Course Overview
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Course Synopsis
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This course provides an overview of non parametric statistics. “Non parametric” can be defined quite broadly, and this course aims to acquaint its students with as many of those areas as possible. “Non parametric” means something rather different now than it has in the past; this course will take a modern view of non parametric statistics, although we will spend some time on traditional rank-based non-parametric. The main idea of this course is to get students acquainted with the fundamentals, basic properties and use of the most important recent non parametric techniques. Some of those ideas are theoretical, others are computational and methodological. Another aim is to familiarize students with research questions in this domain.
This Course deals with the analysis of data for which non parametric methods are indicated. Topics include a revision of statistical inference; the analysis of categorical data using chi-square; and non parametric methods for single samples and for two-sample comparisons.
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Course Learning Outcomes
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At the end of the course, you will know, understand and be able to apply/demonstrate:
- 1. Identify different statistics used in nonparametric statistics, and be able to estimate and interpret these statistics.
- 2. Become familiar with issues in the design, analysis, and interpretation of studies involving nonparametric statistics.
- 3. Detect and allow for violations of the assumptions on which analyses are based.
- 4. Learn non-parametric test such as the Sign Test, Wicoxon Test, Median Test, Chi-Square test for Independence as well as Goodness of Fit.
- 5. Develop oral and written communication skills through the description of analytic strategies and the summarization and interpretation of results.
- 6. Understand and communicate to others the importance and relevance of statistics in the modern world
- 7. Be an independent learner, able to acquire further knowledge with little guidance or support
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Course Calendar
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Week 01
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2
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Measurement Scales:Example
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6
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Examples of Measures of Location: Mean and Median
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7
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Discrete and Continuous Distributions
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9
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One tailed and two tailed tests
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10
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Some Properties of Hypothesis Tests:Power fuction
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11
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Unbiased and consistent tests
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16
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Parametric Test:Introduction
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17
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Parametric Test:Examples
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18
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Non -Parametric Test:Introduction
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19
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Non -Parametric Test:Examples
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Week 02
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21
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The Binomial Test:Example 1
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22
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The Binomial Test:Example 2
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23
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Binomial test: Computer Demonstration:Data Requirement
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24
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Binomial test: Computer Demonstration:Procedure
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25
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Binomial test: Computer Demonstration:Interpretation
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26
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Confidence Interval for Population Proportion
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27
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Confidence Interval for Population Proportion:Computer Demonstration:Data Requirement
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28
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Confidence Interval for Population Proportion:Computer Demonstration:Procedure
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29
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Confidence Interval for Population Proportion:Computer Demonstration:Interpretation
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30
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Sign Test:Introduction
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31
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Sign Test for Population Median
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32
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Large Sample Sign test for Median
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Assignment I
Week 03
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35
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Sign test: Computer Demonstration:Data Requirement
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36
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Sign test: Computer Demonstration:Procedure
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37
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Sign test: Computer Demonstration:Interpretation
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38
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Some variations of the Sign test: The McNemar test
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39
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The McNemar test:Example 1
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40
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The McNemar test:Example 2
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41
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The McNemar test: Computer Demonstration:Data Requirement
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42
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The McNemar test: Computer Demonstration:Procedure
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43
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The McNemar test: Computer Demonstration:Interpretation
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Week 04
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44
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Confidence Interval for Median based on Sign test
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45
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Confidence Interval for Median based on Sign test:Example
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46
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Large Sample Approximation of Confidence Interval for Sign test
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47
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Large Sample Approximation of Confidence Interval for Sign test:Example 1
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48
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Large Sample Approximation of Confidence Interval for Sign test:Example 2
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49
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Contingency Table: The 2 x 2 contingency table
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50
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Chi-square Test for Differences in Probabilities
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51
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Chi-square Test for Differences in Probabilities: Example 1
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52
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Chi-square Test for Differences in Probabilities: Example 2
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53
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Chi-square Test for Differences in Probabilities: Computer Demonstration:Data Requirement
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54
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Chi-square Test for Differences in Probabilities: Computer Demonstration:procedure
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55
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Chi-square Test for Differences in Probabilities: Computer Demonstration:Interpretation
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Week 05
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56
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Chi-square Test for Independence:Introduction
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57
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Chi-square Test for Independence:Example 1
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58
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Chi-square Test for Independence:Example 2
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59
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Chi-square Test for Independence:Computer Demonstration:Data Requirement
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60
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Chi-square Test for Independence:Computer Demonstration:Procedure
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61
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Chi-square Test for Independence:Computer Demonstration:Interpretation
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62
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Chi-square Test of Homogegeneity:Introduction
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63
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Chi-square Test of Homogegeneity:Example
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64
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Chi-square Test of Homogegeneity:Computer Demonstration:Data Requirement
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65
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Chi-square Test of Homogegeneity:Computer Demonstration:Procedure
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66
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Chi-square Test of Homogegeneity:Computer Demonstration:Interpretation
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67
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Procedures About Data from Two Independent Samples
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Quiz-I
Week 06
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68
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The Median Test:Introduction
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69
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The Median Test:Example 1
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70
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The Median Test:Example 2
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71
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The Median Test:Computer Demonstration:Data Requirement
