Consulting

Now you can take advantage of state-of-the-art exact statistical techniques to make optimum use of your data regardless of whether your company has subject matter experts or not. X-Techniques provides consulting and training on these powerful techniques. We undertake projects of any magnitude ranging from minor consulting on how to employ XPro in your exact parametric inference, designing experiments to achieve your objective, to in-depth data analysis using exact statistical methods. The following is a list of some of the areas of research where exact statistics can provide superior solutions on which we provide consulting, design of experiments, and analyze data from such experiments:

  • Industrial experiments including testing of new designs, quality improvement, and measurements systems
  • Engineering applications involving data analysis and statistical inference
  • Socio-economic experiments to test hypotheses and to determine optimum solutions in decision and policy making
  • Bio-medical research data analysis
  • Pharmaceutical pre-clinical and clinical trials to test experimental drugs and treatments
  • Business and market analysis with market research data

    The following is a list of some of the statistical methods on which we provide consulting and data analysis in testing of hypotheses, point and interval estimation, and forecasting:

  • Analysis of Variance (ANOVA) and analysis of covariance
  • Regression analysis
  • Mixed models and variance components
  • Repeated measures and growth curves
  • Multivariate analysis
  • Analysis of categorical data

    Training

    Now you can conveniently train your statisticians and other data analysts about latest methods in exact statistical methods and how to employ the XPro software package to perform exact statistical inference. For this purpose, a number of courses on Exact Parametric Statistical Methods are available from X-Techniques. In the past the American Statistical Association has offered these courses at Joint Statistical Meetings; look forward to additional ASA course offerings on exact parametric methods at forth coming meetings. Contact X-Techniques to arrange to offer any of these courses at your own site for 20 or more course participants. The following is a list of courses currently available from X-Techniques:

  • Exact Methods in ANOVA and Mixed Models
  • Analysis of Repeated Measures by Exact Methods
  • Generalized P-Values with Application to Linear Models

    Course Abstracts

    Exact Statistical Methods in ANOVA and in Mixed Models

    ABSTRACT: Exact statistical methods are especially important in costly experiments and in applications involving small samples, which is usually the case in pharmaceutical and biomedical research. Application of asymptotic tests and tests which ignore heteroscedasticity can lead to very serious repercussions in Biomedical research. Exact methods are particularly useful in early detection of significant and insignificant experimental results from clinical trials.

    The course is applications-oriented. Followed by a brief introduction to exact parametric statistical methods, the course covers some exact methods in one-way and two-way ANOVA with unequal variances, one-way unbalanced random effects model, and higher-way balanced mixed models. Numerous examples will be presented to illustrate the applications and to show how one can take advantage of these methods to avoid misleading conclusions and to obtain tests which are much more powerful than classical F-tests in ANOVA. In mixed models, the course will cover a class of interval estimates of variance components which tend to be much more reliable and efficient than conventional methods.


    Analysis of Repeated Measures by Exact Methods

    ABSTRACT: In this course, a number of linear models, including a variety of mixe d models, growth curves models, and multivariate models appropriate for repeated measures will be dis cussed. Exact methods for comparing treatment groups and other factors, and exac t confidence intervals for underlying variance components will be presented under heterosceda sticity as well as homoscedasticity. The course is applications-oriented with little mathematica l details. Models and proposed methods will be illustrated with numerous examples. Advantages of u sing exact methods will be discussed and demonstrated.

    Application of asymptotic tests and tests which ignore heteroscedasticity can le ad to serious repercussions due to excessive Type I error and/or lack of power. Exact methods are particularly useful in early detection of significant and nonsignificant experimental results .

    Followed by a brief introduction to exact parametric statistical methods, the co urse presents some exact methods, including some classical methods, for a number of mixed models us ed in analyz ing repeated measures. Their counter parts under growth curves models will also be presented. In mixed models, the course will cover a class of interval estimates of variance co mponents which tend to be much more reliable and efficient than conventional methods. The use o f multivariate models to analyze repeated measures will then be discussed.


    Course Outline


  • Introduction
  • Introduction to Mixed Models
  • Randomized block design
  • A brief introduction to generalized p-values
  • Mixed models with subjects nested under treatment groups and observed over time
  • Models in which a number of measurements are taken from a subject
  • Growth curves models under homoscedasticity
  • Growth curves models under heteroscedasticity
  • Multivariate models
  • Comparing treatment groups under the multivariate setting

    Generalized P-Values with Application to Exact Methods in Linear Models

    ABSTRACT: The course provides an introduction to generalized p-values and eneralized confidence intervals. The underlying concepts, theory, and methods will be discussed in an easy to understand manner with many illustrative examples. Since the course should prove to be of value to many statisticians, the material will be presented in a manner that will be appealing to practitioners as well as to researchers. The benefit of extending the definition of the p-value will be demonstrated with some important applications in linear models, in which classical approaches fail to provide exact inference; i.e. tests and intervals based on exact probability statements.

    Exact statistical methods are especially important in applications involving small samples and/or large variances, which is usually the case in many industrial, pharmaceutical and biomedical research, in particular. Application of asymptotic tests and tests which ignore heteroscedasticity can lead to very serious repercussions in such situations. Exact methods are particularly useful in early detection of significant and nonsignificant experimental results.

    Followed by a introduction to new concepts, theory, and methods in generalized p-values and intervals, the course will present some exact methods in two sample problems (normal and exponential distribution based), ANOVA, and in Regression models.

    Course Outline

  • Introduction
  • Motivation with some simple examples where classical methods fail to provide exact inferences
  • Introduction to Generalized p-values
  • Exact tests for comparing means of two exponential distributions
  • Theory and methods in generalized p-value approach
  • Introduction to Generalized confidence intervals
  • History of exact methods in Linear Models
  • Solving Behrens-Fisher problem by generalized approach
  • Generalized t-tests and F-tests in Regression
  • Generalized F-tests in ANOVA

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