Non-parametric Tests

Question 1

what is a distribution free test

Answer 1

tests that dont rely on any assumptions about the pd

Question 2

what are the advantages of distribution free tests

Answer 2

• they can be used with all scales
• easier to compute data
• fewer assumptions are needed
• doesnt need a population parameter

Question 3

what are the disadvantages of distribution free tests

Answer 3

• you can waste info
• hard to compute by hand for large samples
• tables arent widely available
• less efficient

Question 4

what are you looking for in a sign test

Answer 4

how many results are below the expected median

Question 5

what is the first step to a sign test

Answer 5

write out your hypotheses

Question 6

how would the hypotheses always be written

Answer 6

• H0 should always be that he median = x

- then H1 is the other side of the argument

Question 7

what is the second step

Answer 7

draw a table of the given values

Question 8

what is the third step

Answer 8

subtract the median FROM each value on the table

Question 9

what is the fourth step

Answer 9

count the number of +ve and -ve numbers you get

Question 10

what is the fifth step

Answer 10

identify X as something to be used in binomial distribution

Question 11

what is the sixth step

Answer 11

use binomial distribution to get an answer

Question 12

what would usually p be for the binomial distribution

Answer 12

0.5

Question 13

what is the final step

Answer 13

compare value to the significance level and write a conclusion

Question 14

what is the step 1 for the wilcoxon signed rank test

Answer 14

write your hypotheses

Question 15

how should you write your hypotheses

Answer 15

the same way as above (H0: median = x)

Question 16

what is step 2

Answer 16

write the phrase, “Assuming the distribution is symmetrically distributed about the median:”

Question 17

what is step 3

Answer 17

• draw a table

- do the value - mean thing again

Question 18

what is step 4

Answer 18

• calculate the absolute difference between each sample

- basically find the modulus (just make it +ve)

Question 19

what is step 5

Answer 19

• rank the absolute differences from 1 to n

- giving the lowest rank to the smallest absolute difference

Question 20

what is special about how you rank things again

Answer 20

• if you have n of the same numbers to be ranked
• you would work out the of their consecutive ranks
• divide it by n
• and give each of the same number that rank

Question 21

how would you rank, 1,1,1 if they were the first 3 values

Answer 21

• 1 = rank 1
• 1 = rank 2
• 1 = rank 3
• 1+2+3 = 6 / 3 = 2
• so each 1 actually has a rank of 2

Question 22

what is step 6

Answer 22

• for any data value that had its value - mean INITIALLY +ve, keep its rank +ve
• for any data value that had its value - mean INITIALLY –ve, make its rank -ve

Question 23

what is step 7

Answer 23

• calculate W-
• which is the sum of -ve ranks, but actually displayed as a +ve number
• calculate W+
• which is the sum of +ve ranks

Question 24

what is step 8

Answer 24

check that (W- + W+) = 1/2n(n+1) where n is the number of data values

Question 25

what is the test statistic in this method

Answer 25

he smaller value between W- and W+

Question 26

what is the final step

Answer 26

reject H0 is T is less than or equal to the critical value

Question 27

how do you find the critical calue

Answer 27

• by looking in the formula book

- n is the parameter used to find out what your CV is