# Calculating Ranks

## Standardizing Measures

We standardize each measure within each state to the average of counties in that state. Recall that our 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—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 value higher than the average of counties in that state; a negative Z-score indicates a 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 score indicates poorer health (e.g., years of potential life lost before age 75). However, for some of our measures (e.g., high school graduation) a higher score indicates better health or a more desirable value. We have to take this into account before computing summary scores. For these measures we compute the Z-score as usual but multiply it by -1, so that higher scores indicate poorer health. The measures that we reverse code in this manner are:

• Food environment index
• Access to exercise opportunities
• Diabetes monitoring
• Mammography screening
• High school graduation
• Some college (post-secondary education)
• Social associations

## Composite Scores

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

```Composite=∑wi Zi

```

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

All of the summary scores we compute use the formula above, standardized Z-scores for each measure (reverse coded when necessary), and the weights described in previous sections. Remember that we always compute composite scores separately by state.

## Ranking

After we compute composite scores we sort them 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 units we rank in that state.

It is important to note that we do not suggest that the rankings themselves represent statistically significant differences from county to county. That is, the top ranked county in a state (#1) is not necessarily significantly healthier than the second ranked county (#2). See the next section about quartiles for more information.