Advance Spatial Pattern Analysis
All statistical techniques are appropriate if they meet the conditions and analytical requirements for which they were designed.
People have a propensity to try and apply techniques which don't meet these conditions or requirements since the software rarely checks for them. That is largely the job of 'human-ware'.
Should you want to add an extra letter to Getis-Ord G* then have a look at Getis-Ord Gi* ...
The mathematical descriptions and the requirements are well documented in the how it works section ...
The documentation for Getis-Ord general This also has a very good section specifically in the Interpretation and Frequently Asked Questions that should allow one to assess which approach is more appropriate for their data, data form and requirements. This is the human-ware section 
