Non-Parametric Statistics for Applied Linguistics Research

PREFACE v
ACKNOWLEDGMENT viii
1 INTRODUCTION TO STATISTICS AND SLAR 1
1.1. A mole wrench or a pipe wrench 4
1.2. Test power 5
1.2.1. Sample size and power 9
1.2.2. Effect size and power 11
1.2.3. Are nonparametric tests less powerful? 13
2 PARAMETRIC/NONPARAMETRIC ASSUMPTIONS 14
2.1. Scales of measurement 18
2.2. Sample Size 20
2.3. Normality 24
3 NONPARAMETRIC TESTS: REVISITED 26
3.1. NP Tests: When and Why? 27
3.2. Misconceptions about NP Tests 29
3.3. The power of NP tests 30
3.4. Common types of NP tests 32
4 NON-NORMALITY TESTS 37
4.1. The normal distribution 38
4.2. Graphical methods of testing normality 41
4.2.1. Histogram 41
4.2.2. Stem and Leaf Plot 42
4.2.3. Boxplot 43
4.2.4. P-P plot 44
4.2.5. Q-Q plot 45
4.3. Numerical methods of testing normality 46
4.3.1. Skewness 46
4.3.2. Kurtosis 49
4.4. Testing normality using SPSS 52
4.4.1. A normally distributed variable 53
4.4.2. Graphical methods 54
4.4.3. Numerical methods 58
5 NONPARAMETRIC TETS OF DIFFERENCE 65
5.1. Kolmogorov-Smirov test for one sample 66
5.1.1. SPSS for K-S test analysis 66
5.1.2. SLAR literature: Kolmogorov-Smirov test 69
5.2. Mann-Whitney U test 71
5.2.1. Carrying out Mann-Whitney test 73
5.2.2. SPSS for Mann-Whitney test 75
5.2.3. SLAR literature: Mann-Whitney U test 76
5.3. Kruskal-Wallis one-way analysis of variance 78
5.3.1. Carrying out Kruskal-Willis test 79
5.3.2. SPSS for Kruskal-Willis test 80
5.3.3. SLAR literature: Kruskal-Willis test 84
5.4. Wilcoxon matched-pairs signed ranks test 85
5.4.1. SPSS for the Wilcoxon tests 87
5.4.2. SLAR literature: Wilcoxon test 95
5.5. Friedman two-way ANOVA tests 97
5.5.1. SPSS for the Friedman test 103
5.5.2. SLAR literature: Friedman two-way ANOVA 105
6 NP TESTS OF DIFFERENCE: CATEGORICAL 107
6.1. Chi-square test for frequency data 108
6.1.1. SPSS for Chi-square 114
6.1.2. SLAR literature: Chi-square test 114
6.2. Fisher test of categorical data 116
6.2.1. SPSS for the Fisher test 121
7 NONPARAMETRIC TESTS OF ASSOCIATION 122
7.1. NP tests for categorical data 123
7.1.1. Phi Coefficient 123
7.1.1.1. SPSS for Phi Coefficient 125
7.1.2. Contingency Coefficient 132
7.1.3. Cramer's V Coefficient 134
7.2. NP tests for non-categorical data 136
7.2.1. Kendall's rank coefficient correlation 136
7.2.1.1. Kendall's tau a 137
7.2.1.2. Kendall's tau b 140
7.2.1.3. Kendall's tau c 141
7.2.1.4. SLA literature: Kendall's tau tests 144
7.2.2. Spearman's rank order correlation (Rho) 145
7.2.3. Using SPSS for Spearman's Rho 151

APPENDIX1: TWO-TAILED CRITICAL VALUES OF T FOR THE WILCOXON TEST 155
APPENDIX 2: ONE-TAILED CRITICAL VALUES OF T FOR
THE WILCOXON TEST 156
APPENDIX 3: CHI-SQUARE TABLE 157
APPENDIX 4: CRITICAL VALUES OF r (and rs) 158
APPENDIX 5: Z-TABLE 159
APPENDIX 6: T-TABLE 160
REFFERENCES
GLOSSARY