4 - non parametric hype tests

Question 1

single-sample sign test

Answer 1

H0 median =
H1 median isnt
- based on H0 youd expect half the data to be above and half below
- count number of observed above median (x)
X~B(n,1/2)
- find the probability that of it being x or more extreme
if p<sig level
reject H0

Question 2

single sample Wilcoxon signed rank

Answer 2

H0 median =
H1 median isnt
- find different from median
- assign ranks from smallest to biggest
- W+ is sum of pos ranks W- is sum of neg
- T is the smaller of W+ or W-
- use the table to determine the result
if T <= sig level
reject H0

Question 3

matched pairs test

Answer 3

H0: same distribution
H1: different distributions
find the difference between pairs
test that using sign test or Wilcoxon signed rank

Question 4

additional assumption in matched pairs

Answer 4

reject H0 means that the 2 pops are different
but normally also assume
- shapes of both distributions are the same
- if this is the case then any difference between 2 populations is due to a difference in the median

Question 5

wilcoxon rank sum

Answer 5

• take two samples of size m and n where m<=n
• rank all values from lowest to highest
• Rm is sum of the ranks of m
• W is either Rm or m(m+n+1) - Rm
• use the table to conduct the test
  ( m(m+n+1) - Rm is the value if the values had be ranked in order of decreasing size)

Question 6

Normal approximation

Answer 6

for Wilcoxon signed rank or Wilcoxon rank sum
if the sample is very large
you need to use the fact T and W approximately follow a normal distribution
- you can then use normal distribution to calc how liley you are to see the value or more extreme
- use this to conduct the test

Question 7

normal approximation - Wilcoxon signed rank

Answer 7

if H0 is true both W+ and W- can be approximated by normal distribution
mean = 1/4 n(n+1)
variance = 1/24 n(n+1)(2n+1)

Question 8

normal approximation - Wilcoxon rank sum

Answer 8

if H0 is true Rm can be approximated by normal distribution
mean = 1/2 m(m+n+1)
variance = 1/12 mn(m+n+1)

Question 8

normal approximation - wilcoxon signed rank - continuity correction

Answer 8

W+/- is an integer but for normal uses continuous
if W is less than mean you do W + 0.5
if its above the mean do W - 0.5

Question 9

normal approximation - wilcoxon rank sum - continuity correction

Answer 9

if Rm is below mean use Rm + 0.5
if Rm is above use Rm - 0.5