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Chapter 1 Some Fundamental Concepts in Statistics 1

1.1 Descriptive and inferential statistics 2

1.2 Population and sample 3

1.3 Frequency， relative frequency and probability 4

1.4 Classifications of variables and levels of measurement 5

1.4.1 Nominal level of measurement 6

1.4.2 Ordinal level of measurement 6

1.4.3 Interval level of measurement 7

1.4.4 Ratio level of measurement 7

1.4.5 Comparison among the four levels of measurement 8

1.5 Computer softwares for statistical analyses 8

Chapter 2 Descriptive Statistics： Central Tendency and Variability 10

2.1 Measures of central tendency 10

2.1.1 The mean 11

2.1.2 The median 12

2.1.3 The mode 12

2.1.4 Comparison of the three measures of central tendency 13

2.2 Measures of variability 14

2.2.1 The range 15

2.2.2 The interquartile range 15

2.2.3 The mean deviation 16

2.2.4 The variance and the standard deviation 16

2.3 Calculating descriptive statistics using SPSS 18

Chapter 3 Graphical Presentation of Data and Normal Distribution 22

3.1 Frequency table 22

3.2 Frequency distribution 24

3.2.1 Histogram 25

3.2.2 Polygon 26

3.3 Skew and Kurtosis 27

3.4 The normal distribution 28

3.5 Differences in members of the family of normal curves 29

3.6 The standard score 31

3.7 The area under normal curves 32

Chapter 4 Estimation 34

4.1 Estimation 36

4.1.1 Estimation from large samples： the normal distribution 36

4.1.2 Estimation from small samples： the t distribution 39

4.2 Calculation of estimation for both large samples and small samples using SPSS 43

Chapter 5 Project Design and Hypothesis Testing： Basic Principles 47

5.1 Experimental and observational design of investigations 47

5.2 Correlated and independent design 48

5.3 Hypothesis testing 49

5.4 Significance level 52

5.5 Directional （one-tailed） and non-directional（two-tailed） tests 53

5.6 Types of errors 55

5.7 How to choose a test 56

5.7.1 Parametric tests 56

5.7.2 Non-parametric tests 57

Chapter 6 Parametric Tests 59

6.1 Hypothesis testing about one population mean 60

6.1.1 z test for large samples 60

6.1.2 t test for small samples 66

6.1.3 Calculation of statistic t-value using SPSS 67

6.2 Hypothesis testing about the difference between two population means 69

6.2.1 z test for large samples 69

6.2.2 t test for small samples 71

6.2.3 Calculation of the statistic t-value using SPSS 73

6.3 t test for correlated samples 78

Chapter 7 Non-parametric Tests 84

7.1 The Mann-Whitney U test 86

7.2 The Wilcoxon signed-rank test 92

7.3 The sign test 96

Chapter 8 Chi-square Test 100

8.1 Goodness-of-fit test 102

8.2 Hypothesis testing of Chi-square test for the contingency table 107

8.3 Yates’s correction 114

8.4 Hypothesis testing of Chi-square test about more than two categories 116

Chapter 9 F Distribution 119

9.1 The F distribution 119

9.2 Homogeneity of variance 120

9.3 Analysis of variance 123

9.4 Kruskal-Wallis test 130

Chapter 10 Hypothesis Testing About Proportions 135

10.1 Estimation of one population poportion 135

10.2 Estimation of a difference between two population proportions 136

10.3 Hypothesis testing about a single population proportion 137

10.4 Hypothesis testing about two independent population proportions 139

10.5 Hypothesis testing about two dependent population proportions 141

Chapter 11 Regression and Correlation 145

11.1 Regression 146

11.2 Correlation 151

11.2.1 The Pearson product-moment correlation coefficient 152

11.2.2 Spearman’s rank correlation coefficient 155

11.2.3 The Phi correlation coefficient 158

Chapter 12 Factor Analysis 162

12.1 Applications of factor analysis 162

12.2 Basic ideas of factor analysis as a data reduction method 164

12.3 Factor analysis to discover the structure of validity and reliability 173

12.4 Factor analysis used for exploration 176

Appendix Ⅰ The Normal Distribution 179

Appendix Ⅱ The t distribution 181

Appendix Ⅲ The Mann-Whitney U test 183

Appendix Ⅳ The Wilcoxon Signed-ranks Test 185

Appendix Ⅴ The Sign Test 186

Appendix Ⅵ The Chi-square Distribution 187

Appendix Ⅶ The F Distribution 188

Appendix Ⅷ The Person Product-moment Correlation Coefficient 190

Appendix Ⅸ The Spearman Rank Correlation Coefficient 191

Appendix Ⅹ 常用统计学术语表 192

Bibliography 206