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Calculating Ranks

## Standardizing measures

Each measure within each state is standardized to the average of counties in that state. The measures are in a number of different scales — some are percentages, some are rates, some are averages of survey responses, or other metrics. Standardizing each of these measures transforms them to the same metric — with a mean (average) value of 0 and a standard deviation (measure of spread) of 1. We refer to these as Z-scores where:

Z =(County Value) - (Average of Counties in State)(Standard Deviation of Counties in State)

Each Z-score is relative to the other counties in that state—not compared to an absolute standard—and shown in the metric of standard deviations. A positive Z-score indicates a measure value higher than the average of counties in that state; a negative Z-score indicates a measure value for that county lower than the average of counties in that state. For example, if a county has a Z-score on a measure of 1.2 that means the county is 1.2 standard deviations above the state average of counties for that measure. For counties with a population of 20,000 or less, any z-score that is < -3.0 or > 3.0 is truncated to -3.0 or 3.0, respectively.

## Reverse coding

For most of the measures, a higher Z-score indicates worse health (e.g., more years of potential life lost before age 75). However, for some measures (e.g., high school completion) a higher Z-score indicates better health, or a more desirable value. This is taken into account before computing summary scores. For these measures, Z-scores are multiplied by -1, so that higher scores indicate worse health. The ranked measures that are reverse coded in this manner are:

- Food environment index
- Access to exercise opportunities
- Primary care physicians
- Dentists
- Mental health providers
- Flu vaccinations
- Mammography screening
- High school completion
- Some college (post-secondary education)
- Social associations

## Composite scores

Weighted composites of the Z-scores for individual measures are calculated where the weights represent relative importance of the different measures. A weighted composite score is computed by multiplying each Z-score by its measure weight and adding them up. Below is the formula we use for weighted composite scores:

Composite=∑_{}w_{i }Z_{i }

In this formula the Z_{i} values are the Z-scores of the measures used to compute the summary score. The w_{i} values are the weights applied to each Z-score. The ∑ sign simply means to add up all the Z-scores multiplied by their weights.

Each composite score we calculate uses the formula above and composite scores are always calculated separately by state.

## Ranking

After composite scores are calculated, they are sorted from lowest to highest within each state. The lowest score (best health) gets a rank of #1 for that state and the highest score (worst health) gets whatever rank corresponds to the number of county or county equivalents ranked in that state.

It is important to note that the rankings themselves do not necessarily represent statistically significant differences from county to county. The top ranked county in a state (#1) is not necessarily significantly healthier than the second ranked county (#2) and so on.

## Quartiles

Beginning in 2021, Health Outcome and Health Factor quartiles are displayed in the county snapshot. These quartile graphics provide an indication of where the county fares relative to other counties in the state without direct comparison of individual county ranks. Looking at the underlying data and how those data have changed over time provides a better picture of a county's progress.

Health Outcome and Health Factor rankings are grouped into four equally sized groups (quartiles), ranging from the least healthy to healthiest counties within each state. A county with a rank of #1 lies in the healthiest quartile.

For additional information about the rationale behind the County Health Rankings, see these publications.