Preface |
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xix | |
Acknowledgements |
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xxi | |
Author |
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xxiii | |
1 Introduction |
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1 | (8) |
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1.1 Is This the Book for You? |
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1 | (1) |
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2 | (1) |
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1.3 Why Bother with Statistics? |
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3 | (3) |
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1.4 A Note for Lecturers and Teachers |
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6 | (2) |
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8 | (1) |
2 How to Use Statistics |
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9 | (16) |
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9 | (1) |
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10 | (1) |
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11 | (1) |
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2.4 Multiple Working Hypotheses |
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12 | (1) |
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12 | (2) |
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2.6 Probability: Is It Just Luck? |
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14 | (4) |
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2.7 One or Two-Tail Testing |
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18 | (1) |
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19 | (4) |
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23 | (2) |
3 Different Kinds of Data |
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25 | (16) |
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25 | (4) |
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25 | (1) |
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25 | (3) |
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3.1.3 Individual Measurements |
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28 | (1) |
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3.2 Independent or Linked Data? |
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29 | (1) |
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30 | (4) |
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3.3.1 Checking for a 'Normal' or Gaussian Distribution |
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31 | (3) |
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3.4 Choosing the Right Test |
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34 | (4) |
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38 | (3) |
4 Tools of the Trade |
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41 | (18) |
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41 | (1) |
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41 | (2) |
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43 | (1) |
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43 | (7) |
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4.4.1 Assigning Ranks in a Spreadsheet |
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47 | (3) |
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50 | (1) |
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50 | (2) |
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4.7 Descriptive Statistics |
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52 | (5) |
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4.7.1 Measures of the Middle: Mean, Median and Mode |
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52 | (2) |
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4.7.2 Measures of Spread or Dispersion: Range, Variance and Standard Deviation |
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54 | (1) |
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4.7.3 Confidence Limits around the Mean |
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54 | (1) |
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4.7.4 Measures of the Shape of a Distribution: Skewness and Kurtosis |
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55 | (2) |
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57 | (2) |
5 Single Sample Tests |
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59 | (22) |
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59 | (1) |
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60 | (5) |
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60 | (1) |
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5.2.2 What It Is Based On |
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60 | (1) |
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61 | (2) |
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5.2.3.1 Online Calculators |
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61 | (1) |
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61 | (1) |
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5.2.3.3 Companion Site Calculator |
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62 | (1) |
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63 | (1) |
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63 | (1) |
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63 | (1) |
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63 | (2) |
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5.2.4.1 Example: Yes or No Questionnaire Answers |
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63 | (1) |
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5.2.4.2 Example: Is There a Gender Bias in My Sample? |
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64 | (1) |
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5.2.4.3 Example: Have the Limestones Been Removed by Weathering? |
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64 | (1) |
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5.2.4.4 Example: Are There Too Few Black Managers in English Football? |
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65 | (1) |
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5.3 One-Sample Chi-Square (x2) Test |
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65 | (5) |
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65 | (1) |
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65 | (1) |
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5.3.3 What It Is Based On |
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66 | (1) |
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66 | (3) |
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5.3.4.1 Companion Site Calculator |
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67 | (1) |
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67 | (1) |
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68 | (1) |
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68 | (1) |
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69 | (1) |
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5.3.5.1 Example: Beautiful Beaches |
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69 | (1) |
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5.3.5.2 Example: Ethnic Groups |
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69 | (1) |
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5.3.5.3 Example: Dolphin Sightings |
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69 | (1) |
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5.4 Kolmogorov-Smirnov One-Sample Test |
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70 | (3) |
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70 | (1) |
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5.4.2 What It Is Based On |
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70 | (1) |
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71 | (1) |
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71 | (2) |
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5.4.4.1 Example: Are Levels of Agreement Equal? |
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71 | (1) |