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72
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The Median Test:Procedure
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73
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The Median Test:Computer Demonstration:Interpretation
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74
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Chi-squared Test for Goodness of Fit:Introduction
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75
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Chi-squared Test for Goodness of Fit:Example 1
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76
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Chi-squared Test for Goodness of Fit:Example 2
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77
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Chi-squared Test for Goodness of Fit:Computer Demonstration:Data Requirement
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78
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Chi-squared Test for Goodness of Fit:Computer Demonstration:Procedure
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79
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Chi-squared Test for Goodness of Fit:Computer Demonstration:Interpretation
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80
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Two Independent Samples:Mann Whitney U test: Introduction
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81
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Mann Whitney U test: Example 1
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82
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Mann Whitney U test: Example 2
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83
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Mann Whitney U test for tied observations
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84
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Mann Whitney U test for tied observations:Example
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Quiz-II
Week 07
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85
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Large sample Approximation of Mann Whitney U test
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86
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Large sample Approximation of Mann Whitney U test:Example 1
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87
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Large sample Approximation of Mann Whitney U test:Example 2
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88
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Mann Whitney U test: Computer Demonstration:Data Requirement
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89
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Mann Whitney U test: Computer Demonstration:Procedure
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90
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Mann Whitney U test: Computer Demonstration:Interpretation
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91
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Confidence Interval for the Difference Between Two location parameters:Introduction
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92
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Confidence Interval for the Difference Between Two location parameters:Example
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93
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Comparison of two Populations: Paired Samples
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94
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Sign Test Two Related Samples-Introduction
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95
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Sign Test Two Related Samples-One tailed and Two tailed test
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96
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Sign Test Two Related Samples-Example 1
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97
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Sign Test Two Related Samples-Example 2
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98
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Confidence Interval for median based onSign Test for Related Samples-Introduction
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99
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Confidence Interval for median based onSign Test for Related Samples-Example
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100
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Sign Test for Two related Samples-Computer Demonstration-Data Requirement
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101
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Sign Test for Two related Samples-Computer Demonstration-Procedure
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102
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Sign Test for Two related Samples-Computer Demonstration-Interpretation
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Week 08
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103
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McNemar Test for Two Related Samples-Introduction
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104
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McNemar Test for Two Related Samples-Example
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105
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McNemar Test for Two Related Samples-Computer Demonstration-Data Requirement
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106
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McNemar Test for Two Related Samples-Computer Demonstration-Data-Procedure
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107
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McNemar Test for Two Related Samples-Computer Demonstration-Interpretation
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Mid Term
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108
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Wilcoxon Signed Rank Test: Introduction
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109
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Wilcoxon Signed Rank Test: One tailed test
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110
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Wilcoxon Signed Rank Test: One tailed test:Procedure
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111
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Wilcoxon Signed Rank Test: One tailed test:Example 1
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112
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Wilcoxon Signed Rank Test: One tailed test:Example 2
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113
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Wilcoxon Signed Rank Test: Two tailed test
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114
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Wilcoxon Signed Rank Test: Two tailed test:Procedure
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115
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Wilcoxon Signed Rank Test: Two tailed test:Example 1
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116
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Wilcoxon Signed Rank Test: Two tailed test:Example 2
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117
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Wilcoxon Signed Rank Test for Large Samples
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118
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Wilcoxon Signed Rank Test for Large Samples:Example 1
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119
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Wilcoxon Signed Rank Test for Large Samples:Example 2
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Week 09
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120
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Wilcoxon Signed Rank Test: Computer Demonstration:Data Requirement
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121
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Wilcoxon Signed Rank Test: Computer Demonstration:Procedure
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122
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Wilcoxon Signed Rank Test: Computer Demonstration:Interpretation
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123
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Confidence Interval for Median based on Wilcoxon Signed Rank test
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124
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Confidence Interval for Median based on Wilcoxon Signed Rank test:Example
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125
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Comparison of three or more populations:Several Independent Samples
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126
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Kruskal Wallis H test: Introduction
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127
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Kruskal Wallis H test: Procedure
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128
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Kruskal Wallis H test: Example 1
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129
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Kruskal Wallis H test: Example 2
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130
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Kruskal Wallis H test for ties
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131
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Kruskal Wallis H test for ties:Example 1
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132
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Kruskal Wallis H test for ties:Example 2
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133
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Kruskal Wallis H test: Computer Demonstration:Data Requirement
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134
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Kruskal Wallis H test: Computer Demonstration:Procedure
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135
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Kruskal Wallis H test: Computer Demonstration:Interpretation
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136
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Comparison of three or more populations: Several Related Samples
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Quiz-III
Week 10
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137
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Friedman test:Introduction
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138
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Friedman test:Procedure
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139
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Friedman test:Example 1
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140
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Friedman test:Example 2
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141
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Friedman Fr test:Computer Demonstration:Data Requirement
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142
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Friedman Fr test:Computer Demonstration:Procedure
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143
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Friedman Fr test:Computer Demonstration:Interpretation
