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EnvStats pp 149-173 | Cite as

Hypothesis Tests

  • Steven P. Millard
Chapter

Abstract

If you are comparing chemical concentrations between a background area and a potentially contaminated area, how different do the concentrations in these two areas have to be before you decide that the potentially contaminated area is in fact contaminated? In the last chapter we showed how to use prediction and tolerance intervals to try to answer this question. There are other kinds of hypothesis tests you can use as well. R contains several functions for performing classical statistical hypothesis tests, such as t-tests, analysis of variance, linear regression, nonparametric tests, quality control procedures, and time series analysis (see the R documentation and help files). EnvStats contains modifications of some of these functions (e.g., summaryStats and stripChart), as well as functions for statistical tests that are not included in R but that are used in environmental statistics, such as the Shapiro-Francia goodness-of-fit test, Kendall’s seasonal test for trend, and the quantile test for a shift in the tail of the distribution (see the help file Hypothesis Tests). This chapter discusses these functions. See Millard et al. (2014) for a more in-depth discussion of hypothesis tests.

Keywords

Lognormal Distribution Test Statistic Parameter Seasonal Kendall Test Probability Plot Correlation Coefficient Linear Rank Test 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Chen, L. (1995a). A Minimum Cost Estimator for the Mean of Positively Skewed Distributions with Applications to Estimation of Exposure to Contaminated Soils. Environmetrics 6, 181−193.CrossRefGoogle Scholar
  2. Chen, L. (1995b). Testing the Mean of Skewed Distributions. Journal of the American Statistical Association 90(430), 767−772.CrossRefMATHGoogle Scholar
  3. Conover, W.J. (1980). Practical Nonparametric Statistics. Second Edition. John Wiley & Sons, New York, 493 pp.Google Scholar
  4. Filliben, J.J. (1975). The Probability Plot Correlation Coefficient Test for Normality. Technometrics 17(1), 111−117.CrossRefMATHGoogle Scholar
  5. Fisher, L.D., and G. van Belle. (1993). Biostatistics: A Methodology for the Health Sciences. John Wiley & Sons, New York, 991 pp.Google Scholar
  6. Gibbons, R.D. (1994). Statistical Methods for Groundwater Monitoring. John Wiley & Sons, New York, 286 pp.Google Scholar
  7. Hirsch, R.M., J.R. Slack, and R.A. Smith. (1982). Techniques of Trend Analysis for Monthly Water Quality Data. Water Resources Research 18(1), 107−121.CrossRefGoogle Scholar
  8. Johnson, R.A., S. Verrill, and D.H. Moore. (1987). Two-Sample Rank Tests for Detecting Changes That Occur in a Small Proportion of the Treated Population. Biometrics 43, 641−655.MathSciNetCrossRefMATHGoogle Scholar
  9. Mann, H.B. (1945). Nonparametric Tests Against Trend. Econometrica 13, 245-259.Google Scholar
  10. Millard, S.P., P. Dixon, and N.K. Neerchal. (2014). Environmental Statistics with R. CRC Press, Boca Raton, Florida.Google Scholar
  11. Millard, S.P., and N.K. Neerchal. (2001). Environmental Statistics with S-Plus. CRC Press, Boca Raton, Florida, 830 pp.Google Scholar
  12. Neerchal, N. K., and S. L. Brunenmeister. (1993). Estimation of Trend in Chesapeake Bay Water Quality Data. In Patil, G.P., and C.R. Rao, eds., Handbook of Statistics, Vol. 6: Multivariate Environmental Statistics. North-Holland, Amsterdam, Chapter 19, 407−422.Google Scholar
  13. Singh, A., N. Armbya, and A. Singh. (2010b). ProUCL Version 4.1.00 Technical Guide (Draft). EPA/600/R-07/041, May 2010. Office of Research and Development, U.S. Environmental Protection Agency, Washington, D.C.Google Scholar
  14. USEPA. (2002d). Calculating Upper Confidence Limits for Exposure Point Concentrations at Hazardous Waste Sites. OSWER 9285.6-10, December 2002. Office of Emergency and Remedial Response, U.S. Environmental Protection Agency, Washington, D.C.Google Scholar
  15. USEPA. (2009). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities: Unified Guidance. EPA 530-R-09-007, March 2009. Office of Resource Conservation and Recovery, Program Implementation and Information Division, U.S. Environmental Protection Agency, Washington, D.C.Google Scholar
  16. van Belle, G. (2008). Statistical Rules of Thumb. Second Edition. John Wiley and Sons, New York.Google Scholar
  17. Vogel, R.M. (1986). The Probability Plot Correlation Coefficient Test for the Normal, Lognormal, and Gumbel Distributional Hypotheses. Water Resources Research 22(4), 587−590. (Correction, Water Resources Research 23(10), 2013, 1987.)Google Scholar
  18. Wilk, M.B., and S.S. Shapiro. (1968). The Joint Assessment of Normality of Several Independent Samples. Technometrics 10(4), 825−839.MathSciNetCrossRefGoogle Scholar
  19. Zar, J.H. (2010). Biostatistical Analysis. Fifth Edition. Prentice-Hall, Upper Saddle River, NJ.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Steven P. Millard
    • 1
  1. 1.Probability, Statistics and InformationSeattleUSA

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