Natural Breaks Algorithm
For each indicator, Greater Louisville Project assigns cities into one of three groups (high-performing, middle-of-the-pack, and low-performing) based on how they compare to other cities. The assignment is based on how cities naturally cluster on that indicator. Sometimes, the differences between cities are very small, and the difference between a city ranked 5th and 6th could simply be a matter of the sampling error that arises from using survey data. Thus, rather than always make a division that declares the top 5 to be the top tier, we use a natural breaks algorithm to look for a cluster of cities that is outperforming the rest, a cluster that is about average, and a cluster that is lagging. This clustering gives us a better indication of where Louisville is thriving and where Louisville has room to learn from cities that are doing better.
Z-Scores
Z-scores (or standardization) is a way to combine data with different units of measurement into a single index. The z-score is a measure of how far away a city (or census tract, etc.) is from the average city. In order to be comparable across different units of measurement, the z-score is the distance from the mean measured in standard deviations (e.g. if Louisville has a z-score of 1 it means Louisville is 1 standard deviation above the mean of its peer cities).
Data from the Robert Wood Johnson Foundation's County Health Rankings use z-scores and all z-scores are relative to the mean of Louisville's peer cities. (On the County Health Rankings site z-scores are relative to all the counties in each state - thus z-scores reported by GLP will be different, because we are using a different reference group). The Greater Louisville Project also uses z-scores in our multidimensional poverty index, which compares each census tract to the mean of all census tracts in Louisville.