LEC 7 Non-Parametric Test ll Flashcards
Statistical test for
- Continuous data (non-normal distribution)
- Ordinal data
> 2 independent groups
Kruskal-Wallis test
If significant difference (rej Ho), do post-hoc test
- Wilcoxon Rank Sum test
Post-Hoc analysis for One-Way ANOVA vs Kruskal-Wallis
One-Way ANOVA
- Bonferroni adjustment (very conservative)
- LSD (least conservative)
- Tukey’s (more conservative)
- Scheffe’s (most conservative)
- Dunnett’s (control)
Kruskal-Wallis
- Wilcoxon Rank Sum test but use adjusted alpha value even if use statistical software
Kruskal-Wallis test assumptions (2)
- The samples are random samples of their populations
2. The underlying populations are independent
Kruskal-Wallis test
A generalisation of Wilcoxon Rank Sum test
Hence, process is similar
Kruskal-Wallis test hypothesis
Ho :
- All the medians of the underlying populations are the same
H1 :
- Not all the medians of the underlying populations are the same
OR
- The medians of at least 2 of the underlying populations are different
For Kruskal Wallis test,
If Ho is true,
- all the medians of the underlying populations are the same
- we would expect the ranks to be distributed randomly among the groups
- average ranks for each samples should be approximately equal
Wilcoxon-Signed Rank test assumptions (3)
- The samples are random samples of their populations
- The two underlying populations are paired
- The underlying distribution of the difference is symmetrical (normal distribution)
Wilcoxon-Signed Rank test hypothesis
Ho :
- Median difference = 0
H1 :
- median difference =/ 0 (two-tailed)
- median difference > 0 (one-tailed)
- median difference < 0 (one-tailed)
Wilcoxon-Signed Rank test
- calculate the difference first then rank them
- takes into account both the signs and magnitudes
For Wilcoxon Signed-rank test,
if Ho is true,
- median difference of the underlying populations = 0
- expect the samples to have approximately equal numbers of positive and negative ranks
- the sum of positive ranks to be comparable in magnitude to the sum of negative ranks
Computation of Z statistic for Wilcoxon-Signed Rank test
Use +ve or -ve rank sum will still derive to the same Z value