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

Question

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!

LaurenGriffin · Answer

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-relationships.htm#GUID-F6CB66DC-6B46-42BE-96C2-EEFF4BFC13D9 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-relationships.htm#GUID-DB9C20A7-51DB-4704-A0D7-1D4EA22C23A7

I hope this helps!

Very best wishes on your project,

Lauren Griffin, Esri

MasoodShaikh · Answer

Thanks a lot, I emailed you my data.

LaurenGriffin · Answer

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