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5.4.4.2 Example: Is My Sample Representative? |
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72 | (1) |
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5.5 One Sample Runs Test for Randomness |
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73 | (6) |
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73 | (1) |
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5.5.2 What It Is Based On |
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73 | (1) |
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74 | (1) |
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5.5.3.1 Companion Site Calculators |
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74 | (1) |
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74 | (1) |
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75 | (1) |
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75 | (6) |
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5.5.4.1 Example: Nominal Data and Small Sample Sizes |
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75 | (2) |
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5.5.4.2 Example: Large Sample of Individual Numbers |
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77 | (2) |
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79 | (2) |
6 Two-Sample Tests for Counts in Two Categories |
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81 | (30) |
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81 | (1) |
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81 | (3) |
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81 | (1) |
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6.2.2 What It Is Based On |
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82 | (1) |
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82 | (1) |
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82 | (1) |
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83 | (1) |
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6.2.5.1 Example: Checking Exam Improvement |
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83 | (1) |
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6.2.5.2 Example: Crystal Healing |
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83 | (1) |
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6.2.5.3 Example: Footpath Erosion |
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84 | (1) |
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6.3 McNemar's Test for Significance of Changes |
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84 | (7) |
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85 | (1) |
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6.3.2 What It Is Based On |
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85 | (1) |
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86 | (1) |
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86 | (1) |
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86 | (1) |
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6.3.6 Correction for Continuity |
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87 | (1) |
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87 | (1) |
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6.3.7.1 Companion Site Calculator |
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87 | (1) |
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6.3.7.2 Online Calculators |
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87 | (1) |
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87 | (1) |
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87 | (1) |
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88 | (5) |
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6.3.8.1 Example: Opinions on Fracking |
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88 | (1) |
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6.3.8.2 Example: Land Management |
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89 | (1) |
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6.3.8.3 Example: Golf Green Hydrophobicity (Bad Test) |
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89 | (2) |
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6.4 Tests for Independent Samples Arranged as 2 x 2 Contingency Tables |
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91 | (2) |
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6.5 Risk Ratio and Odds Ratio |
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93 | (1) |
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93 | (1) |
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93 | (1) |
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6.6 Confidence Limits of the Odds Ratio and Risk Ratio |
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94 | (2) |
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95 | (1) |
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6.6.1.1 Companion Site Calculator |
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95 | (1) |
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6.6.1.2 Using an Online Calculator |
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95 | (1) |
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96 | (1) |
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96 | (1) |
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6.7 Sample Size Assumptions |
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96 | (2) |
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6.7.1 Calculating Expected Values |
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96 | (2) |
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6.8 Chi-Square Test for a 2 x 2 Contingency Table |
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98 | (4) |
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98 | (1) |
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6.8.2 What It Is Based On |
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99 | (1) |
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6.8.3 Calculating Chi-Square |
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99 | (2) |
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6.8.4 Continuity Correction (Yates's Correction) |
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101 | (1) |
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6.8.5 Effect Size: Cramer's V |
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101 | (1) |
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6.9 Conducting the Chi-Square Test |
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102 | (5) |
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6.9.1 Companion Site Calculator |
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102 | (1) |
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102 | (1) |
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102 | (1) |
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103 | (1) |
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104 | (3) |
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6.9.5.1 Example: Organic Produce |
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104 | (1) |
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6.9.5.2 Example: Erratic Content |
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104 | (1) |
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6.9.5.3 Example: Large Sample Parametric Approach |
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105 | (1) |
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6.9.5.4 Example: Common Error with a Solution |
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106 | (1) |
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107 | (3) |
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107 | (1) |
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6.10.2 What It Is Based On |
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108 | (1) |
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108 | (1) |
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6.10.3.1 Real Statistics Resource Pack for Excel |
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108 | (1) |
