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hi everybody this is Eugene alarcón lecture in computing at the national college of ireland and welcome to my series of short how-to videos in this video we're going to learn how to perform a wilcoxon signed-rank test and we're going to learn how to do this by hand so before we start any calculations let's take a look at some data here we have some sample data from lorrison satires in 2004 and these are examples here where the measured content are in the would of 13 popular three cones growing in a polluted area was taken in August and in November the figures here represent the concentrations of aluminium in micrograms of aluminium program of wood and this is these are the figures that are shown here and we'd like to determine if there's significant difference between the August and November figures now we won't group tested twice in August in November which means that these are paired data normally when we want to see if there's a significant difference between parrots as the data we might use a student t-test but we can't use that if one or more of the samples are not normally distributed and if that's the case then we use the wilcoxon signed-rank test so before this video I've conducted a quick Shapiro whip test on each of the August and November sets of data at an alpha value at 0.05 I've scored a p-value in August of 0.071 which indicates that the data are normal but the p-value is less than 0.001 for the November figure indicating that the November data are not normally distributed and I think if you look at the data you can see that particularly the last three values here are very very high and that they are skewing the November data therefore it's not normal we cannot use a t-test and we must use a nonparametric test in this case a signed-rank test so as always at the beginning of other statistical tests let's set up our null and alternate hypothesis our null hypothesis is that the median difference between the pairs of observations are zero and note that the hypothesis is based on the median our alternative hypothesis is that the median difference between pairs of observations is not zero we're going to conduct our test about they have an alpha value of zero five and we've got 13 pairs of data so we have a value of n of 13 which we are going to need a little bit later on so to set myself up for doing the calculations I'm just removing that top sheet and I'm using the same data and I've added in three extra columns that I'm going to need to use here to calculate the test statistic for this wilcoxon signed-rank test so the first of these here is I want to know the differences between the November and the August data which is simply a cracked subtracting one value...