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144
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Confidence intervals for the Differences between the two location parameters
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145
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Confidence Interval for the Differences between the two location parameters :Example
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146
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Cochran's test:Introduction
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147
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Cochran's test for related observations:Procedure
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148
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Cochran Q test:Example 1
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149
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Cochran Q test:Example 2
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150
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Cochran Q test:Computer Demonstration:Data Requirement
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151
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Cochran Q test:Computer Demonstration:Procedure
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152
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Cochran Q test:Computer Demonstration:Interpretation
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153
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Measures of Rank Correlation: Spearman's Rank Correlation:Introduction
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154
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Spearman's Rank Correlation:Example 1
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155
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Spearman's Rank Correlation:Example 2
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156
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Spearman's Rank Correlation test for ties
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157
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Spearman's Rank Correlation test for ties:Example 1
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158
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Spearman's Rank Correlation test for ties:Example 2
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Week 11
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159
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Spearman's Rank Correlation:Computer Demonstration:Data Requirement
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160
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Spearman's Rank Correlation:Computer Demonstration:Procedure
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161
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Spearman's Rank Correlation:Computer Demonstration:Interpretation
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162
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Kendall's tau test:Introduction
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163
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Kendall's tau test:Example 1
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164
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Kendall's tau test:Example 2
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165
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Kendall's tau test for ties:Introduction
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166
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Kendall's tau test for ties:Example 1
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167
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Kendall's tau test for ties:Example 2
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Week 12
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168
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Kendall's tau test:Computer Demonstration:Data Requirement
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169
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Kendall's tau test:Computer Demonstration:Procedure
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170
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Kendall's tau test:Computer Demonstration:Interpretation
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171
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Lillieforce Test for Normality:Introduction
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172
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Lillieforce Test for Normality:Example 1
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173
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Lillieforce Test for Normality:Example 2
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Assignment-II
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174
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Shapiro-Wilk Test for Normality:Introduction
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175
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Shapiro-Wilk Test for Normality:Example 1
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176
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Shapiro-Wilk Test for Normality:Example 2
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Week 13
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177
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Shapiro-Wilk Test for Normality:Computer Demonstration:Data Requirement
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178
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Shapiro-Wilk Test for Normality:Computer Demonstration:Procedure
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179
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Shapiro-Wilk Test for Normality:Computer Demonstration:Interpretation
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180
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Kolmogrov Smirnov Test for Normality:Introduction
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181
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Kolmogrov Smirnov Test for Normality:Example 1
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182
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Kolmogrov Smirnov Test for Normality:Example 2
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183
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Kolmogrov Smirnov Test for Normality:Computer Demonstration:Data Requirement
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184
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Kolmogrov Smirnov Test for Normality:Computer Demonstration:Procedure
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185
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Kolmogrov Smirnov Test for Normality:Computer Demonstration:Interpretation
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186
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Runs Test for Randomness:Introduction
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187
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Runs Test for Randomness:Example 1
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188
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Runs Test for Randomness:Example 2
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Week 14
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189
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Large Sample Approximation for Runs test
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190
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Large Sample Approximation for Runs test:Example 1
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191
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Large Sample Approximation for Runs test:Example 2
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192
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Runs Test for Randomness:Computer Demonstration:Data Requirement
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193
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Runs Test for Randomness:Computer Demonstration:Procedure
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194
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Runs Test for Randomness:Computer Demonstration:Interpretation
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Quiz-IV
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195
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Seigel Tukey Test for Scale Differences-Introduction
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196
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Seigel Tukey Test for Scale Differences:Example 1
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197
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Seigel Tukey Test for Scale Differences:Example 2
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198
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Test for scale Differences-Computer Demonstration-Data Requirement
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199
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Test for scale Differences-Computer Demonstration-Procedure
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200
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Test for scale Differences-Computer Demonstration-Interpretation
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201
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Squared Ranks test for Variances:Introduction
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202
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Squared Ranks Test for Variances-Example 1
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203
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Squared Ranks Test for Variances-Example 2
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Week 15
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204
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Simple Linear Regression Analysis: Thiel's Method
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205
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Simple Linear Regression Analysis:Thiel's Method-Assumptions
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206
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Simple Linear Regression Analysis:Thiel's Method-Procedure
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207
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Simple Linear Regression Analysis:Thiel's Method: Estimation of Slope (1)
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208
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Simple Linear Regression Analysis:Thiel's Method: Estiamtion of Slope-Example
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209
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Simple Linear Regression Analysis:Thiel's Method-Example 1
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210
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Simple Linear Regression Analysis:Thiel's Method-Example 2
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211
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Simple Linear Regression Analysis:Thiel's Method:Example 3.
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212
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Test for Parallelism of Two Regression Lines: Introduction (1)
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213
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Test for Parallelism of Two Regression Lines-Procedure (1)
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214
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Test for Parallelism of Two Regression Lines: Example 1
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Final Term
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