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6.10.3.2 Online Calculators |
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108 | (1) |
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109 | (1) |
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109 | (1) |
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109 | (3) |
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6.10.4.1 Example: Small Sample of Snails |
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109 | (1) |
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6.10.4.2 Example: Start-Up Companies |
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110 | (1) |
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110 | (1) |
7 Two-Sample Tests for Counts in Several Categories |
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111 | (38) |
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111 | (1) |
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7.2 Two-Sample Chi-Square Test |
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112 | (15) |
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112 | (1) |
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7.2.2 What It Is Based On |
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113 | (1) |
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7.2.3 Expected Frequencies |
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113 | (4) |
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7.2.4 Sample Size Assumptions |
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117 | (2) |
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7.2.5 Strength of the Relationship (Cramer's V) |
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119 | (3) |
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7.2.5.1 Calculating Cramer's V |
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120 | (1) |
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7.2.5.2 Where Are the Differences? |
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120 | (2) |
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7.2.6 How to Conduct a Two-Sample Chi-Square Test |
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122 | (1) |
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7.2.6.1 Companion Site Calculators |
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122 | (1) |
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7.2.6.2 Online Calculators |
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122 | (1) |
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122 | (1) |
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123 | (1) |
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123 | (4) |
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7.2.7.1 Example: Garden Visitors |
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123 | (1) |
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7.2.7.2 Example: Snails (Small Sample) |
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124 | (1) |
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7.2.7.3 Example: Misuse of Chi-Square |
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125 | (1) |
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7.2.7.4 Example: Common Mistake and a Solution |
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126 | (1) |
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7.3 Fisher's Exact Test for More Than Two Categories |
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127 | (5) |
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127 | (1) |
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128 | (1) |
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128 | (1) |
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129 | (1) |
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129 | (3) |
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7.3.3.1 Example: Snails (Small Sample) |
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129 | (1) |
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7.3.3.2 Example: Small Questionnaire |
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129 | (1) |
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7.3.3.3 Example: Failed Test and a Solution |
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130 | (2) |
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7.4 Two-Sample Tests for Counts in Ordered Categories |
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132 | (1) |
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7.5 Kolmogorov-Smirnov Two-Sample Test |
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132 | (11) |
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133 | (1) |
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7.5.2 How to Perform the Kolmogorov-Smirnov Two-Sample Test with Counts in Categories |
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134 | (2) |
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7.5.2.1 Equal Sample Sizes |
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134 | (1) |
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7.5.2.2 Unequal Sample Sizes |
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135 | (1) |
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136 | (2) |
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138 | (1) |
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139 | (1) |
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7.5.5.1 Companion Site Calculators |
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139 | (1) |
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7.5.5.2 Real Statistics Resource Pack |
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140 | (1) |
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140 | (1) |
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140 | (3) |
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7.5.6.1 Example: Different Shaped Distributions |
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140 | (1) |
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7.5.6.2 Example: Likert Scale, Small Samples |
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141 | (1) |
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7.5.6.3 Example: Likert Scale, Large Samples |
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141 | (1) |
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7.5.6.4 Example: Odd Case with a Bimodal Distribution |
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142 | (1) |
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7.6 Scoring Categorical Data for Parametric Tests |
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143 | (4) |
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7.6.1 How to Code Categorical Data |
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146 | (1) |
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147 | (2) |
8 Two-Sample Tests for Individual Measurements |
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149 | (42) |
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149 | (1) |
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8.2 Wilcoxon's Matched-Pairs Signed-Ranks Test |
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150 | (9) |
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150 | (1) |
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8.2.2 What It Is Based On |
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150 | (2) |
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152 | (1) |
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152 | (1) |
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153 | (2) |
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153 | (1) |
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8.2.5.2 Real Statistics Resource Pack |
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153 | (1) |
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8.2.5.3 Companion Site Calculator |
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153 | (1) |
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8.2.5.4 Online Calculators |
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154 | (1) |
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154 | (1) |
