Post on 14-Jun-2015
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Statistics One
Lecture 22 Non-parametric statistics
Two segments
• Parametric vs. non-parametric statistics • Examples
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Lecture 22 ~ Segment 1
Parametric vs. non-parametric statistics
Parametric vs. non-parametric
• Parametric statistics are used to make inferences about population parameters
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Parametric vs. non-parametric
• Examples covered in this course • Regression coefficient • Regression model R-squared • Group mean • Difference between group means • Proportion of cases distributed across
categories
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Parametric vs. non-parametric
• In all these cases inferences were based on the sample statistics as well as NHST and/or confidence intervals
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Parametric vs. non-parametric
• As well, in all these cases we assumed a particular sampling distribution • t • F • Chi-square
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Parametric vs. non-parametric
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Parametric vs. non-parametric
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Parametric vs. non-parametric
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Parametric vs. non-parametric
• Inferences about population parameters are not valid if all assumptions are not met
• When assumptions are violated sometimes a “quick fix” is possible and the parametric approach is still considered to be valid
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Parametric vs. non-parametric
• However, sometimes it is best to abandon the parametric approach and use a non-parametric procedure
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Parametric vs. non-parametric
• Non-parametric statistics do not assume that the data or population have any characteristic structure
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Parametric vs. non-parametric
• Correlation • Regression • t-tests • ANOVA • Chi-square
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Parametric vs. non-parametric
• Correlation • Spearman’s rank correlation coefficient • Kendall’s tau
• Regression • Non-parametric regression
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Parametric vs. non-parametric
• t-tests • Independent: Mann-Whitney U test • Dependent: Wilcoxan signed-rank test
• ANOVA • Kruskal-Wallis one-way • Friedman two-way
• Chi-square • McNemar’s test • Fisher’s exact test
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Segment summary
• Parametric statistics are used to make inferences about population parameters
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Segment summary
• Inferences about population parameters are not valid if all assumptions are not met
• When assumptions are violated sometimes a “quick fix” is possible and the parametric approach is still considered to be valid
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Segment summary
• However, sometimes it is best to abandon the parametric approach and use a non-parametric procedure
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Segment summary
• Non-parametric statistics do not assume that the data or population have any characteristic structure • Many procedures available
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END SEGMENT
Lecture 22 ~ Segment 2
Non-parametric statistics Examples
Non-parametric examples
• Two simple and popular tests covered in this course • Paired samples t-test • Independent t-test
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Non-parametric examples
• Here we will illustrate the non-parametric equivalent of these tests • Wilcoxan’s ranking method • Mann-Whitney U test
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Wine tasting!
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Non-parametric examples
• Wilcoxan ranking method (Wilcoxan, 1945) – Null hypothesis • Median difference between pairs = 0
– Alternative hypothesis • Median difference between pairs != 0
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Non-parametric examples
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Wilcoxan: Null hypothesis true Red White Sign(S) ABS Rank(R) S*R
1 65 60 -‐1 5 1 -‐1
2 60 70 +1 10 2 2
3 65 80 +1 15 3 3
4 85 65 -‐1 20 4 -‐4
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Wilcoxan: Null hypothesis false Red White Sign(S) ABS Rank(R) S*R
1 65 70 +1 5 1 1
2 60 70 +1 10 2 2
3 65 80 +1 15 3 3
4 65 85 +1 20 4 4
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Wilcoxan: R output
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Non-parametric examples
• Mann Whitney U (Mann & Whitney, 1947) – Adapted Wilcoxan’s ranking method to compare
independent groups – Arrange all observations, regardless of group,
into a single ranked series
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Non-parametric examples
• Mann Whitney U (Mann & Whitney, 1947) – The sum of all ranks, Sum = N(N+1) / 2 • For example, Sum = 4(5) / 2 = 10
– R = Sum of Ranks from one group – U = Sum - R
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Mann Whitney: Null hypothesis true
Ra3ng Group Rank(R)
1 60 A 1
2 70 B 2
3 80 B 3
4 90 A 4
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Mann Whitney: Null hypothesis false
Ra3ng Group Rank(R)
1 60 A 1
2 70 A 2
3 80 B 3
4 90 B 4
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Non-parametric examples
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Non-parametric examples
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Segment summary
• Two simple and popular tests covered in this course • Paired samples t-test • Independent t-test
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Segment summary
• Here we illustrated the non-parametric equivalent of these tests • Wilcoxan’s ranking method • Mann-Whitney U test
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END SEGMENT
END LECTURE 22