Study Question 6. Is there seasonality in the concentrations?

C.6 Study Question 6: Is there seasonality in the concentrations?

Most statistical tests assume statistical independence of the sample data. Temporally dependent groundwater data violate the assumption of independence. High levels of variability unrelated to the long-term temporal trend also make it difficult to identify statistically significant long-term trends and to estimate attenuation rates and remediation time frames (McHugh et al. 2011).

When temporal variability exists because of the distribution of the timing of the sample collection, the distribution exhibits time dependence or 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). (for example, a cyclical pattern of data affected by the seasons). To verify statistical independence, demonstrate a low correlationAn estimate of the degree to which two sets of variables vary together, with no distinction between dependent and independent variables (USEPA 2013b). between the concentration and the time of the sampling event. Evaluate the cyclical change (seasonal variation) to adequately understand the 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. of the population. A cyclical pattern can biasSystematic deviation between a measured (observed) or computed value and its true value. Bias is affected by faulty instrument calibration and other measurement errors, systematic errors during data collection, and sampling errors such as incomplete spatial randomization during the design of sampling programs (Unified Guidance). the variance of the distribution or create a slope of the concentration that is not monotonic. You can evaluate the temporal evaluation and adjust the distribution to evaluate the trend accordingly.

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

Selecting and Characterizing the Data Set

Refer to Section 3.4: Common Statistical Assumptions for further discussion of how the following requirements may affect 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 autocorrelation between seasonal sampling events.
The ability to detect trends can be impacted by aggregating data across wells.
In general, you can obtain better detection of trends using longer records of data, but in many cases, attenuation rates will differ based on remedial methods.
See also Section 4.1: Considerations for Statistical Analysis.

If the test does not assume a distribution, then no testing of the distribution is necessary. However, if a substantial number of nondetectsLaboratory analytical result known only to be below the method detection limit (MDL), or reporting limit (RL); see "censored data" (Unified Guidance). are present, then the test cannot indicate autocorrelation. The samples should cover multiple years with an observable seasonal pattern each year. Each season should include at least three measurements.

When the objective is to determine if there is a temporal change or pattern to the data, simple graphical procedures can reveal significant trends. However, if cyclical effects complicate the pattern of the data then consider other statistical methods listed below to answer this study question.

Statistical Methods and Tools

Determine if there is a significant cyclical pattern in the data that creates autocorrelation between the samples; statistical independence of the data is a key assumption for many statistical tests. When the objective is to determine if there is a temporal change or pattern to single series data, use the sample autocorrelation function or Rank von Neumann ratio test to identify correlated samples from specific seasons. When the objective is to determine if there is a temporal change or pattern to a group of wells, use time series plots or the Kruskal-Wallis test to identify correlated samples related to specific seasons.

Sample Autocorrelation Function

Data must follow normal distributionSymmetric distribution of data (bell-shaped curve), the most common distribution assumption in statistical analysis (Unified Guidance). for this test.
A minimum of 8 to 10 measurements are recommended, although a greater number of measurements may be necessary to obtain the desired confidence levelDegree of confidence associated with a statistical estimate or test, denoted as (1 – alpha) (Unified Guidance)..
This test is very sensitive to extreme values (outliers).

Rank von Neumann Ratio Test

This test requires no distribution assumptions.
This test cannot handle a substantial number of tied values or nondetect values.
A minimum of 10 to 12 observations from a single well is recommended.

Time Series Plots

Standardize the concentration on y-axis versus time on x-axis.
Assign values to nondetects.
Plot parallel lines for several wells.

Kruskal-Wallis Test

As a nonparametricStatistical test that does not depend on knowledge of the distribution of the sampled population (Unified Guidance). test, normality of the data is not required.
At least three groups of data (see Section 5.8.2) must be present.
If applied to a group of wells, little to no spatial variation should exist.

Interpretation of Results and Associated Uncertainty

The temporal trend analyses explain whether and how contaminant concentrations are changing over time. As discussed above, a nonparametric test such as the seasonal Mann-Kendall test does not require assumptions regarding the data distribution. However, significant seasonal fluctuations in the data will cause false negativeIn hypothesis testing, if the alternative hypothesis (Hᴀ) is true but is rejected in favor of the null hypothesis (H₀) which is not true, then a false negative (Type II, β) error has occurred (Unified Guidance). errors in the statistical test methods. Temporally dependent and autocorrelated data generally contain both a truly random and nonrandom component. Only strong correlations are likely to affect the results of further statistical testing. See also Section 4.5.1 and Section 4.6.2.