Non-Parametrics

Question 1

What are parametric statistics?

Answer 1

data that can be analysed using parametric statistics have a known distribution we can parametrise

Question 2

what are non-parametric statistics?

Answer 2

they model data that cannot be characterised in terms of a known probability distribution

non-parametric data is rank data, such as user preferences or ratings

Question 3

how do we measure the central tendency of non-parametrics? why not the mean?

Answer 3

mode or median

the mean is undefined, ordinal data has no numerical information separating the different ranks

Question 4

what is the sign test?

Answer 4

a non-parametric test

• we have n paired observations (X1, Y1), (X2, Y2) …
• we compute the differences between the pairs (Y1 - X1)…
• differences that are zero are ignored, resulting in n’ observations
• r^- is the number of differences that are < 0
• r^+ is the number of differences that are > 0

r = max of r+ and r-
H0 says that r- and r+ follow a binomial distribution B(n,p) with p = 0.5 and n = n’

use the B(n,p) to find the probability of observing a value or r or higher given p = 0.5 and n = n’

this probability is doubld because the test is two sided

this is our p value

if its less than .05 then we cnan reject