!!Wilcoxin Test!!

Does anyone know how to do this?
I have tried but i have gotten very confused on the ranking and the overall test!

:confused:

Reply 1

Tainturier

I hope you've figured this out alreayd but just in case: A wilcoxon test is used on ordinal data for a related samples design. Follow the following steps to analyse by hand:

1) organise your data into the following table format for ease:

Participant Number X1 X2 Differences (X1-X2) Rank

X1 will be the score collected in the first part of testing i.e. X1 might be the first rating a person gives themselves, and X2 might be the second rating a person gives themselves.

2) fill it in so that you take x1 away from x2

3) rank the data... It took me a while to get to grips with this when i did it at A level, but the easiest way of doing it is by reordering the results on a separate page so that they are in ascending order of value. I.e. if particpant one has a difference score of 4 and participant 2 has a difference score of 2, then write in a list 2,4...
Do this until you have a list of scores for all of your participants i.e. for my imaginary 14 participants the rearranged difference scores are: 2,4,4,4,5,6,6,8,8,8,9,10,12,12.

In order to rank these you give the lowest score the rank of one so 2 has a rank of one. You then give the next number the rank of 2, but because there are three of the next number in this example (4) you have to give the first 4 the rank of 2 the second for the rank of 3 the third 4 the rank of 4. Because these are all the same number. You then work out the average rank for the 4's, which in this case would be the average of 2-4 which is 3.

Because the next number is 5, and because we've already given away the ranks of 1-4 we give 5 the rank of 5. Because the next two numbers are both 6, the first 6 gets the rank of 6 and the second 6 gets the rank of 7 the average of which is 6.5 and so on...

The ranks for the above data would therefore be:
2,4,4,4,5,6,6,8,8,8,9,10,12,12
-2 = 1
4 = 3
-4 = 3
4 = 3
5 = 5
-6 = 6.5
6 = 6.5
8 = 9
8 = 9
8 = 9
9 = 11
10 = 12
12 = 13.5
-12 = 13.5

You ignore any negatives during the ranking process.

4) because some of the differences that you worked out will be negative and some will be positive, find which one is least common. So if there are 4 negative and 10 positives, then you next use the four negatives in this next stage.

Find the ranks that correspond to the negative difference scores, and add these ranks together. I.e. in my example these will be 1 + 3+ 6.5 + 13.5 =24 as these were the four ranks from negative difference values.

24 is the value of your tobs (t observed). and this is the statistic you have caulated!

5) In order to check for significance you need the value of N. (The total number of participants in the study. In this case N is 14. (if in your data you have any difference scores of 0, then do not count these as art of N.)

6) Look up a Wilcoxon critical value table online, the first column of which is at a the .05 significance level:
n T
5 1
6 3
7 4
8 6
9 9
10 11
11 14
12 18
13 22
14 26
15 31
16 36
17 42
18 48
19 54

We can see from this that when N = 14 the t value should be 26. because our t value was 24 this is less than 26 and we therefore have a significant result at the p <. 05 level of significance.

Hope that helps, PM me if you get stuck!