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155 | (1) |
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155 | (4) |
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8.2.6.1 Example: Attitudes to Recycling |
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155 | (1) |
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8.2.6.2 Example: Grazing and Plant Diversity |
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155 | (4) |
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8.3 Paired-Samples Student's t-Test |
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159 | (3) |
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159 | (1) |
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159 | (1) |
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159 | (2) |
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159 | (1) |
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8.3.3.2 Companion Site Calculator |
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159 | (1) |
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160 | (1) |
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160 | (1) |
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8.3.3.5 Using a Calculator |
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160 | (1) |
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8.3.3.6 Online Calculators |
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160 | (1) |
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161 | (3) |
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8.3.4.1 Example: Examination Marks |
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161 | (1) |
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8.4 Two-Sample Tests for Independent Data with Individual Measurements |
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162 | (2) |
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164 | (10) |
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164 | (1) |
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8.5.2 What It Is Based On |
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165 | (1) |
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8.5.3 Dealing with Tied Ranks |
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165 | (1) |
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166 | (1) |
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166 | (4) |
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8.5.5.1 Online Calculators |
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166 | (1) |
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8.5.5.2 Real Statistics Resource Pack |
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166 | (2) |
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168 | (1) |
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8.5.5.4 Companion Site Calculator |
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169 | (1) |
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8.5.5.5 Using R Commander |
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169 | (1) |
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170 | (1) |
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170 | (4) |
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8.5.6.1 Example: Exam Performance and Gender |
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170 | (1) |
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170 | (1) |
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8.5.6.3 Example: Schmidt Hammer and Glacial Moraines |
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171 | (3) |
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8.6 Student's t-Test for Two Independent Samples |
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174 | (7) |
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174 | (1) |
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8.6.2 What It Is Based On |
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174 | (1) |
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175 | (1) |
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175 | (3) |
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175 | (1) |
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8.6.4.2 Online Calculators |
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176 | (1) |
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8.6.4.3 Companion Site Calculator |
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176 | (1) |
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177 | (1) |
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177 | (1) |
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178 | (3) |
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8.6.5.1 Example: Male Underperformance |
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178 | (3) |
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8.7 Two Independent Samples: Tests for Difference in Variability |
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181 | (1) |
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8.8 The F-Test for Equality of Variance |
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181 | (3) |
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181 | (1) |
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8.8.2 What It Is Based On |
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182 | (1) |
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182 | (1) |
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8.8.3.1 In a Spreadsheet or Companion Site Calculator |
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182 | (1) |
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182 | (1) |
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183 | (1) |
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8.8.3.4 Online Calculators |
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183 | (1) |
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183 | (1) |
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8.8.4.1 Example: Organic Strawberries |
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183 | (1) |
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8.9 Non-Parametric Tests for Equality of Variance |
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184 | (1) |
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184 | (3) |
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184 | (1) |
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8.10.2 What It Is Based On |
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184 | (1) |
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185 | (1) |
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8.10.3.1 Online Calculators and Spreadsheets |
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185 | (1) |
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186 | (1) |
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186 | (1) |
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186 | (1) |
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8.10.4.1 Example: Extremity of Opinion |
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186 | (1) |
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8.10.5 'Measuring from the Middle' Approach |
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187 | (1) |
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8.11 Kolmogorov-Smirnov Two-Sample Test for Continuous Data |
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187 | (3) |
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187 | (1) |
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188 | (6) |
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8.11.2.1 Companion Site Calculator |
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189 | (1) |
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8.11.2.2 In SPSS and R Commander |
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189 | (1) |
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190 | (1) |
9 Comparing More Than Two Samples |
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191 | (44) |
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191 | (1) |
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9.2 'Family-Wise' Error and the Bonferroni Correction |
