I have two algorithms
B which have to compute a solution to some problem. Each solution is given some objective value which indicates the quality of the solution. I need to perform a Wilcoxon Signed-Rank Test to test whether there is any evidence that these two algorithms perform statistically significantly different from one another.
I have performed 12 trials of each algorithm and tabulated the objective values from solutions found during each trial. A smaller objective value is better.
A B 878 890 872 888 865 879 877 874 872 870 890 886 873 871 887 879 868 873 888 882 878 881
I am confused about a few details of performing this test.
Should I do a one-tailed or two-tailed test?
I'm not sure what my null hypothesis is. What should it be, given I want to find out whether algorithm
Bperform significantly different from one another?
If $\ p$-value $> 0.05$, what does this mean?
If $\ p$-value $< 0.05$, what does this mean?