Statistics in Steps

When do you use statistics? 11

1 Doing research 17
1.1 Phase 1 – The design phase of research 17
1.2 Phase 2 – Data collection 19
1.3 Phase 3 – Data analysis 24
1.4 Phase 4 – Evaluating and reporting on your results 26

2 Descriptive statistics – one variable 29
2.1 Measurement levels 30
2.1.1 Nominal 30
2.1.2 Ordinal 31
2.1.3 Interval 32
2.1.4 Ratio 33
2.2 Frequency distributions 36
2.3 Graphs for one variable 40
2.3.1 Pie charts 40
2.3.2 Bar chart 41
2.3.3 Histogram 41
2.3.4 Line graphs 43
2.3.5 Box plots 43
2.3.6 Scatter plots and dot plots 44
2.3.7 Graphs in SPSS and Excel 47
2.4 Measures of central tendency 49
2.4.1 Mode 49
2.4.2 Median 51
2.4.3 Mean 52
2.5 Measures of variability 57
2.5.1 Range and interquartile range 57
2.5.2 Population variance 59
2.5.3 Sample variance 61
2.5.4 From variance to standard deviation 64
2.6 Special properties of standard deviation 66
2.7 Assignments for Chapter 2 69

3 Descriptive statistics – two variables 75
3.1 Cross tabulations 76
3.1.1 Percentages in cross tabulations 78
3.1.2 Cross tabulations in SPSS 79
3.2 Graphs of two variables 81
3.2.1 Bar chart 83
3.2.2 Scatter plots 85
3.2.3 Box plots 87
3.2.4 Graphs for two variables in SPSS 88
3.2.5 The SPSS Syntax window 90
3.3 Assignments for Chapter 3 91

4 Probability distributions 99
4.1 What is probability? 100
4.2 Probability rules 102
4.3 Probability distribution 106
4.4 Hypergeometric distribution 109
4.5 Binomial distribution 113
4.6 Normal distribution 116
4.6.1 Linear transformations: from normal to standard normal 116
4.6.2 From transformation to probability 120
4.6.3 Looking up p values in the z table 122
4.7 Assignments for Chapter 4 127

5 Estimation and hypothesis testing 131
5.1 Point estimates 132
5.1.1 Estimating the mean 134
5.1.2 Estimating the proportion 136
5.2 Confidence intervals 137
5.2.1 Mean confidence intervals for known variance 139
5.2.2 Confidence intervals for the mean with unknown variance 141
5.2.3 Confidence interval for a proportion 146
5.3 Formulating and testing hypotheses 147
5.3.1 Drafting and testing hypotheses 148
5.3.2 One-tailed or two-tailed tests 150
5.4 W8 test procedure 154
5.5 The power of tests and errors in interpretation 155
5.6 Assignments for Chapter 5 157

6 Testing differences between two populations 163
6.1 Tests for one mean 164
6.1.1 Z test for one mean 164
6.1.2 Testing using a t distribution 166
6.1.3 T tests for one mean 168
6.2 Paired t tests 170
6.3 Independent z test for two means 173
6.4 Independent t tests for two means 174
6.4.1 One-tailed or two-tailed tests revisited 176
6.4.2 Notations for t test results in APA 178
6.4.3 Independent t tests in SPSS 178
6.5 Correcting t tests 180
6.6 Assignments for Chapter 6 183

7 Correlation and regression 189
7.1 Correlation 190
7.1.1 Calculating the Pearson correlation coefficient 192
7.1.2 Interpreting correlations 194
7.2 Univariate linear regression analysis 197
7.2.1 Best-fitting line 197
7.2.2 Regression coefficients 200
7.2.3 Calculating intercepts 200
7.3 Explained variance or: does the model fit the data? 201
7.4 Testing hypotheses using regression analysis 205
7.4.1 An SPSS example 206
7.4.2 Multiple regression analysis 208
7.5 The power of tests 209
7.6 Assignments for Chapter 7 210

8 Analysis of variance 215
8.1 Testing hypotheses using analysis of variance 215
8.2 ANOVA using W8 procedure 218
8.3 ANOVA in SPSS 223
8.4 Analysis of variance taken a step further 228
8.4.1 Multivariate analysis of variance 228
8.4.2 F tests in regression analysis 229
8.5 Assignments for Chapter 8 231

9 Non-parametric tests 237
9.1 Chi-square tests 238
9.1.1 Testing hypotheses using the chi-square test 242
9.1.2 Chi-square tests in SPSS 244
9.2 The rank sum test – differences between two independent groups 247
9.2.1 Ranking and rank sum 247
9.2.2 Wilcoxon rank sum test 247
9.2.3 Rank sum test in SPSS 249
9.3 Signed rank test – differences between two dependent groups 253
9.3.1 Ranking and signed rank 254
9.3.2 Wilcoxon signed rank test 255
9.3.3 Signed rank test in SPSS 256
9.4 Kruskal-Wallis test– comparing more than two independent groups 258
9.5 Spearman’s rank correlation test 263
9.5.1 SPSS procedure for rank correlation test 265
9.5.2 Tau-b and tau-c 266
9.6 Assignments for Chapter 9 266

Consulted sources 273

Appendix 275

Index 281
About the author 287