I have 4 sets of data points and for each I want to see how much these values vary from zero.

I used the tool for calculating the results of the test on this page but I'm having trouble understanding the results.

The results for my 4 sets of data points are:

W+ = 3,       W- = 12,      N = 5,   p <= 0.3125     for 101 data points
W+ = 12,      W- = 3,       N = 5,   p <= 0.3125     for 101 data points
W+ = 451,     W- = 1089,    N = 55,  p <= 0.007618   for 297 data points
W+ = 950.50,  W- = 427.50,  N = 52,  p <= 0.01746    for 297 data points


Please could you tell me which values I should be looking at and what the mean in terms of the above results?

Do the low p values mean that the variance from zero is not significant?

Thanks.

• The Wilcoxon signed rank test you linked to is for paired data. You don't seem to have paired data. Are you trying to see if the mean is different from 0? Or the median? Or something else? – Peter Flom Sep 8 '11 at 11:08
• @Peter, my data is formed of pairs, so by one data point I mean one pair of values. For a pair (x, y) I have the actual value for X and y is always zero (the expected value). I want to know how significantly the x values vary from zero. – Griffin Sep 8 '11 at 11:20
• @PeterFlom In fact the signed rank test tests whether a univariate (one-sample) median is different from zero, assuming symmetry under the null. When applied to differences among pairs, it's a paired test that satisfies the symmetry-in-differences by assuming the pairs have the same distributional shape. This is the same issue as we have with the sign test - it's actually a univariate test for a median of zero, but when applied to differences between pairs becomes a paired test. I'm guessing you already knew all that - but it might mislead people with less statistical background. – Glen_b Mar 5 '13 at 9:48