WHAT IS THE WILCOXON TEST?
This is an inferential test created by Frank Wilcoxon (left). It is used when:
(* it’s easy to turn interval/ratio level data into ordinal data: you just put the scores into rank order)
The Edexcel exam might ask you about the appropriateness of the Wilcoxon test – when you would use it. But you could be asked to calculate the test. The process and tables are provided at the front of the exam booklet.
If you are using an independent groups design, use the Mann-Whitney U test instead.
Yes, Wilcoxon is so straightforward you don’t get a mathematical formula: just the instructions on how to do it
MAKING THE CALCULATIONS
Of course, most researchers use computers to do their statistical tests. There are lots of websites that will let you input your data from an experiment and carry out the Wilcoxon test for you.
The Exam expects you to be able to work out the Wilcoxon test "by hand" and, actually, it's not that difficult.
You are trying to work out the value of T and to do this you need to take the score in one condition away from its matched score in the other condition. This leaves you with a "difference" that may be positive, negative or zero.
You next rank all the differences, leaving out the 0s. The smallest difference gets ranks 1, the next smallest rank 2, and so on. Treat positive and negative differences as being the same for purposes of ranking.
Once this is done, work out the sum of the ranks that are positive and then the sum of the ranks that are negative (ignoring the 0s). Choose the lowest total to be T.
You also need a value of N, which is the number of non-zero differences.
Before you can look up the critical value, you need to know two things:
Is your experimental hypothesis 1-tailed (directional) or 2-tailed (non-directional)? You look on a different table for each.
What value of probability (p) are you considering? Normally, a classroom experiment would be considered at a value of p≤0.05
If you look closely at these tables, you'll notice that the critical values for 2-tailed tests are a bit lower than the values for 1-tailed tests. This reflects the fact that, being a bit more vague, 2-tailed tests require stronger evidence of difference.
If your value of T is equal to or less than the critical value, you can refute your null hypothesis (and cautiously accept your hypothesis).
If T is greater than the critical value, you must accept your null hypothesis and reject your experimental hypothesis.
If your value of U is equal to or less than the critical value, you can refute your null hypothesis (and cautiously accept your hypothesis).
If the value of U is greater than the critical value, you must accept your null hypothesis and refute your experimental hypothesis.
A STATEMENT OF STATISTICAL SIGNIFICANCE
You can sum up your statistical test with a statement of statistical significance. This will include:
The results were subjected to a Wilcoxon test
The observed value (T) was 9, which is lower than the critical value of 11 for a 1-tailed test where p≤0.05
Therefore, the null hypothesis can be refuted
APPLYING WILCOXON'S TEST IN PSYCHOLOGY