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