I am comparing the monthly losses for actual and forecast losses for the same time period to see if our forecasts are in line with actuals. This is for a 12 month period. I am bit confused about the assumptions of the Wilcoxon signed rank test in order to apply this test for my purpose. Our data are not normally distributed and are correlated. Can anyone please help me understand the assumptions below in simple language so I can see if this test can be used for my data? I am not sure if i understand the assumption #1 about "independently drawn". In some places the assumptions of Wilcoxon sigend rank is also stated as "difference of paired samples should be independent". Some books states that "the Sample should be paired and dependent ". Some articles says that " the Paired differences should be Symmetrical". What are the actual assumptions and what is true ? I also don't understand the assumption about Independence and dependence. What does it actually mean?
Independence – The Wilcoxon sign test assumes independence, meaning that the paired observations are randomly and independently drawn.
Dependent samples – the two samples need to be dependent observations of the cases. The Wilcoxon sign test assess for differences between a before and after measurement, while accounting for individual differences in the baseline.
Continuous dependent variable – Although the Wilcoxon signed rank test ranks the differences according to their size and is therefore a non-parametric test, it assumes that the measurements are continuous in theoretical nature. To account for the fact that in most cases the dependent variable is binomially distributed, a continuity correction is applied.