Study Question 5. Is there a trend in contaminant concentrations?

C.5 Study Question 5. Is there a trend in contaminant concentrations?

Whether concentrations are increasing, decreasing, periodic, or stable over time is a question that generally requires analysis beyond simple graphical methods, especially when data fluctuate or exhibit high variability. The tests described below for general trend testing are closely related to the tests used for season or period trend analyses or for calculating attenuation rates (Study Question 6, Study Question 7). Statistical trend tests can be used as a diagnostic tool to determine if the meanThe arithmetic average of a sample set that estimates the middle of a statistical distribution (Unified Guidance). of the population is stationaryA distribution whose population characteristics do not change over time or space (Unified Guidance). to qualify the use of the distribution for many other statistical tests. Trend tests can also be used to demonstrate decreases in contaminant concentrations over time. Temporal trend analysis of groundwater monitoring results often reveals differences in results between wells. Even at sites with overall decreasing chemical concentrations, the trend analysis often identifies some wells with statistically significant decreasing concentrations, some wells with decreasing concentrations that are not statistically significant, and some wells with increasing concentrations.

This question is usually relevant in the remediation, monitoring, and closure stages of the project life cycle.

Selecting and Characterizing the Data Set

Verify that the data set can support trend analyses and modeling. Refer to Section 3.4: Common Statistical Assumptions for further discussion of how the following requirements may impact statistical analysis results.

Check for outliersValues unusually discrepant from the rest of a series of observations (Unified Guidance). using box plots, probability plots, Dixon's test, or Rosner's test.
Check for autocorrelationCorrelation of values of a single variable data set over successive time intervals (Unified Guidance). The degree of statistical correlation either (1) between observations when considered as a series collected over time from a fixed sampling point (temporal autocorrelation) or (2) within a collection of sampling points when considered as a function of distance between distinct locations (spatial autocorrelation). between successive sampling events.
Ability to detect trends can be impacted by pooling data across wells.
In general, longer records of data are better at detecting trends but in many cases trends will differ based on remedial methods.
See also Section 4.1: Considerations for Statistical Analysis.

Statistical Methods and Tools

To determine if there is a temporal change or pattern to the data, first use simple graphical techniques to observe significant trends. However, if cyclical effects complicate the pattern of the data consider other statistical methods to answer this study question. The statistical methods described below focus on the monotonic trendThe long-term movement in an ordered series, which regarded together with the oscillation and random component, generates observed values that are entirely increasing or decreasing. (EPA 2006c)s, as well as systematic variation in a temporal setting.

Time Series Plots

These plots show concentration on the y-axis versus time on the x-axis.
You must assign values to nondetects for these plots.

ANOVA

Data must follow a normal distributionSymmetric distribution of data (bell-shaped curve), the most common distribution assumption in statistical analysis (Unified Guidance). and have a constant varianceThe square of the standard deviation (EPA 1989); a measure of how far numbers are separated in a data set. A small variance indicates that numbers in the dataset are clustered close to the mean. or spread of sample results.
You must assign values to nondetectsLaboratory analytical result known only to be below the method detection limit (MDL), or reporting limit (RL); see "censored data" (Unified Guidance)..

Spearman's Test

This nonparametricStatistical test that does not depend on knowledge of the distribution of the sampled population (Unified Guidance). test does not require that data are derived from a particular statistical distribution.
Spearman's test is not influenced by outliers or extreme values.
This test is not appropriate for data sets with a large number nondetects.

Mann-Kendall Trend Test

This nonparametric test does not require that data are derived from a particular statistical distribution.
This test is not influenced by outliers or extreme values.
This test is not appropriate for data sets with a large number of nondetects.

Theil-Sen Trend Line

This test identifies the slope of the trend line.
Confidence limits can be calculated around the slope of the trend line to ascertain whether the trend is statistically significant.
Like the Mann-Kendall, this test does not require a normal distribution and can handle extreme values.
This test is not appropriate for data sets with a large number of nondetects.

Pearson's Test

This test requires a normal distribution.
This test is sensitive to outliers or extreme values.
This test requires a constant dispersion of the data over sampling events.

Linear Regression

This test requires a normal distribution.
This test is sensitive to outliers.
This test requires constant dispersion of the data.

Interpretation of Results and Associated Uncertainty

Temporal trend analyses show whether and how chemical concentrations are changing over time. As discussed above, nonparametric tests, such as the Mann-Kendall test and Theil-Sen trend line, do not require assumptions regarding the data distribution. In contrast, linear regression analysisA parametric statistical method to measure the linear trend of a data set using data point regression residuals that are based on assumptions of normality, homoscedasticity, and independence (Unified Guidance). requires an assumption regarding the pattern of change over time (such as monotonically decreasing). Additionally, parametricA statistical test that depends upon or assumes observations from a particular probability distribution or distributions (Unified Guidance). regression analysisA statistical tool for evaluating the relationship of one of more independent variables to a single continuous dependent variable (Kleinbaum et al. 2007). assumes that the variability not associated with the temporal trend is normally-distributed. If the required assumptions are not satisfied, then the accuracy of the regression analysis is reduced. However, if the assumptions are satisfied, regression analysis will be more accurate than the Mann-Kendall test because the regression analysis uses the information concerning data distribution as part of the test.

If the p-valueIn hypothesis testing, the p-value gives an indication of the strength of the evidence against the null hypothesis, with smaller p-values indicating stronger evidence. If the p-value falls below the significance level of the test, the null hypothesis is rejected. is less than 0.05, then typically the change in concentration over time is statistically significant. A statistically-significant trend depends on a number of factors including the length of the monitoring record and the magnitude of variability not associated with the long-term trend relative to the magnitude of the long-term trend. In data sets with high variability, longer monitoring records are needed to identify statistically significant trends. See also Section 4.5.1: Monitoring for Concentration Changes and Section 4.6.2: Trends Toward Compliance Criteria.