I am undertaking spatial autocorrelation (Global Moran's I) in ArcMap 10.3. The p value returned is 0, does this just mean its extremely significant or is this an incorrect result?
A z-score of 15 gives a p-value (using R) of:
> pnorm(15, lower.tail=FALSE)
[1] 3.670966e-51
Yes, 0.00000000000000000000000000000000000000000000000000367
Assuming you haven't done anything wrong, like feeding it the wrong attribute value or constructing a silly adjacency matrix, I'd say that was significant. Note that Moran's I will usually be significant if there's a large-scale trend in the data, so make sure you plot the map and eyeball anything like that first, then detrend it and look for residual spatial correlation with your Moran I then.
I'd also only ever say p < 0.01 in this sort of case.
Also, I assume that diagram of a Normal distribution is just illustrative. Your data is FIFTEEN standard deviations from the mean. On my screen, that would put it somewhere in the next door office :)
p-value = 6.398e-11which is as near to zero as makes no odds, so maybe ArcMap is rounding? Show some maps and the output from the Moran function. What's your neighbourhood structure? So many questions... – Spacedman Apr 7 '17 at 7:35