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191 | (3) |
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194 | (2) |
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194 | (2) |
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196 | (7) |
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196 | (1) |
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9.4.2 What It Is Based On |
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196 | (1) |
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9.4.2.1 The Data are Counts, Not Percentages or Proportions |
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196 | (1) |
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9.4.2.2 The Data Must Be Independent |
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196 | (1) |
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9.4.2.3 Adequate Sample Size |
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197 | (1) |
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197 | (1) |
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197 | (2) |
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198 | (1) |
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198 | (1) |
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9.4.4.3 Online Calculators |
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199 | (1) |
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199 | (4) |
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9.4.5.1 Example: Typical Act of Desperation |
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199 | (3) |
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9.4.5.2 Example: Glacial Deposits |
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202 | (1) |
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9.5 Fisher's Exact Calculation for Small Samples |
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203 | (2) |
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203 | (1) |
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203 | (1) |
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203 | (1) |
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203 | (1) |
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9.5.2.3 Online Calculators |
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203 | (1) |
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203 | (2) |
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203 | (1) |
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9.5.3.2 Example: Use of Space |
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204 | (1) |
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9.6 Kruskal-Wallis H-Test |
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205 | (7) |
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205 | (1) |
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9.6.2 What It Is Based On |
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206 | (1) |
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9.6.3 Obtaining a Probability Value |
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206 | (1) |
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207 | (1) |
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207 | (1) |
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207 | (5) |
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9.6.6.1 Real Statistics Resource Pack for Excel |
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207 | (1) |
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9.6.6.2 Companion Site Calculator |
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208 | (1) |
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9.6.6.3 Online Calculators |
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209 | (1) |
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209 | (1) |
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209 | (3) |
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9.7 Dunn's Test (Post Hoc Tests for Kruskal-Wallis Test) |
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212 | (4) |
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213 | (1) |
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213 | (3) |
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9.7.2.1 Example: Soil Compaction |
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213 | (2) |
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9.7.2.2 Example: Tourist Spending |
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215 | (1) |
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9.8 Jonckheere-Terpstra Trend Test |
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216 | (5) |
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216 | (1) |
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217 | (1) |
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9.8.3 One- and Two-Tail Testing, Post Hoc Tests and Effect Size |
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218 | (1) |
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218 | (1) |
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218 | (1) |
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9.8.4.2 Companion Site Calculator |
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219 | (1) |
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219 | (2) |
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9.8.5.1 Example: Age Group Opinions |
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219 | (2) |
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221 | (7) |
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221 | (1) |
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9.9.2 What It Is Based On |
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221 | (1) |
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9.9.3 One- and Two-Tail Testing, Post Hoc Tests and Effect Size |
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222 | (1) |
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222 | (2) |
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9.9.4.1 Real Statistics Resource Pack for Excel |
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223 | (1) |
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9.9.4.2 Companion Site Calculator |
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223 | (1) |
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223 | (1) |
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224 | (1) |
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224 | (4) |
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9.9.5.1 Example: Exam Performance |
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224 | (1) |
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9.9.5.2 Example: Icons of Nationalism |
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225 | (3) |
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228 | (7) |
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228 | (1) |
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9.10.2 What It Is Based On |
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228 | (1) |
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9.10.3 One- and Two-Tail Testing, Post Hoc Tests and Effect Size |
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229 | (1) |
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229 | (1) |
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230 | (3) |
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9.10.5.1 Example: Metal Pollution in a River |
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230 | (1) |
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9.10.5.2 Example: Rental Prices with Distance from City Centre |
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231 | (2) |
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233 | (2) |
10 Correlation |
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235 | (26) |
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235 | (2) |
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10.2 Assumptions of Correlation Analysis |
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237 | (5) |
