# Wilcoxon test interpretation to compare three observations

I am performing the Wilcoxon test to 3 variables. The box plot of each variable is the next one.

Performing the Wilcoxon test I get the next results: testing if there is any difference between A1 and A2 Wilcoxon rank sum test with continuity correction

 data:  scale(A1[, 2]) and scale(A2[, 2])
W = 1.1252e+10, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0


Testing if there is any difference between A1 and A3

Wilcoxon rank sum test with continuity correction

data:  scale(A1[, 2]) and scale(A3[, 2])
W = 1.3025e+10, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0


Testing if there is any difference between A2 and A3 Wilcoxon rank sum test with continuity correction

data:  scale(mAB.12[, 2]) and scale(mAB.13[, 2])
W = 1.2868e+10, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0


As you can see the p values are smaller than the significance level, i.e I conclude that the three samples comes from a different distribution.

Is ok my conclusion? I am doing this since I need to perform a classification algorithm I have several groups more. Every group is in group of three that represent three obervations in different times. If there is no difference I can consider A1, A2 or A3 as the same group, Otherwise like in this case I should consider that the three groups are different.

I am in a correct way? or the three observations comes from the same distribution?

• The tiny p values and your degenerate boxplots suggests that you have a huge amount of data - so much that any departure from equality will be statistically significant. How much data do you have? – Stephan Kolassa Mar 13 '18 at 12:32
• Every observation has approximately 150000 rows – Boris Mar 13 '18 at 12:44
• What about if I perform the Wilcoxon test for many samples of size 100 or 1000? I did it briefly and I got bigger p-values, can I conclude that the observations comes from the same distribution? – Boris Mar 13 '18 at 12:49