non-parametric tests

Question 1

parametric tests

Answer 1

assume a specific distribution with parametric methods
has parameters
eg. normal with mew and sigma as parameters

Question 2

non-parametric

Answer 2

minimal assumptions
use properties of any distribution like the mean
based on ranking data
means and medians are more robust than t-tests
if normal, t tests are more powerful
assumes continuous density (no tied ranks)

Question 3

paired data: wllcoxon ranks test

Answer 3

• paired data has a one-to one correspondence

- measurements are dependent on each other in a pair eg. before and after tests in an experiment

Question 4

hypothesis in wilcoxon ranks

Answer 4

H0: differences between pairs have a symmetric distribution about 0
Ha: differences between pairs do not have a symmetric distribution about 0

Question 5

test procedure wilcoxon ranks

Answer 5

1. match pairs
2. work out the difference as Di
3. differences are ranked smallest to largest and keep track of +/- signs
4. where ties occur, average ranks

work out W+ and W-

W+ + W- = 1/2n(n+1)

and then use equations to calculate p value, assuming normal distribution

Question 6

wilcoxon zero differences

Answer 6

for continuous density - no exactly zero

ordinal data might have exact zeros and remove offending pairs

Question 7

Two-sample tests: Mann Whitney-Wilcoxon test characteristics

Answer 7

two independent (unpaired) samples 
samples might not be the same size

Question 8

Two-sample tests: Mann Whitney-Wilcoxon test Hypotheses

Answer 8

H0: the two popuations have the same distribution or the same median etc.
two sided or one sided

Question 9

Two-sample tests: Mann Whitney-Wilcoxon test basic idea

Answer 9

• combine data in a pooled sample
• look at X’s position relative to Y
• XXXYYY suggests Y is on the right XYXYXY suggests no real difference

Question 10

Test procedure Two-sample tests: Mann Whitney-Wilcoxon test

Answer 10

• order pooled samples smallest to largest
• Wx and Wy are calculated from the ranks
• very small values of Wx or wy would suggest H0 isn’t true

Question 11

Two-sample tests: Mann Whitney-Wilcoxon test distribution theory

Answer 11

under H0, if m is greater or equal to 10 and so is n, Wx and Wy are normal

use equations to work our test statistic

for smaller samples, compute the rank sum for smaller samples only