LEC 6 Non-Parametric Test l

Question 1

Parametric test assumptions (2)

Answer 1

1. Samples are drawn from normally distributed populations

2. The underlying populations have equal variance

Question 2

Non-parametric tests (3)

Answer 2

• distribution-free tests
• place fewer restrictions on underlying distributions or equal variances
• used when assumptions of parametric tests are not met

Question 3

Advantages of non-parametric tests (4)

Answer 3

1. Do not incorporate all the restrictive assumptions characteristic of parametric tests

Use ranks rather than actual values of the observations :

2. Can be performed relatively quickly for small samples
3. Less sensitive to measurement errors and outlying values
4. Suitable for continuous non-normal data, nominal and ordinal datas

Question 4

Disadvantage of non-parametric tests

Answer 4

Less powerful than parametric tests, if the assumptions underlying a parametric test are satisfied
- require larger sample size to maintain same statistical significance value

Question 5

Statistical test for :

• continuous non-normal data
• ordinal data
• 2 independent groups

Answer 5

Wilcoxon Rank Sum test (Mann-Whitney U test)

Question 6

Assumptions of Wilcoxon Rank Sum test (Mann-Whitney U test) (2)

Answer 6

1. The samples are random samples of their populations

2. The 2 underlying populations are independent

Question 7

Wilcoxon Rank Sum test (Mann-Whitney U test) hypothesis

Answer 7

Null hypothesis
- there is no difference between the medians of the 2 underlying populations

Alternate hypothesis

• median 1 =/ median 2 (two-tailed)
• median 1 > median 2 (one-tailed)
• median 2 > median 1 (one-tailed)

Question 8

Normality tests

Answer 8

1. Shapiro-Wilk (n<50)

2. Kolmogorov-Smirnov (n>=50)

Question 9

Normality tests hypothesis

Answer 9

Null hypothesis
- normal distribution

Alternate hypothesis
- not normal distribution

Question 10

If 2 groups, 1 normal and 1 not normal distribution, what test to use?

Answer 10

Non-parametric cos parametric req both groups to follow normal distribution

Question 11

For Wilcoxon Rank Sum test, if sample size n>=10,

Answer 11

we can assume distribution of W (sum of smaller sample group) to be normal

Question 12

For Wilcoxon Rank Sum test, if sample size n<10,

Answer 12

• we CANNOT assume distribution of W (sum of smaller sample group) to be normal.
• need to use a specific table (nL)

Question 13

W distribution graph

Answer 13

Symmetrical

If two-tailed test, multiply p-value by 2

Question 14

Which p-values from statistical test report to use?

Answer 14

1. Exact sig

2. Asymp sig