LEC 7 Non-Parametric Test ll

Question 1

Statistical test for

1. Continuous data (non-normal distribution)
2. Ordinal data

> 2 independent groups

Answer 1

Kruskal-Wallis test

If significant difference (rej Ho), do post-hoc test
- Wilcoxon Rank Sum test

Question 2

Post-Hoc analysis for One-Way ANOVA vs Kruskal-Wallis

Answer 2

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

Question 3

Kruskal-Wallis test assumptions (2)

Answer 3

1. The samples are random samples of their populations

2. The underlying populations are independent

Question 4

Kruskal-Wallis test

Answer 4

A generalisation of Wilcoxon Rank Sum test

Hence, process is similar

Question 5

Kruskal-Wallis test hypothesis

Answer 5

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

Question 6

For Kruskal Wallis test,

If Ho is true,

Answer 6

• 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

Question 7

Wilcoxon-Signed Rank test assumptions (3)

Answer 7

1. The samples are random samples of their populations
2. The two underlying populations are paired
3. The underlying distribution of the difference is symmetrical (normal distribution)

Question 8

Wilcoxon-Signed Rank test hypothesis

Answer 8

Ho :
- Median difference = 0

H1 :

• median difference =/ 0 (two-tailed)
• median difference > 0 (one-tailed)
• median difference < 0 (one-tailed)

Question 9

Wilcoxon-Signed Rank test

Answer 9

• calculate the difference first then rank them

- takes into account both the signs and magnitudes

Question 10

For Wilcoxon Signed-rank test,

if Ho is true,

Answer 10

• 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

Question 11

Computation of Z statistic for Wilcoxon-Signed Rank test

Answer 11

Use +ve or -ve rank sum will still derive to the same Z value