tertile

A tertile is a type of quantile used in statistics to divide a dataset into three equal-sized parts. The data are separated at two cutpoints, corresponding to the 33.333...th percentile and the 66.666...th percentile. The three resulting groups are commonly referred to as the lower tertile, the middle tertile, and the upper tertile. In practice, a tertile categorizes a continuous variable so that each group contains roughly one third of the observations.

Computing tertiles typically involves sorting the data and determining the values at probabilities p = 1/3 and p = 2/3. Because real datasets are finite and may contain ties, different conventions exist for handling the exact cutpoints, especially in small samples. Many statistical software packages compute these cutpoints as quantiles at p = 1/3 and p = 2/3, often with interpolation between data points when necessary.

Use of tertiles offers a simple, non-parametric way to summarize and compare distributions, or to stratify analyses by exposure or risk levels. They are common in epidemiology and social sciences for creating grouped analyses (e.g., comparing outcomes across low, middle, and high categories). Limitations include sensitivity to the sample distribution and the presence of ties; tertile boundaries can vary with different calculation methods, and converting continuous data to categories may lead to information loss and reduced statistical power.

Tertiles are a specific case of quantiles; they generalize into quartiles, deciles, percentiles, and other fixed-proportion divisions used to describe and analyze data.