5. Statistical Tests and Methods

This section includes practical information for some of the common statistical tests and methods used to evaluate groundwater data for cleanup sites. When evaluating data and making decisions at sites with impacted groundwater, project managers must consider a variety of information such as site history, site and area geology and hydrogeology, and data for other media. Statistics can provide an additional “line of evidence” under a multiple lines of evidence approach to decision making.

Statistical methods are grouped in this section based on their application. Information that applies to the entire group of methods is presented in the beginning of each subsection and method-specific information follows. Where USEPA’s Unified Guidance describes a method, a reference is provided. USEPA guidance regarding the application of certain tests has been modified over time; information relating to these changes and modifications is provided in Appendix B, Unified Guidance.

Before applying statistical methods, you must confirm that the data collected is appropriate to the question being posed. For example, different data needs might be required for health and safety evaluations as compared to plume stability or mass flux across a property boundary. Site data should be reviewed for both temporal and spatial applicability to the question at hand. Different degrees of confidence in data may be acceptable, depending upon client or regulatory needs. The statistical powerStrength of a test to identify an actual release of contaminated groundwater or difference from a criterion (Unified Guidance)., accuracy, and statistical certainty or confidence (see Section 3.6.1) of an analysis depend on the number of statistically usable measurements (also termed the sample size). As a general rule for parametricA statistical test that depends upon or assumes observations from a particular probability distribution or distributions (Unified Guidance). tests and many nonparametricStatistical test that does not depend on knowledge of the distribution of the sampled population (Unified Guidance). ones as well, the larger the sample size the greater the powerSee "statistical power." and the smaller the decision error risk (false positives and false negatives). Although recommended minimum sample sizes are provided for many statistical tests discussed in this document, various project needs or regulatory frameworks may require a sample size different than that recommended.

Section 3 provides a discussion of the general statistical approach, including systematic planning processes and conceptual site models, defining a target population, data quality, exploratory data analysis, common statistical assumptions, and statistical design. Review Section 3 when applying the statistical tests and methods included in this section to a specific project.

Section 6 of this document includes information about data management for implementing the tests and methods described here using software tools. Appendix D includes descriptions for some commonly used software packages. Appendix F includes information about checking the underlying assumptions of statistical tests.

Publication Date: December 2013