I'm now doing a project about spatial hotspot analysis. I read many literatures, however, I can't find any papers tell how they determine the data size they used.
I mean, suppose we have crime location data, in some small cities, maybe our data size is relatively small. Under this condition, is our hotspots reliable? I though there must be a minimum requirement for data size in spatial hotspot analysis. Anyone knows how to determine the data size?
Thank you very much!
You need to read the original paper by Getis and Ord that introduces the G statistics:
Getis A, Ord JK. 1992. The analysis of spatial association by use of distance statistics. Geographical Analysis 24:189-206.
See the paragraph that begins at the bottom of page 191.
To paraphrase, the sampling distribution of $G_i$ under the null hypothesis (of complete spatial randomness..."CSR") is asymptotically normal. The expected value is based on the number of points $j$ that are connected to point $i$ relative to the total number of points. When the distance is sufficiently small such that the expected value is small, normality is lost; likewise, normality is lost when all points $j$ are connected to $i$.
This suggests that it is OK to use the normal approximation when you have a lot of points and your expected values are not too close to zero or one. This also suggests that this decision is somewhat context dependent: it depends on the number of points and their configuration.
You can also use a permutation test to assess the significance of $G_i$ or $G_i^*$. If the P-values obtained based on the normal approximation are wildly different from those obtained by the permutation test, it might suggest that your expected values are violating the assumption of the normal approximation.
I really like @coreydevinanderson answer above, going back to the foundational work can usual provide some insight into things. I would like to add that the amount of data needed might be dependant on the spatial scale and variability of the measured/collected data. For instance the data needed for a 10 x 10 m area might be different from a 10 x 10 km area. A power analysis could be useful to determine the data needed from a variability perspective but from a spatial scale perspective a simulation study might be needed to understand the needed spatial scale to detect a change/clustering in the data.
After reading this post I got curious and did a quick search and found this paper that might be useful. The paper looks at the sensitivity of the weights used to calculate the Getis-Ord statistic.
