Friedman test and Wilcoxon I recently conducted research where I have chosen the Friedman nonparametric test to check if there are significant differences in dependent variable values obtained on 4 different occasions. 
I find it strange that Friedman test is not significant. Subsequently, I tested pairwise with the Wilcoxon signed-rank test and i got 2 pairs statistically significant. Please explain!
 A: Did you adjust the Wilcoxon test results for multiple comparisons?
See here: https://en.wikipedia.org/wiki/Multiple_comparisons_problem for some detail on the problem with multiple comparisons.  it is fairly easy to find/simulate examples where an overall test fails to find significance, but a few out of the multiple pairwise comparisons are.
A: The Friedman test compares multiple differences of location. The Wilcoxon signed-rank test tests differences of location of the data for pairwise data only, and as per @GregSnow would need correction for multiple comparisons. Location testing is like difference of means or medians but isn't quite median difference testing for the Wilcoxon test, or probably either for the Friedman test. 
Also, note that different tests, even when adjusted to test for the same things, have different powers. That is, sometimes one test is better at showing a significant difference than another. We can generally get some idea of which test is better if we have enough data, or enough tests so that how good the tests are becomes obvious. The Wilcoxon signed-rank test generally has good power. 
