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hello this is dr. Grande welcome to my video on the wilcoxon signed-rank test now this test is the nonparametric equivalent of the paired samples t-test so it's used when you have it within subjects design we would use this test instead of the paired samples t-test when the assumptions of a paired samples t-test were violated for example if we're using ordinal data and that's what I've done in this example I have here 90 participants and I have a pretest and post-test scores which are ordinal and I'll switch to the variable view so you can see that so let's assume that this is a Likert scale so in this study we're measuring the severity of depressive symptoms so we have a pretest and the lowest severity would be a zero this will be on a Likert scale and the highest severity on the Likert scale will be 5 so it's a six-point Likert scale and then we have a treatment that occurs after the pretest and then we have a post-test which is the same measurement the zero is the lowest severity represents the lowest severity of depressive symptoms and the 5 represents the highest severity so we would hope that our treatment was successful and moving from the pretest to the post-test that the scores would decrease so the severity of the depressive symptoms as measured by this instrument would decrease so in this case with the pretest using a pretest and a post-test variable the wilcoxon signed-rank test test the null hypothesis that the median of the differences between the post-test and the pretest equals zero so to run this analysis we go to analyze then tune on metric tests then legacy dialogues and then select two related samples because this is a within subjects design from this dialogue two related samples tests I'm going to put the pretest in variable one and the post-test in variable two wilcoxon is checked off by default as the test type and the options I'm going to leave the same except for I am going to select descriptive statistics click continue then click OK and you can see the results are fairly straightforward there's three tables in the first table you can see that there's 90 pretest scores and 90 post-test scores both variables had a minimum score of 0 and a maximum score of 5 the standard deviations are provided and you can see the mean for the pretest is higher than the mean for the post S so before we even look further down at the other tables we know that we it's looking good for our hope that the post-test will be lower without looking down further we wouldn't know if there's statistical significance but we know the direction and that is that the post-test is lower the mean is two point three one for the post post-test and two point seven six for the pretest so then moving down to the ranks SPSS provides us the number of participants that have negative ranks positive ranks and ties so what that means in this case is that there were 37 cases where the post-test score was lower than the pretest score which is core is of course what we'd be hoping for there were 21 cases where the post-test score was higher than the pretest score so in that case the participant had a higher severity of depressive symptoms as measured on the post-test and then there were 32 cases where there was a tie that is the post-test was equal to the pretest so as we looked out the test statistics we see the Z is negative two point seven eight three and the significance is point zero zero five so if we set the Alpha point zero five which is fairly common in the social sciences this would be statistically significant so we would reject null hypothesis we would presume there is a difference here between the pretest and the post-test and we know from this descriptive statistics table that the post-test was lower so the direction of the difference is that the severity of symptoms decreased as measured by the post-test when compared to as measured by the pretest so in analyzing this data we would presume that the treatment was successful so it's important to note here that if you look at these ranks and a little more carefully there's 21 instances here twenty-one cases where the post-test score was greater than the pretest so you know we would hope of course the post-test would be lower so there's 21 instances with severity of symptoms or higher and then of course 32 where there was no change so there was only 37 of the 90 that actually improved another important aspect to look at is the sum of the ranks which is also provided here as one thousand two hundred seven point five for the negative ranks and only 503 point five for the positive ranks I hope you found this video on the wilcoxon signed-rank test to be useful as always if you have any questions or concerns feel free to contact and I'll be happy to assist you