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10.2.1 Assumption 1: Data Are Continuous |
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238 | (1) |
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10.2.2 Assumption 2: Most of the Data Are Near the Middle, or They Are Evenly Distributed |
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239 | (1) |
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10.2.3 Assumption 3: The Relationship Forms a Straight Line Rather Than a Curve |
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240 | (1) |
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10.2.4 Assumption 4: No Outliers or Extreme Values |
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240 | (2) |
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10.2.5 Assumption 5: Sample Size Is Large Enough |
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242 | (1) |
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10.3 Pearson's Correlation Coefficient |
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242 | (6) |
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10.3.1 R-Squared, r-Values and the Effect Size |
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243 | (1) |
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243 | (3) |
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10.3.2.1 Companion Site Calculator |
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243 | (1) |
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10.3.2.2 In a Spreadsheet |
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244 | (1) |
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10.3.2.3 Real Statistics Resource Pack for Excel |
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245 | (1) |
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10.3.2.4 Online Calculators |
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245 | (1) |
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246 | (1) |
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246 | (1) |
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246 | (3) |
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10.3.3.1 Example: Tree Growth and Summer Temperature |
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246 | (1) |
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10.3.3.2 Example: Opinions on Global Issues |
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247 | (1) |
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10.4 Point-Biserial Correlation |
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248 | (1) |
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10.5 Spearman's Rank Correlation or Spearman's Rho |
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249 | (5) |
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249 | (1) |
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10.5.2 What It Is based On |
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249 | (1) |
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249 | (1) |
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249 | (5) |
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10.5.4.1 Example: As-Used for Pearson's Correlation |
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249 | (1) |
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10.5.4.2 Example: Coastal Zone Vegetation |
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250 | (1) |
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10.5.4.3 Example: Use of Space |
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251 | (1) |
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10.5.4.4 Example: Using Rank Order Rather Than Numbers |
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252 | (1) |
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10.5.4.5 Example: Grumpy Old Men |
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253 | (1) |
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10.6 Tests for Comparing Two Correlation Coefficients |
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254 | (4) |
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10.6.1 Independent Correlation Coefficients |
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254 | (1) |
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254 | (1) |
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10.6.1.2 Worked Example: Incompetent Marking |
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255 | (1) |
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10.6.2 Linked Correlation Coefficients |
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255 | (3) |
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10.7 Kendall's Tau and Other Approaches to Correlation |
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258 | (1) |
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259 | (2) |
11 Regression Analysis |
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261 | (36) |
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11.1 Simple Linear Regression |
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261 | (1) |
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11.2 The Straight Line Equation |
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261 | (4) |
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11.3 Best-Fit Regression Lines |
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265 | (3) |
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11.4 Assumptions of Simple Linear Regression |
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268 | (4) |
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269 | (1) |
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11.4.2 Independence of Residuals |
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270 | (1) |
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11.4.3 Outliers and Extreme Values |
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271 | (1) |
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11.5 Conflating Variables |
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272 | (1) |
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11.6 Interpreting Regression Results |
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272 | (5) |
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11.6.1 Statistical Significance |
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272 | (2) |
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11.6.2 Effect Sizes in Regression: r, R2 and Slope |
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274 | (1) |
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11.6.3 Uncertainty of the Slope Parameter |
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275 | (1) |
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11.6.4 Estimating Goodness of Fit and Uncertainty |
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275 | (2) |
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11.7 Performing Simple Linear Regression Analysis |
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277 | (4) |
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277 | (1) |
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11.7.2 Companion Site Calculators |
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278 | (1) |
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278 | (1) |
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278 | (1) |
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279 | (10) |
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11.7.5.1 Example: Predicting the Weather |
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279 | (1) |
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11.7.5.2 Example: Predicting Degree Outcomes |
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280 | (1) |
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11.8 Tests for Comparing Two Regression Analyses |
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281 | (3) |
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11.9 Standardising (z-Scoring) and Variance Scaling |
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284 | (3) |
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11.10 Reduced Major Axis Regression |
