It is very difficult to provide advise on a field as diverse as spatial statistics without any context to the underlying question. When posting, more information is always better. It is not clear on why you think that the results are not correct. Morans-I and Gearys-C provide an indication of 1st order (global) spatial relationships and result in a single coefficient. Morans-I is the most common 1st order statistic and the one available in ArcMap. As mentioned in the previous post it should range from -1 to 1. Where 0 is indicative of a random spatial process, values ranging towards 1 demonstrate uniform clustering and approach perfect correlation between observations, and -1 is representative of spatial diffusion/repulsion. Geary's-C is a very nice and interpretable statistic. It ranges 0-1 and is, in essence, a global semivariogram. Geary's-C is not as sensitive to the specification of the neighbor matrix and as such can be a much more stable statistic than Moran's-I. However, it does not indicate diffusion/repulsion process if present in the data.
I have a feeling that you are more interested in the 2nd order spatial variation (local autocorrelation). I would highly recommend investigating point pattern statistics. There are a very large array of these statistics but some useful ones are available in ArcMap. In the "Mapping Clusters" toolbox look at the Getis-Ord (Gi*) and LISA (local Moran's-I) statistics. These are indicative of local autocorrelation/nonstationarity and are probably going to be more informative. You will need to investigate the influence of bandwidth and specification of the spatial weights matrix. Please note that significance testing is a critical step in all of these statistics. The one thing to be mindful of is that; if you observe high 2nd order variation it most likely indicating a spatial dependency (external variable(s) influencing the autocovariance). If this is the case it necessitates models such as Conditional Autoregressive models (CAR), Spatial Autoregressive models (SAR), mixed models and geographically weighted regression (GWR) (available in ArcMap). Bayesian hierarchical models and nonparametric approaches such as spline regression or multivariate adaptive regression splines can be most useful as well.
