Statistics Definitions > Seasonal Kendall Test

You may want to read this article first: What is the What is the Mann kendall Trend Test?

## What is the Seasonal Kendall Test?

The Seasonal Kendall test (SK test) is a nonparametric test that analyzes data for monotonic trends in seasonal data. Developed by Hirsch, Smith, and Slack (for the U.S. Geological Survey) in the 1980s, it is the most popular trend test in environmental studies. “Monotonic” means a consistent upwards or downwards trend. “Seasonal” means that data is collected for periods where trends can are upwards or downwards. While it can refer to Spring, Summer etc., “seasonal” can also refer to other time periods, like hours, days, or months. For example, seasonal sales data for November and December each year may be upwards.

## How the Test is Run

**The SK test is a special case of the Mann Kendall Trend Test;** If your data is **not **seasonal, you should use that test instead. The seasonal Kendall test runs a separate Mann Kendall trend test on each of *m* seasons separately, where m is the number of seasons. Data is only compared to the same season. For example, Spring would be only be compared with Spring and Summer would only be compared with Summer. The overall S_{k} statistic is calculated from summing each season’s Kendall S statistic:

## Regional Kendall Test for Trend

A **modified seasonal Kendall test** called the **regional Kendall test** can be run if you are more interested in *spatial differences* than seasonal. For example, you might want to study if a particular factor is present throughout an entire region. The regional Kendall substitutes location for season before running a regular SK test. For more information about the regional Kendall, see this USGS article.

**Reference**:

Dennis R. Helsel * and Lonna M. Frans (2006). Regional Kendall Test for Trend. Environ. Sci. Technol., 40 (13), pp 4066–4073.

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