Row standardization option with K nearest neighbors?

[NaciDilekli]

I am looking at the Generate Spatial Weights matrix tool. I am trying to understand how it works. When K nearest neighbors option is selected, row standardization can still be clicked. How does that change anything? If I select K nearest neighbors, enter 8 as the number of neighbors, the weight will always be 0.125 no matter row standardization is selected or not right? In that case, I don't understand why row standardization option is available. In addition, however, I see very slightly different results with such configurations using my dataset. Here they are:

K nearest neighbors option, 8 neighbors, row standardization NOT enabled, Moran's Index I: 0.243726

K nearest neighbors option, 8 neighbors, row standardization enabled, Moran's Index I: 0.243721

Why are there such differences? Thanks!

[DanPatterson_Retired]

The answer is in the interpretation of your results...

For polygon features, you will almost always want to choose Row for the Row Standardization parameter. Row Standardization mitigates bias when the number of neighbors each feature has is a function of the aggregation scheme or sampling process, rather than reflecting the actual spatial distribution of the variable you are analyzing.

Which means that this wasn't an issue in your case.

Standardization is explained here (PRO help, but it is the same in either package)

So, your results show no bias and the differences in the resultant Moran's are completely insignificant whether it is on or off.

[NaciDilekli]

I know why row standardization is advised for polygon features, I just don't understand why it makes any difference at all when K nearest neighbors option is used. When K nearest neighbors option is used, the weights will be the same across all the features no matter row standardization is selected or not. 

[DanPatterson_Retired]

So you are questioning the 6th decimal place? ... could be simply floating point math carry-forward, but that would require dissecting the equations in detail to see if that is the case.  Other than that, it would be possibly the influence on what was chosen for the 'Number_of_Neighbors'  option and whether that wasn't being met, whereby the selection becomes "For polygons with fewer than this number of contiguous neighbors, additional neighbors will be based on feature centroid proximity".  I suppose that muddies the interpretation but there is no mention of row standardization being ignored just because k nearest neighbours is chosen