Correlation tells us how well two measurements of the same thing compare to each other. Correlation has two nice properties:

```
(1) It is a simple number without dimension (ex., feet or seconds or calories). This means we can use it to compare different types of measurements.
(2) Its magnitude falls between 0 and 1. This means there is a clear best value and a clear worst value.
```

What's not so clear is what the in-between values mean. How good is good enough? That depends on the application. To get some intuition for correlation we can look at several examples. First, let me explain where these examples come from.

## Cheaper Measurements

One way to evaluate the precision of a measurement is to compute the correlation of the device's measurement with a known, "true" value. Since genuinely "true" values are unknowable, usually a measurement from a more precise -- but usually also more expensive -- reference measuring device stands in for the true value.

The interest in evaluating measurements this way usually stems from the desire to take a certain kind of measurement more cheaply. (I'm using "cheaply" in a generic sense: less complex, less difficult, or just costing less money.)

For example, the motivation for studying the Body Mass Index (BMI) -- a proxy for body fat -- was that BMI is very easily computed from height and weight. Alternative measures of body fat can be labor intensive when applied to many people (ex., skin calipers) or even when applied to one person (ex., weighing a person under water).

To evaluate the quality of BMI, one could compare BMI for many individuals to one of the more expensive methods of measuring body fat. If BMI were to correlate well with the more expensive measurement, you could then rely on BMI alone for future measurements. This was the approach taken by Indices of relative weight and obesity in 1972. BMI is still widely used today.

In the blog posts Precision and Dynamics we took the same approach with Pertinacity's fist-sized portion proxy for calories and Pertinacity's method of setting a limit for proxy calories. In these measurements we used as the "true", or reference, values the calorie values found in a calorie database.

## Examples

Below are some examples of published correlation values for familiar measurement devices and indicators along with Pertinacity's correlations.

*(The numbers prefixed by ~ are mean values of the numbers that follow in parentheses. The means were calculated by me, whereas the numbers in parentheses are given in the reference publication.)*