Non-parametric Tests Flashcards
what is a distribution free test
tests that dont rely on any assumptions about the pd
what are the advantages of distribution free tests
- they can be used with all scales
- easier to compute data
- fewer assumptions are needed
- doesnt need a population parameter
what are the disadvantages of distribution free tests
- you can waste info
- hard to compute by hand for large samples
- tables arent widely available
- less efficient
what are you looking for in a sign test
how many results are below the expected median
what is the first step to a sign test
write out your hypotheses
how would the hypotheses always be written
- H0 should always be that he median = x
- then H1 is the other side of the argument
what is the second step
draw a table of the given values
what is the third step
subtract the median FROM each value on the table
what is the fourth step
count the number of +ve and -ve numbers you get
what is the fifth step
identify X as something to be used in binomial distribution
what is the sixth step
use binomial distribution to get an answer
what would usually p be for the binomial distribution
0.5
what is the final step
compare value to the significance level and write a conclusion
what is the step 1 for the wilcoxon signed rank test
write your hypotheses
how should you write your hypotheses
the same way as above (H0: median = x)
what is step 2
write the phrase, “Assuming the distribution is symmetrically distributed about the median:”
what is step 3
- draw a table
- do the value - mean thing again
what is step 4
- calculate the absolute difference between each sample
- basically find the modulus (just make it +ve)
what is step 5
- rank the absolute differences from 1 to n
- giving the lowest rank to the smallest absolute difference
what is special about how you rank things again
- 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
how would you rank, 1,1,1 if they were the first 3 values
- 1 = rank 1
- 1 = rank 2
- 1 = rank 3
- 1+2+3 = 6 / 3 = 2
- so each 1 actually has a rank of 2
what is step 6
- 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
what is step 7
- 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
what is step 8
check that (W- + W+) = 1/2n(n+1) where n is the number of data values
what is the test statistic in this method
he smaller value between W- and W+
what is the final step
reject H0 is T is less than or equal to the critical value
how do you find the critical calue
- by looking in the formula book
- n is the parameter used to find out what your CV is
