ENVIRONMENTAL IMPACT ASSESSMENT: "PSEUDOREPLICATION" IN TIME?'

A recent monograph by Hurlbert raised several problems concerning the appropriate design of sampling programs to assess the impact upon the abundance of biological populations of, for example, the discharge of effluents into an aquatic ecosystem at a single point. Key to the resolution of these issues is the correct identification of the statistical parameter of interest, which is the mean of the underlying probabilistic "process" that produces the abundance, rather than the actual abundance itself. We describe an appropriate sampling scheme designed to detect the effect of the discharge upon this underlying mean. Although not guaranteed to be universally applicable, the design should meet Hurlbert's objections in many cases. Detection of the effect of the discharge is achieved by testing whether the difference between abundances at a control site and an impact site changes once the discharge begins. This requires taking samples, replicated in time, Before the discharge begins and After it has begun, at both the Control and Impact sites (hence this is called a BACI design). Care needs to be taken in choosing a control site so that it is sufficiently far from the discharge to be largely beyond its influence, yet close enough that it is influenced by the same range of natural phenomena (e.g., weather) that result in long-term changes in the biological populations. The design is not appro- priate where local events cause populations at Control and Impact sites to have different long-term trends in abundance; however, these situations can be detected statistically. We discuss the assumptions of BACI, particularly additivity (and transformations to achieve it) and independence.

[1]  H. Weisberg,et al.  Social Experimentation: A Method for Planning and Evaluating Social Intervention. , 1975 .

[2]  J. Kiefer Optimum Experimental Designs , 1959 .

[3]  H. Jeffreys,et al.  The Theory of Probability , 1896 .

[4]  George E. P. Box,et al.  Intervention Analysis with Applications to Economic and Environmental Problems , 1975 .

[5]  Seymour Geisser,et al.  Logic of Statistical Inference. , 1967 .

[6]  D. F. Andrews,et al.  A note on the selection of data transformations , 1971 .

[7]  Robert Schlaifer,et al.  On the nature and discovery of structure , 1981 .

[8]  Maxwell L. King,et al.  Testing for autocorrelation in linear regression models: a survey , 1987 .

[9]  Emanuel Parzen,et al.  Stochastic Processes , 1962 .

[10]  James O. Berger,et al.  STATISTICAL DECISION THEORY: FOUNDATIONS, CONCEPTS, AND METHODS , 1984 .

[11]  E. Bleken New Ghosts of Competition: Reply to Connell , 1983 .

[12]  Edward R. Tufte,et al.  The Visual Display of Quantitative Information , 1986 .

[13]  Donald B. Rubin,et al.  Bayesian Inference for Causal Effects: The Role of Randomization , 1978 .

[14]  J. Pratt A discussion of the question: for what use are tests of hypotheses and tests of significance , 1976 .

[15]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[16]  D. Basu Randomization Analysis of Experimental Data: The Fisher Randomization Test , 1980 .

[17]  John W. Pratt,et al.  On the nature and discovery of structure , 1981 .

[18]  J. Gastwirth,et al.  The Behavior of Robust Estimators on Dependent Data , 1975 .

[19]  O. Kempthorne The Design and Analysis of Experiments , 1952 .

[20]  J. Tukey One Degree of Freedom for Non-Additivity , 1949 .

[21]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[22]  D. B. Preston Spectral Analysis and Time Series , 1983 .

[23]  T. Cook,et al.  Quasi-experimentation: Design & analysis issues for field settings , 1979 .

[24]  Howard Wainer How to Display Data Badly , 1984 .

[25]  T. M. F. Smith,et al.  On the validity of interferences from non-random samples , 1983 .

[26]  R. Green,et al.  Sampling Design and Statistical Methods for Environmental Biologists , 1979 .

[27]  S. Hurlbert Pseudoreplication and the Design of Ecological Field Experiments , 1984 .

[28]  D. Campbell,et al.  EXPERIMENTAL AND QUASI-EXPERIMENT Al DESIGNS FOR RESEARCH , 2012 .

[29]  Joseph H. Connell Interpreting the Results of Field Experiments: Effects of Indirect Interactions , 1983 .

[30]  Herman Chernoff,et al.  The Use of Faces to Represent Points in k- Dimensional Space Graphically , 1973 .

[31]  A. Birnbaum On the Foundations of Statistical Inference , 1962 .

[32]  B. I. Hart Significance Levels for the Ratio of the Mean Square Successive Difference to the Variance , 1942 .

[33]  J. Neyman Tests of statistical hypotheses and their use in studies of natural phenomena , 1976 .

[34]  R. Serfling The Wilcoxon Two-sample Statistic on Strongly Mixing processes , 1968 .

[35]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[36]  I. Good Good Thinking: The Foundations of Probability and Its Applications , 1983 .

[37]  H. Grimm Parzen,E.: Stochastic Prozesses. Holden-Day, Inc., San Francisco,London, Amster dam 1962 (2. Nachdruck, Mai 1964). XI + 324 S., Preis $ 11,95 , 1967 .

[38]  D. Hinkley,et al.  The Analysis of Transformed Data , 1984 .

[39]  For what use are tests of hypotheses and tests of significance , 1976 .

[40]  L. L. Eberhardt,et al.  Quantitative ecology and impact assessment , 1976 .

[41]  Frederick Mosteller,et al.  Data Analysis and Regression , 1978 .

[42]  Herman Rubin,et al.  Effect of Dependence on the Level of Some One-Sample Tests , 1971 .