Contents
1.1 Parametric Inference, Recalled
1.2 When Parametric Inference Will Not Do
1.3 Population and Sample
1.4 Hypothesis Tests, Recalled
1.5 The Rationale of \(H_0\) and \(\alpha \)
1.6 Types of Hypotheses
1.7 A First Non-Parametric Test
1.8 Practice Problems
2 Some Tests Based on the Binomial Distribution
2.1 Sign Test
2.2 Confidence Interval for the Median
2.3 Order Statistics
2.4 Quantile Functions
2.5 Percentile and Quartile
2.6 Quartile Test
2.7 Practice Problems
3 Some Tests Based on Ranks
3.1 Ranks
3.2 Mid Ranks
3.3 The Wilcoxon Signed-Rank Test
3.4 Zeros and Ties in the Signed-Rank Test
3.5 General Two Sample Problem
3.6 The Wilcoxon- Mann-Whitney Test
3.7 Wilcoxon Rank Sum
3.8 Wilcoxon- Mann- Whitney Test
3.9 Ties in the Rank-Sum Test
3.10 Practice Problems
4 Tests for Three or More Samples
4.1 Kruskal-Wallis Test
4.2 Assumption of Kruskal-Wallis Test
4.3 The Friedman Test
4.4 Multiple Comparisons
4.5 Practice Problems
5 Non-Parametric Measures of Correlation
5.1 Association and Correlation
5.2 Rank correlation
5.3 Spearmans Rank Correlation
5.4 Computing the Coefficient \((r_s)\) Spearman correlation
5.5 Tied Ranks
5.6 Tests
5.7 Kendall’s Tau
5.8 Practice Problems
6 Kolmogorov-Smirnov (K-S) Test
6.1 The K-S One Sample Test (goodness-of-fit test)
6.2 Rationale Of K-S
6.3 Two Sample Test
6.4 The K Sample K-S Statistic
6.5 Practice Problems
7 Two Further Tests
7.1 The Runs Test for Randomness
7.2 The Median Test
7.3 Practice Problems
8 Non-Parametric Methods for Trend
8.1 The Mann–Kendall Test
8.2 The Variance of \(S\), With Ties
8.3 The Theil–Sen Slope
8.4 Serial Correlation, and Why It Breaks the Test
8.5 A Warning Not Found in the Textbooks
8.6 Testing Many Series at Once
8.7 Seasonality
8.8 Practice Problems
Rationale _______________________________________________________________________________________________
The parametric statistical methods depend so much on the underlying distributions of the random
variable and independence of measurements. However there are many situations when the assumption
of the underlying distribution and or independence do not hold. Non-parametric statistical methods
are then required. This course gives students techniques and skills to perform some non-parametric
procedures.
Objectives
At the end of the course, students should be able to :-
- 1.
- Explain the difference between non-parametric and parametric procedures.
- 2.
- Perform some statistical tests based on Binomial distributions (Binomial test, Quantile test).
- 3.
- Perform some statistical tests based on ranks for one sample, two samples, one-way ANOVA and two-way ANOVA.
- 4.
- Perform goodness of fit tests.
Pre-requisites: Mathematical Statistics and Analysis and Design of Experiments.
Course Content ______________________________________________________________________________________
- 1.
- Introduction
Populations, samples and statistics. Estimation. Hypothesis testing. Some properties of hypothesis tests. Some comments on non-parametric statistics. - 2.
- Some test based on Binomial Distribution
Binomial test. Quantile test. Sign test and its variations. - 3.
- Some tests based on Ranks
One and two independent samples. Several independent samples, Kruskal-Wallis one-way analysis of variance. Friedman two-way analysis of variance. The one-sample or matched-pairs case. Measures of rank correlation. - 4.
- Statistics of Kolmogorov-Smirnov type
The Kolmogorov goodness-of-fit test. Tests on two independent samples. Tests on several independent samples.