Trend Analysis

statistics

Mann-Kendall and Seasonal Mann-Kendall trend tests with Theil-Sen slope estimation.

Each value column is

Data

One sampling event per line. Columns can be separated by spaces, commas, semicolons or tabs, so you can paste straight from Excel.

Column	What it is	Example
1. Date	dd/mm/yyyy, or a numeric time such as a year	15/01/2024
2. Analyte	One value column per analyte; add as many as you have	12.4

A line looks like 15/01/2024 12.4

A header row naming the analytes is kept and used. One column per analyte, all from the same monitoring location. For a result below the laboratory limit of reporting, enter it as <LOR, e.g. <0.5.

Drop a CSV or Excel file here, or

Read in your browser and put in the box below. The file itself is not uploaded.

The columns above do not need to line up. Tabs, commas and runs of spaces are all read the same way, so a long name can push the display out of alignment without changing the result. Up to 5 analyte columns per run; leave no cell blank in a space-separated paste - use tabs or commas if a result is missing.

Options

Seasonality Confidence (p value and slope interval)

Alternative hypothesis (p value)

These two settings drive the reported p value and slope confidence interval. The concentration trend itself follows the GSI Mann-Kendall rules, which use fixed 90% and 95% Confidence Factor thresholds.

Unit of measureLabels the chart's value axis and the rate of change. It does not affect the test, which works on ranks.

Chart

Log concentration scale Results spanning orders of magnitude are all readable at once; on a linear axis the smaller one flattens into the baseline. Ignored where a reading is zero or negative.

Paste your data and run the analysis

Results and a trend chart will appear here.

What this calculates

Monotonic trend testing for time series: the Mann-Kendall test, the Seasonal Mann-Kendall test (Hirsch, Slack and Smith 1982) and the Theil-Sen slope estimator with a rank based confidence interval (Gilbert 1987). Dates plot on a true time axis and slopes are per year; several columns can be analysed from one pasted table, either as analytes at one location or as one analyte across several locations. With dated data the seasonal tests assign seasons from the calendar (for 2 seasons, October–March vs April–September); otherwise observations are assigned cyclically in time order.

Concentration trend classification

The headline result follows the GSI Mann-Kendall Toolkit, which resolves the test into six categories - Increasing, Probably Increasing, No Trend, Stable, Probably Decreasing and Decreasing - from three metrics: the Kendall S statistic for direction, the Confidence Factor (CF = 1 − p, read from the exact Mann-Kendall probability table for 4 to 40 sampling events) for the strength of that direction, and the coefficient of variation, which separates a flat record (Stable) from a scattered one (No Trend) when the CF is below 90%. CF above 95% gives a firm call; 90% to 95% earns the “Probably” qualifier. GSI notes that a No Trend result may be reported as stable, but that is a judgement for the assessor rather than something this tool decides.

Non-detects

Enter a result below the limit of reporting as <LOR and it is read at the reporting limit, and counted as a sampling event. The GSI spreadsheet has no such parser: typing “<100” into it leaves the cell as text, which Excel drops from the calculation, so a record with non-detects will show a smaller n and a different S there than it does here.

Method references

Mann (1945), Kendall (1975), Hirsch, Slack and Smith (1982), Gilbert (1987) Statistical Methods for Environmental Pollution Monitoring, GSI Environmental GSI Mann-Kendall Toolkit User's Manual section 2, and Aziz et al. (2003) MAROS.