 | (1) |
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228 | (1) |
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5.5 Other useful analyses |
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228 | (10) |
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5.5.1 Non-parametric analyses |
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228 | (1) |
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5.5.1.1 When to use a non-parametric test |
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229 | (1) |
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5.5.1.2 Non-parametric tests |
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230 | (1) |
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5.5.2 Testing the difference between proportions |
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231 | (1) |
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5.5.2.1 Analysis procedure |
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232 | (1) |
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232 | (1) |
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5.5.2.3 Fisher's exact test |
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233 | (1) |
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234 | (1) |
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5.5.3.1 The survival function |
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235 | (1) |
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236 | (2) |
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6 Analysis using InVivoStat |
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238 | (55) |
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238 | (3) |
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238 | (1) |
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6.1.1.1 Single measure format |
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238 | (1) |
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6.1.1.2 Repeated measures format |
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239 | (1) |
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6.1.2 Importing a dataset into InVivoStat: Excel import |
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240 | (1) |
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6.1.3 Importing a dataset into InVivoStat: text file import |
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240 | (1) |
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240 | (1) |
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6.1.5 Running an analysis |
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240 | (1) |
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6.1.6 Warning and error messages |
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241 | (1) |
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241 | (1) |
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241 | (1) |
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6.2 Summary Statistics module |
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241 | (2) |
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242 | (1) |
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243 | (1) |
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6.3 Single Measure Parametric Analysis module |
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243 | (9) |
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243 | (2) |
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245 | (3) |
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248 | (1) |
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6.3.3.1 Analysis of large factorial experiments |
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248 | (1) |
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6.3.3.2 Analysis of small factorial experiments |
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248 | (1) |
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6.3.3.3 Analysis of experiments involving blocking factors |
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249 | (2) |
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6.3.3.4 Analysis of crossover trials |
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251 | (1) |
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6.3.3.5 Analysis of designs with missing factor combinations |
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252 | (1) |
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6.4 Repeated Measures Parametric Analysis module |
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252 | (6) |
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252 | (3) |
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255 | (1) |
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255 | (3) |
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6.5 P-Value Adjustment module |
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258 | (2) |
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259 | (1) |
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259 | (1) |
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6.6 Non-Parametric Analysis module |
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260 | (2) |
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260 | (2) |
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262 | (1) |
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262 | (1) |
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262 | (1) |
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263 | (1) |
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6.8 Power Analysis module |
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263 | (4) |
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263 | (2) |
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265 | (2) |
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6.9 Unpaired t-test Analysis module |
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267 | (5) |
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267 | (4) |
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271 | (1) |
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6.10 Paired t-test/within-subject Analysis module |
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272 | (5) |
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6.10.1 Analysis procedure |
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272 | (4) |
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276 | (1) |
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6.11 Dose-Response Analysis module |
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277 | (5) |
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6.11.1 Technical details on curve fitting |
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277 | (1) |
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6.11.2 Fitting logistic curves to data |
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278 | (1) |
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6.11.3 Analysis of quantitative assays |
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278 | (1) |
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6.11.4 Analysis procedure |
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279 | (2) |
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6.11.5 Worked example: a biological assay |
|
|
281 | (1) |
|
6.11.6 User-defined equation option |
|
|
282 | (1) |
|
6.12 Chi-squared Test and Fisher's Exact Test module |
|
|
282 | (3) |
|
6.12.1 Analysis procedure |
|
|
283 | (1) |
|
|
284 | (1) |
|
|
285 | (1) |
|
6.14 Nested Design Analysis module |
|
|
285 | (4) |
|
6.14.1 Analysis procedure |
|
|
286 | (3) |
|
|
289 | (1) |
|
6.15 Survival Analysis module |
|
|
289 | (4) |
|
6.15.1 Analysis procedure |
|
|
289 | (2) |
|
|
291 | (2) |
|
|
293 | (2) |
Glossary |
|
295 | (2) |
References |
|
297 | (6) |
Index |
|
303 | |