I have been asked by a colleague if ArcGIS estimates confidence intervals (CI) to Moran's index coefficient. In the results window and report for Spatial Autocorrelation (Global Moran's I), I see it only provides p-values and z-scores, but no CI. The reviewer of the manuscript is asking for CI. Does anyone know if/how this can be done?

Hi Charlene,

Yes, it's possible to construct confidence intervals for the Moran's I index. The statistical test is based on a classical Z-distribution test, so you can build a confidence interval using some of the numbers that appear in the messages window. When the tool runs, you should see something like this:

The numbers you need to use are the

Moran's IndexandVariance. First, take the square root of the variance to calculate the standard deviation. Next, you need to decide a confidence level and look up the associated Z-value for that confidence level. For 95% confidence, this Z-value is 1.96, but you can look up other values in Z-tables online. The confidence interval is then the Moran's Index plus/minus the Z-value times the standard deviation:95% Confidence Interval: (Moran's Index) +/- 1.96 * (Standard Deviation)

So you can check your work, the numbers in the image above, a 95% confidence interval is:

0.304063 +/- 1.96 * SquareRoot(0.000411) = (0.264328, 0.343798)

Please let me know if you have any other questions.

-Eric