Wilcoxon Signed Rank test - the best test to use?

Hi - could anyone help me with this please?

I am trying to choose the best statistical test for a problem I have - I am looking at rainfall anomalies for E. Africa and evaluating how ocean modes influence them (ENSO and Indian Ocean Dipole). I have seasonal averages for every Spring (so one value per year) and have categorized the data into years where the there was an El Nino event, or an Indian Ocean Dipole event, or a La Nina event and so on.

In the paper I am referencing they have used the Wilcoxon Sign Rank test to see whether categorization shows a significant difference on rainfall (the title of their data table is: testing for significant difference of median from zero (Wilcoxon Signed Rank Test) - the address for the paper is: http://www.mssanz.org.au/modsim2013/L8/mekanik.pdf

and the area I am talking about is at the bottom of page 3 and refers to table 2 - I don't expect anyone to read it but thought it may help you understand my problem better than I have explained it here - I am essentially trying to replicate the stats for my study but for another area.

Any help would be much appreciated as have spent a long time reading to figure it out rather than take any of your time but alas!