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Lois's dr. Ghani welcome my video on conducting a wilcoxon signed-rank test and calculating the effect size I will be conducting the wilcoxon signed-rank test in spss and calculating the effect size using Excel so the wilcoxon signed-rank test is the nonparametric equivalent of a paired-samples t-test so we would use this in a situation where our data do not meet the assumptions for paired samples t-test so looking at these fictitious data have load in the data view these are ordinal pretest and posttest this is based on a Likert scale you can see here so that would not meet the assumption for a paired samples t-test and it wilcoxon signed-rank test would be appropriate so let's presume with these data that we have an ID variable has a hundred participants and they are tested two times have a pretest and a post-test so between these two observations there was some sort of treatment and let's say this is measuring anxiety with higher scores higher ranks each variable representing a higher anxiety level so if I switch back to the view where you can see the labels you can see at the high end of the scale we have extremely high and at the low end and scale extremely low so a zero is extremely low and a five is extremely high an easier way to view this is in variable view to go to the values associated with pretest and post-test they're the same values associated with both of these and you can see zero extremely low there we go to low somewhat low somewhat high high and extremely high so we would hope for if this were a real study would be that the post-test scores were lower than the pretest scores meaning that the participants improved whatever treatment was administered was effective and the post-test scores would be lower than the pretest scores so let's run the wilcoxon signed-rank test and take a look at the output and see what type of difference there is between the pretest and posttest ranks so to analyze nonparametric tests legacy dialogues want two related samples that's the wilcoxon signed-rank test there are a couple other options here under test type let me reset this this is what it looks like by default there's wilcoxon which is what we'll be using there's also sign and Mac Tamar sign is not used particularly often it ignores the magnitude it's simply interested in whether the difference in ranks is positive and negative MacNamara is used quite a bit and it's appropriate when you have nominal data as opposed to ordinal data as we're using in this example so to configure the wilcoxon signed-rank test we see we have pair one here and variable one variable two so I'm just going to drag pretest in the variable one and post-test in the variable two under options I'm going to add descriptive to the statistics they'll be generating the output click continue and then click OK to run the analysis so you can see we have three tables here we have descriptive statistics and this is important to look at first we want to see the mean for pretest and post-test and see what direction it moved from the pretest to post-test in this case you see the mean was two point two nine for the pretest in a dropped to two point zero six for the post-test so overall we could presume the participants that improve now until we look further down we wouldn't that's a statistically significant improvement but it improved the standard deviations very similar and of course the minimum the maximum this was a Likert scale going 0 through 5 so a six-point Likert scale so there's no surprise here that the minimum and the maximum are identical for the pretest and the post-test in the next table we have ranks you'll see I have post-test pretest here and there's negative ranks positive ranks and theis and of course the total which we know is 100 so you can see from the superscript here it's a a B and C and for negative ranks there are 23 if you look here at the a it's instances where the post-test was less than the pretest so this is what we would want to see happen this is improvement if the post-test is less than the pretest that's consistent with our theory that the treatment is effective so it have a hundred pairs of observations 23 and 23 occasions the post-test rank was lower than the pretest rank the mean rank is also provided as well as the sum of ranks so you can see the sum of ranks here 444 0.5 then we have positive ranks so these are instances where the post-test was greater than pretest so in this example this would be this is 12 positive ranks so in 12 cases the participant reported higher anxiety and the post-test then was reported in the pretest and again we have the mean rank and the sum of ranks 185 point five so the number of negative ranks is higher the number of positive ranks and the sum of ranks for negative ranks is higher than the sum of ranks for positive ranks then in 65 cases the post-test was identical to the pretest so there was 65 participants that showed no change neither positive nor negative and then moving down here to the test statistics we have a z- 2.21 and we're going to use this value to calculate the effect size as you see effect size is not part of the output here in SPSS we can calculate it fairly easily in Excel and then for the p-value Oh point zero two sevenths of the Alpha is point zero five this is a statistically significant result so in this instance we would reject the null hypothesis that there is no difference between the pretest and post-test scores so we know we have a statistically significant finding but we do not know the effect size yet but there's only two pieces of information we need to take over in this case I'll use Excel to calculate the effect size one is this value here negative two point two one the Z value and the other is the end but the end in this case is not 100 that's the total number of cases the N is equal to the total number of observations so we have a hundred pairs so n we equal 200 so if I move over to Excel you can see here is the equation for effect size for wilcoxon signed-rank test it's also the same for a man Whitney you it's the same formula so first we have the value for Z which we know is negative two point two one and then we have the N which as I mentioned is 200 and then we need to calculate the square root of N and in Excel that's fairly straightforward it's equal sign and then sq RT and then this case cell c4 the 14 point 14 and then our is Z divided by the square root of n so B equal sign Z divided by square root of n gives us negative 0.15 so that's the effect size in this case that would be a small effect size for an effect size to be considered moderate you would want to see a value here of less than negative 0.3 and for a large effect size of value less than negative 0.5 I hope you found this video on conducting a wilcoxon signed-rank test and calculating the effect size to be useful as always if you have any questions or concerns feel free to contact me and I'll be happy to assist you
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