The Esri Guide to GIS Analysis, Volume 2: Spatial Measurements and Statistics, second edition by Mitchell Andy & Mitchell Andy & Griffin Lauren Scott & Griffin Lauren Scott

Author:Mitchell, Andy & Mitchell, Andy & Griffin, Lauren Scott & Griffin, Lauren Scott
Language: eng
Format: epub
Tags: Technology and Engineering, Geographic Information Systems, Probability and Statistics, Spatial Analysis, Data Visualization
Publisher: Esri Press
Published: 2020-11-24T00:00:00+00:00

Testing the significance of the G-statistic

Once the GIS has calculated the observed and expected values of G, you can test whether the observed G is significantly different than the expected G (that is, significantly different than a random distribution) at a given confidence level.

The test involves calculating a z-score. First the GIS calculates the variance for the expected G. The variance represents the average amount that values differ from the mean value for all the features in the study area. Then the expected G is subtracted from the observed G and divided by the square root of the variance (that is, the standard deviation).

Transcription ZGd=Gdo-GdeSDGd Annotation: The Z-score for the G-statistic at distance (d)

Numerator: The expected G value at the distance is subtracted from the observed G…

Denominator: …and the difference divided by the standard deviation for the expected G for that distance

If the observed G is larger than the expected G (that is, high values are clustered), the numerator is positive and the z-score is positive. If the observed G is less than the expected G (low values are clustered), the numerator is negative and the z-score is negative.

For example, a negative z-score below the significant value (−1.96 at a confidence level of 95 percent) indicates that low values tend to be found together and you can be 95 percent sure the pattern is not due to chance. See “A Closer Look: Testing Statistical Significance” for more on the z-score.

With a G-statistic value higher than expected for a random distribution, and a z-score of 4.21, the clustering of high values is significant at a confidence level of 0.01 (99 percent). With a G-statistic value lower than the expected G for a random distribution (indicating clustering of low values), but a z-score of −1.26, the clustering is not statistically significant.

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