What Are Density Intervals?

Introduction

• Density intervals show the redundancy of a variable in discrete intervals of data. For example, if you want to know how many cereal boxes at a grocery store are priced in a certain range, you can create discrete intervals of zero to $1, $1.01 to $2, $2.01 to $3, and so on. The density interval of an interval is how many cereal boxes fit within a designated range, such as $1.01 to $2. The highest density interval is the discrete interval with the highest density.

Advantages

• The advantage of using density intervals is that it allows you to create a visual representation of data. The common representation is in the form of a histogram, which shows density intervals as rectangular regions on a graph. The height of the density interval is the frequency with which the variable appears in that interval, and the width of the interval is its range. The density, then, is the height divided by the width.

Disadvantages

• Because density intervals partition data into discrete bins, the data is interpreted by a distorting factor, the range of the interval itself. A different range produces a completely different density even though the data is the same and the frequency of the variable in the population has not changed. One solution to this distorting effect in density estimation problems is to use a kernel density estimation tool, which represents the frequency of a variable without using discrete intervals or bins.

Applications

• Density intervals have wide application in statistical representations. They are used to show the distribution of populations by a certain variable, such as age, race or sex; how frequently types of errors occur in a software platform; disease occurrences across species; the presence of inputs in logical statements; and much more. Density intervals for different variables can be overlaid on one another to compare variable spreads in a population, such as the frequency of coffee drinkers, tea drinkers, or coffee and tea drinkers in an urban setting. The common feature of these different applications is the use of bins to separate different frequencies of a variable.