Moran's I is not significant on unprojected data but significant on projected data (area less than 30 degrees)

[MasoodShaikh]

Hi,

When analyzing point data spanning about 26 degrees, I obtained a Moran's I value that is not statistically significant. However, after projecting my shapefile, the p-value becomes highly significant.

Although the area covered by the points is definitely less than 30 decimal degrees, I'm uncertain about how to proceed. Would it be acceptable to use the projected data and report the results in a scientific journal article? If so, could you provide any references that recommend this approach?

Thank you!

[EdwardGause]

I am curious about the answer to this question that Masood Shaikh has asked as well. I think I had something similar happen a few years ago, but just thought I messed up somewhere along the way so I ignored it and started over with my process.
After seeing this message thought, its got me wondering about the two Map Projections I was using myself. Most data we use from external sources is in NAD83 Geographic Coordinates, however since our Engineers work in NAD83 South Carolina State Plane 3901, I had converted the data to State Plane and afterwards I got different results with Moran's I. Is this because the coordinates are larger numbers than the Lat\Long coordinates. I mean Degrees are up to 3 whole number digits and the rest is fractional, where as State Plane is in the tens of thousands of feet from Origin, could this throw off the statistic? Our County is the furthest from the origin of South Carolina State Plane to the North East of the Origin.

[LaurenGriffin]

Hi Masood and Edward,

For Masood: I would be interested to know what you mean by unprojected. Do you mean NAD83 Geographic Coordinates (or some other Geographic Coordinate System - GCS) or do you mean an UNKNOWN coordinate system. Also, what Conceptualization of Spatial Relationships are you using and why? 

For Masood and Edward: For tools like Global Moran's I that have a distance component, I always try to find the most appropriate projected coordinate system for my data. Projected coordinate systems try to minimize distortion for your particular study area (state plane, for example, is great if your study area happens to be a state). Keep in mind, there are NO projections that perfectly preserve distances (so different projections will produce different distance measurements... and you will get different results). If you decide to use a Geographic Coordinate System (GCS), distances will be based on Chordal Distances: Chordal distances are based on a sphere rather than the true oblate ellipsoid shape of the earth. Given any two points on the earth's surface, the chordal distance between them is the length of a line, passing through the three dimensional earth, to connect those two points. 

Just for yuks, I ran Global Moran's I on data covering most of the continental USA based on a NAD83 Geographic Coordinate System and a couple other projected coordinate systems (North America Albers Equal Area Conic and Web Mercator) and the results I got for all 3 were very similar using a Fixed Distance Conceptualization of Spatial Relationships. In the past, I've tried different Conceptualizations of Spatial Relationships as well, and got very similar results. I think if you are comparing a GCS version of your data to a reasonable projected version of your data, it would be odd to see vastly different results ??? I do suppose it might depend on the distribution of your data and where in the world your data is located.

In any case, if this doesn't help please let me know and I'll do my very best to clarify, or please feel free to send me your data and I'm happy to look into it further. LGriffin@esri.com

Thank you both for your excellent questions! 

Lauren Griffin, Esri

[MasoodShaikh]

Thanks a lot, I emailed you my data.

[LaurenGriffin]

Thanks so much for sending me your data. Unfortunately, I wasn't able to reproduce your results. I tried GCS WGS 1984 in relation to the PCS projection you're using and also in relation to a custom PCS projection appropriate for your study area. In all cases, the GCS results matched the PCS results closely. In all cases except using inverse distance without row standardization, the clustering was statistically significant (and even for inverse distance, there was no difference between the projected and the "unprojected" GCS data results). Given your study area (large) and the distribution of some of the points (several are spatially isolated), inverse distance probably isn't a good choice for the Conceptualization of Spatial Relationships parameter because the influence of neighbors drops off very quickly. Also, with Inverse Distance, row standardization is strongly recommended.

Projection	Conceptualization	Standardization	Z-Score	p-value
WGS 1984	Fixed Distance, 100,000m	None	15.7	0
Your PCS projection	Fixed Distance, 100,000m	None	15.7	0
Custom PCS projection	Fixed Distance, 100,000m	None	15.6	0
WGS 1984	Fixed Distance, 100,000m	Row	16.5	0
Your PCS projection	Fixed Distance, 100,000m	Row	16.5	0
Custom PCS projection	Fixed Distance, 100,000m	Row	16.6	0
WGS 1984	Number of Neighbors, 16	N/A	16.7	0
Your PCS projection	Number of Neighbors, 16	N/A	16.7	0
Custom PCS projection	Number of Neighbors, 16	N/A	16.6	0
WGS 1984	Inverse Distance, 100,000m	None	1.6	0.11
Your PCS projection	Inverse Distance, 100,000m	None	1.6	0.11
Custom PCS projection	Inverse Distance, 100,000m	None	1.6	0.11
WGS 1984	Inverse Distance, 100,000m	Row	12.5	0
Your PCS projection	Inverse Distance, 100,000m	Row	12.5	0
Custom PCS projection	Inverse Distance, 100,000m	Row	12.6	0

For information about selecting an appropriate Conceptualization of Spatial Relationships value, please see: https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-statistics/modeling-spatial-relation... including the section titled Best Practices for Selecting a Conceptualization of Spatial Relationships. To help you determine if you want to Row Standardize or not, please see: https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-statistics/modeling-spatial-relation...

I hope this helps!

Very best wishes on your project,

Lauren Griffin, Esri