Preface |
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xiii | |
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1 Introduction to statistics |
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1 | (14) |
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1.1 Statistics and scientific inquiry |
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1 | (2) |
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3 | (7) |
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1.2.1 Validity and reliability |
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3 | (1) |
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1.2.2 Variables and constants |
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4 | (1) |
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1.2.3 Independent and dependent variables |
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5 | (1) |
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1.2.4 Control and experimental groups |
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6 | (1) |
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1.2.5 Scales of measurement and variables |
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6 | (2) |
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1.2.6 Samples and statistics, populations and parameters; descriptive and inferential statistics; a few words about sampling |
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8 | (2) |
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10 | (2) |
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12 | (1) |
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13 | (1) |
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13 | (2) |
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2 Frequency distributions and graphs |
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15 | (16) |
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2.1 Frequency distributions of qualitative variables |
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15 | (3) |
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2.2 Frequency distributions of numerical discontinuous variables |
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18 | (2) |
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2.3 Frequency distributions of continuous numerical variables |
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20 | (5) |
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25 | (3) |
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25 | (2) |
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27 | (1) |
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27 | (1) |
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28 | (1) |
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28 | (1) |
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29 | (2) |
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3 Descriptive statistics: measures of central tendency and dispersion |
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31 | (23) |
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3.1 Measures of central tendency |
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31 | (9) |
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31 | (2) |
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3.1.2 Computing the mean of frequency distributions |
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33 | (1) |
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34 | (1) |
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3.1.4 Computing the median of frequency distributions |
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35 | (4) |
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39 | (1) |
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3.2 Measures of variation |
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40 | (11) |
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40 | (1) |
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3.2.2 The population variance and standard deviation; the definitional formulae |
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41 | (2) |
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3.2.3 The sample variance and standard deviation; the definitional formulae |
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43 | (2) |
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3.2.4 The population and sample variance and standard deviation; the computational (`machine') formula |
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45 | (2) |
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3.2.5 The computational (`machine') formula with frequency distributions |
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47 | (4) |
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3.3 A research example of descriptive statistics |
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51 | (1) |
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52 | (1) |
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52 | (2) |
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4 Probability and statistics |
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54 | (23) |
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4.1 Random sampling and probability distributions |
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54 | (1) |
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4.2 The probability distribution of qualitative and discontinuous numerical variables |
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55 | (2) |
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4.3 The binomial distribution |
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57 | (3) |
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4.4 The probability distribution of continuous variables |
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60 | (9) |
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64 | (4) |
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4.4.2 Percentile ranks and percentiles |
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68 | (1) |
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4.5 The probability distribution of sample means |
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69 | (4) |
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4.6 A research example of z scores |
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73 | (1) |
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74 | (1) |
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74 | (3) |
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77 | (19) |
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5.1 The principles of hypothesis testing |
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77 | (4) |
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5.2 Errors and power in hypothesis testing |
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81 | (4) |
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5.2.1 Type I error (Alpha) |
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81 | (1) |
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5.2.2 Type II error (Beta) |
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82 | (1) |
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5.2.3 Power of statistical tests (1-Beta) |
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83 | (2) |
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5.3 Examples of hypothesis tests using z scores |
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85 | (2) |
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5.4 One- and two-tail hypothesis tests |
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87 | (2) |
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5.5 Assumptions of statistical tests |
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89 | (1) |
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5.6 Hypothesis testing with the t distribution |
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90 | (2) |
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5.7 Examples of hypothesis tests with t scores |
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92 | (2) |
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5.8 Reporting hypothesis tests |
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94 | (1) |
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95 | (1) |
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95 | (1) |
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6 The difference between two means |
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96 | (17) |
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96 | (4) |
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6.2 Assumptions of the un-paired t test |
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100 | (3) |
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6.3 A research example of the un-paired t test |
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103 | (1) |
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6.4 The comparison of a single observation with the mean of a sample |
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104 | (1) |
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6.5 The comparison of paired samples |
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105 | (2) |
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6.6 Assumptions of the paired t test |
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107 | (2) |
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6.7 A research example of the paired t test |
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109 | (1) |
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109 | (1) |
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109 | (4) |
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7 Analysis of variance (ANOVA) |
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113 | (17) |
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113 | (1) |
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7.2 ANOVA procedure and nomenclature |
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114 | (7) |
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121 | (1) |
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7.4 Post ANOVA comparison of means |
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121 | (5) |
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122 | (4) |
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7.5 A research example of an ANOVA |
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126 | (1) |
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127 | (1) |
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127 | (3) |
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8 Non-parametric comparison of samples |
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130 | (21) |
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131 | (1) |
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8.2 The Mann-Whitney U test for an un-matched design |
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132 | (5) |
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8.3 A research example of the Mann-Whitney U test |
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137 | (1) |
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8.4 The Kruskal-Wallis instead of a one-way, model I ANOVA |
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138 | (6) |
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8.5 A research example of the Kruskal-Wallis test |
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144 | (1) |
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8.6 The Wilcoxon signed-rank test for a paired design |
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144 | (3) |
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8.7 A research example of the use of the Wilcoxon signed-rank test |
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147 | (1) |
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148 | (1) |
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148 | (3) |
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9 Simple linear regression |
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151 | (28) |
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9.1 An overview of regression analysis |
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152 | (4) |
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9.2 Plot and inspection of the data |
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156 | (1) |
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9.3 Description of the relation between X and Y with an equation |
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156 | (2) |
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9.4 Expression of the regression analysis as an analysis of variance of Y |
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158 | (3) |
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9.5 Test of the null hypothesis H0: Beta=0 |
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161 | (1) |
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9.6 Use of the regression equation to predict values of Y |
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161 | (4) |
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165 | (10) |
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9.8 A research example of the use of regression |
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175 | (1) |
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176 | (1) |
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176 | (3) |
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179 | (13) |
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10.1 The Pearson product-moment correlation |
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179 | (6) |
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10.2 A research example of the use of Pearson correlation |
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185 | (1) |
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10.3 The Spearman correlation |
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185 | (4) |
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10.4 A research example of the Spearman correlation coefficient |
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189 | (1) |
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190 | (1) |
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190 | (2) |
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11 The analysis of frequencies |
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192 | (12) |
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11.1 The X^2 test for goodness-of-fit |
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192 | (3) |
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11.2 A research example of the X^2 test for goodness-of-fit |
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195 | (1) |
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11.3 The X^2 test for independence of variables |
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196 | (4) |
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11.4 A research example of the X^2 test for independence of variables |
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200 | (1) |
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11.5 Yates' correction for continuity |
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200 | (2) |
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202 | (1) |
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203 | (1) |
References |
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204 | (3) |
Appendix A: Answers to selected exercises |
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207 | (9) |
Appendix B: A brief overview of SAS/ASSIST |
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216 | (3) |
Appendix C: Statistical tables |
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219 | (18) |
Table 1. The unit normal table |
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219 | (3) |
Table 2. Critical values of the t distribution |
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222 | (1) |
Table 3. Upper 5 and 1% points of the maximum F-ratio |
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223 | (1) |
Table 4. Critical values of the F distribution |
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224 | (4) |
Table 5. Critical values of U, the Mann-Whitney statistic |
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228 | (4) |
Table 6. Critical values of the chi-square distribution |
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232 | (2) |
Table 7. Critical values of T for the Wilcoxon signed-rank test |
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234 | (1) |
Table 8. Critical values of the Pearson correlation coefficient r |
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235 | (2) |
Index |
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237 | |