Why Spatial autocorrelation (Global Moran's I) is producing a p value of 0?

Question

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?

Answer 1

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 :)