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I am working with an imbalanced (5%/95%) presence/absence dataset. I've created 25x25 m. raster cells that are categorized '1' or '0'. My Geary's C result (~0.993) and Moran's I result (~0.0045) are each nearly ideal- the expectation for each, respectively, would be 1 and 0 in the absence of spatial autocorrelation. Previous research into these results tells me that this is pretty darn close to random enough.

I also created a spherical semivariogram which displays pretty constant semivariance across all distances, save for a few outliers near the nugget and sparsely dotted across a few other sections. These outliers near the nugget do suggest there may be some autocorrelation present, but I'm really not sure- we're talking perhaps 2-3 dozen dots in relation to about 10,000 others.Semivariogram #1 ...and Semivariogram #2

My question is, why would my Moran's I and Geary's C statistics indicate very strongly against extant autocorrelation if there truly is some remaining in the data? Should I weigh each result (semivariogram, MI, GC) equally, or trust one result more than the others?

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If your data is in fact binary, please look at the math behind these statistics. Nither Moran's or Gearys are appropriate for binary data thus nullifying your results. For this problem you are somewhat limited to a joins-count statistic.

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