Mann-Kendall Trend

Often, we have the need to evaluate data to see if the data is following a trend and if the trend is increasing or decreasing.  Some regulators now require data to be evaluated for trends.  The Mann-Kendall test is the test often used and/or required.  The following is information regarding the method and includes spreadsheets that can be used to perform the calculations.

General Information

The following is adapted from Guidance On Natural Attenuation For Petroleum Releases by Wisconsin Department of Natural Resources available online at www.dnr.state.wi.us/Org/aw/rr/archives/pubs/RR614.pdf  (also attached below).

The Mann-Kendall (M-K) Test is a simple test for trend. Mann-Kendall is a non-parametric test and as such, it is not dependent upon:

• The magnitude of data, 

• Assumptions of distribution (does not have to have a normal / bell shape distribution), 

• Missing data or 

• Irregularly spaced monitoring periods. 

Mann-Kendall assesses whether a time-ordered data set exhibits an increasing or decreasing trend, within a predetermined level of significance.

Mann-Kendall Limitations 

• Non-Seasonal Effects - The M-K test requires 4 to 10 rounds of data (note there are modification that allow larger data sets) that are NOT influenced by seasonal effects. This means the investigator must either determine that the data is not influenced seasonally or collect data from the same season of the year for at least 4 years. Another option is to use the Seasonal Kendall test (Gibbons, 1994) which includes seasonal variability in the analysis.  When the data appear to be seasonally affected, one way to reduce the seasonal bias in the M-K test is to include only data collected from the particular season with the highest contaminant concentrations.  This would require a longer period of monitoring to collect sufficient data.  Note:  One method of evaluating whether the data follows a seasonal trend is to plot concentration or log concentration vs. groundwater elevation to determine if there is a trend.

• More is Better - Statistical confidence increases with the number of data points available. The more data there are, the more likely that the M-K test will discern a trend. While the test can use as few as 4 data points, often these are not enough data to detect a trend. A “no trend” finding with few data points does not always indicate a stable dataset. This situation more likely indicates there are too few data to determine a trend. Therefore, it is highly recommended that at least 6 or more data rounds be collected before using the M-K test to assess data trends.

• Censored data / Non-Detects - If you have censored data (Non-Detects) and they are different values, you have to address this otherwise you will be measuring the trend of the reporting limits.  Normally, replacing the censored data with ½ of the lowest reporting limit for the dataset works best.

Spreadsheets

Learn before you use!!!  I personally think it is always best to do a method by hand 1st so you know how it works and how data changes affect it.  The Mann-Kendall method is very easy to do by hand and I would recommend seeing the examples in the “EPA - Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities”.

IDEM’s Mann-Kendall Spreadsheet

Indiana Department Environmental Management (IDEM) has a spreadsheet that evaluates data for trends using the Mann-Kendall.  It allows you to determine if there is a trend and if  a trend exists, if it is increasing or decreasing.  The web page is http://www.in.gov/idem/4213.htm (also attached below).  It is a great tool as it will do 5 wells at a time and evaluates data points as well as generating graphs of data:

• Quarters 1-8, 5-13, 7-16,

• Quarters 1-12, 1-16

• Year 1-2, Year 2-3, Year 3-4, Year 1-3, and Year 1-4

Please find attached an original version and a version that I’ve modified and an example of the output.

Wisconsin Department of Natural Resources has a spreadsheet that evaluates between 4 and 10 data points.  A copy of the spreadsheet can be downloaded from:  http://dnr.wi.gov/org/aw/rr/archives/pubs/4400-215.zip (also attached below) Information about the spreadsheet is covered in www.dnr.state.wi.us/Org/aw/rr/archives/pubs/RR614.pdf (also attached below).