LEC 7 Non-Parametric Test ll Flashcards

1
Q

Statistical test for

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

> 2 independent groups

A

Kruskal-Wallis test

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

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2
Q

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

A

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

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3
Q

Kruskal-Wallis test assumptions (2)

A
  1. The samples are random samples of their populations

2. The underlying populations are independent

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4
Q

Kruskal-Wallis test

A

A generalisation of Wilcoxon Rank Sum test

Hence, process is similar

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5
Q

Kruskal-Wallis test hypothesis

A

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

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6
Q

For Kruskal Wallis test,

If Ho is true,

A
  • 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
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7
Q

Wilcoxon-Signed Rank test assumptions (3)

A
  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)
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8
Q

Wilcoxon-Signed Rank test hypothesis

A

Ho :
- Median difference = 0

H1 :

  • median difference =/ 0 (two-tailed)
  • median difference > 0 (one-tailed)
  • median difference < 0 (one-tailed)
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9
Q

Wilcoxon-Signed Rank test

A
  • calculate the difference first then rank them

- takes into account both the signs and magnitudes

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10
Q

For Wilcoxon Signed-rank test,

if Ho is true,

A
  • 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
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11
Q

Computation of Z statistic for Wilcoxon-Signed Rank test

A

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

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