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287 | (2) |
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11.11 The Durbin-Watson Test for Autocorrelation of Residuals |
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289 | (2) |
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291 | (1) |
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11.12 Tests for Validation or Verification |
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291 | (3) |
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11.13 More Complicated Regression Models |
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294 | (2) |
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11.13.1 Non-Linear Regression |
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294 | (1) |
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11.13.2 Multiple Linear Regression |
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294 | (2) |
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296 | (1) |
12 Tables of Critical Values |
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297 | (30) |
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297 | (1) |
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12.2 Chi-Square Distribution |
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298 | (1) |
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12.2.1 Critical Values of x2 (Two-Tail) |
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298 | (1) |
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12.2.2 Critical Values of x2 for Two-Sample Chi-Square Tests |
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298 | (1) |
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12.3 Kolmogorov-Smirnov One-Sample Test |
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299 | (1) |
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12.4 One Sample Number of Runs Test for Randomness |
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300 | (4) |
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12.4.1 One-Tail Test, p = 0.05 Small/Unequal Sample Sizes |
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300 | (1) |
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12.4.2 One-Tail Test, p = 0.01 Small/Unequal Sample Sizes |
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300 | (1) |
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12.4.3 Two-Tail Test, p = 0.05 Small/Unequal Sample Sizes |
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301 | (1) |
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12.4.4 Two-Tail Test, p = 0.01 Small/Unequal Sample Sizes |
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301 | (1) |
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12.4.5 One-Tail Test, Equal Sample Sizes |
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302 | (1) |
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12.4.6 Two-Tail Test, Equal Sample Sizes |
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303 | (1) |
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12.5 Kolmogorov-Smirnov Two-Sample Test |
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304 | (4) |
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12.5.1 Two-Tail Tests, Small Unequal Sizes n = 5-20 |
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304 | (1) |
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12.5.2 Two-Tail Tests, Small Unequal Sizes n = 15-30 |
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304 | (1) |
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12.5.3 One-Tail Tests, Small Unequal Sizes n = 5-20 |
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305 | (1) |
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12.5.4 One-Tail Tests, Small Unequal Sizes n = 15-30 |
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305 | (1) |
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12.5.5 Two-Tail Tests, Equal Sample Sizes |
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306 | (1) |
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12.5.6 One-Tail Tests, Equal Sample Sizes |
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307 | (1) |
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12.6 Wilcoxon's Matched-Pairs Signed-Ranks Test |
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308 | (1) |
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309 | (2) |
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309 | (1) |
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310 | (1) |
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311 | (5) |
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12.8.1 Small Samples of Equal Size: Sum or Ranks |
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311 | (1) |
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12.8.2 Two-Tail Tests, Small Unequal Samples |
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312 | (1) |
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12.8.3 One-Tail Tests, Small Unequal Samples |
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313 | (1) |
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12.8.4 Two Tail Tests, Equal Sample Sizes |
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314 | (1) |
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12.8.5 One Tail Tests, Equal Sample Sizes |
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315 | (1) |
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12.9 F-Test for Equality of Variance |
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316 | (2) |
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12.9.1 Two-Tail Tests, Equal Sample Sizes |
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316 | (1) |
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12.9.2 One Tail Tests, Equal Sample Sizes |
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317 | (1) |
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318 | (2) |
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12.10.1 Three to Six Categories |
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318 | (1) |
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12.10.2 Seven to Ten Categories |
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319 | (1) |
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12.11 Pearson's Correlation Coefficient (r-Value) |
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320 | (2) |
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12.11.1 Two-Tail Probabilities |
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320 | (1) |
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12.11.2 One Tail Probabilities |
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321 | (1) |
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12.12 Spearman's Rank Correlation Coefficient (Rho) |
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322 | (2) |
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12.12.1 Two-Tail Probabilities |
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322 | (1) |
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12.12.2 One-Tail Probabilities |
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323 | (1) |
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324 | (2) |
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12.13.1 One-Tail Critical Values p = 0.05 |
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324 | (1) |
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12.13.2 One-Tail Critical Values p = 0.01 |
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325 | (1) |
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12.14 Critical Values from the Standard Normal Distribution (Significance of z-Scores) |
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326 | (1) |
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12.14.1 Single Test Critical Values |
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326 | (1) |
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12.14.2 Applying a Bonferroni Correction for Multiple Testing |
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326 | (1) |
Index |
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327 | |