World Aquaculture Society Meetings

Statistics in Aquaculture - Continuing Education

Professional Development/Continuing Education Workshop

To be presented on Monday, February 22 at Aquaculture America 2016, Las Vegas, NV

Statistics in Aquaculture – Multiple Comparisons and Response Surfaces including Mixture Experiments


Dallas E. Johnson, Kansas State University, Manhattan, KS.


Dallas Johnson is Professor Emeritus and former Head of the Department of Statistics at Kansas State University. In a career spanning 35+ years, Dallas has held numerous consulting, research and teaching appointments and continues to teach short courses and workshops on a variety of topics in statistics. His outstanding teaching and professional achievements have been recognized through several awards from professional societies, faculty, and students alike, including election as a Fellow of the American Statistical Association. In addition to co-authoring Volumes 1, 2, and 3 of the seminal series Analysis of Messy Data, now in its second edition, he is the founding editor of the Journal of Agricultural, Biological, and Environmental Statistics and has served on the editorial boards of The American Statistician, Communications in Statistics - Statistical Reviews, and Communications in Statistics - Simulations and Computations.

Workshop Description

Several studies have pointed out the misuse of multiple comparison tests in agricultural sciences. Aquaculture researchers have only recently begun to pay attention to this area of data analysis. However, misconceptions and a lack of understanding are evident in our journal articles. The current workshop will critically address a variety of mean comparison techniques and give you the tools to understand and correctly apply those techniques to your data. Response surface models are especially useful when one of the important goals of an experiment is to determine values for a set of treatment factors that will give near-optimum responses for the variable(s) being modeled. Consider an experiment where one desires to study the effects of k different factors,X1, X2, X3, …, Xk, on one or more dependent variables y. It is assumed that y is a function of the k different factors, i.e., y = f(X1, X2, X3, …, Xk) + e and that the function f(X1, X2, X3, …, Xk) can be approximated by a polynomial function,. such as a quadratic function when k = 2, as in . Mixture experiments will also be considered where there are restrictions on the predictor variables such as X1 + X2 + X3+… + Xk = 1.

Be sure to add this workshop when registering for Aquaculture 2016. Register online with the menu option to the left.


$100 Students
$150 USAS/AFS members
$250 Non-members

Workshop Outline

    Morning Session

  1. The One-way Means Model with Homogeneous errors
    • Inferences on contrasts and linear combinations
    • Linear, quadratic, and cubic contrasts
    • Simultaneous tests on several contrasts/linear combinations
    • Model Comparison Methods
    • Examples and computer analyses
  2. The One-way Means Model with Heterogeneous errors
    • Tests for homogeneity of variances
    • Inferences on contrasts and linear combinations
    • Simultaneous tests on several contrasts/linear combinations
    • Examples and computer analyses
  3. Simultaneous Inference Procedures and Multiple Comparisons Error rates
    • All pairwise comparison methods (Fisher’s LSD; Bonferroni’s; Scheffe’s; Tukey-Kramer; Simulation methods; Sidak Procedure)
    • Comparing all treatments to a control (Multivariate t method; Dunnett’s procedure)
    • Sequential Rejective Methods (Bonferroni-Holm; Sidak-Holm)
    • Multiple Range Tests (Student-Newman-Keul’s; Duncan’s procedure)
    • Simultaneous methods for orthogonal polynomial contrasts
    • Examples using SAS (Examples of the above methods; SAS-Multtest Procedure)

    Afternoon Session

  4. Response Surfaces
    • First order polynomial models
    • Second order polynomial models
    • Maximizing and/or minimizing the response
    • Quadratic response surface model
  5. Response Surface Designs
    • First order designs
    • Quadratic response surface designs
    • SAS –ADX
    • Statistical analyses of RSDs
    • Examples using SAS
  6. Mixture Experiments
    • Mixture designs
    • Simplex-lattice designs
    • Modeling mixture experiments (Linear, Quadratic, and Cubic models)
    • Mixture designs with restrictions
    • Statistical analyses of mixture experiments
    • Examples using SAS
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