What is XPro?

XPro is a specialized statistical software tool, specifically designed to perform exact parametric methods.

What's so special about XPro?

XPro computes exact p-values for testing hypotheses and computes confidence intervals based on exact probability statements. In particular, it supports exact inference in various linear models. It has been proven to be able to detect significant and nonsignificant experimental results early, even with small sample sizes.

What is "Exact Statistics"?

Exact Statistics is a branch of statistics that was developed to provide more accurate results pertaining to statistical testing and interval estimation by eliminating some of the unreasonable assumptions that traditional statistical methods use, solely for computational ease. The topic of Exact Statistics is described in detail in "Exact Statistical Methods for Data Analysis", Springer-Verlag, New York, (authored by Dr. S. Weerahandi). Exact Statistical methods has also been taught at numerous ASA courses and other forums.

What is wrong with classical statistical methods?

Traditional tests and confidence intervals provided by "all purpose" statistical software are based on unreasonable assumptions or are approximate methods that were developed prior to the computer age. Therefore, for the sake of computational simplicity, they were designed to rely on outdated approximate methods that can introduce unnecessary risks into decisions. For example, many statistical procedures such as classic F-tests in linear models are based on the assumption of equal error variances, an assumption made for simplicity and mathematical tractability, rather than accuracy of results. While there is nothing wrong with these procedures when the assumptions are reasonable and/or when the sample size is large, these requirements are often not met in real world situations. Application of a statistical procedure when its performance is poor can lead to very serious repercussions, especially in biomedical and other types of experiments.

Can you demonstrate advantages of Exact Parametric Statistical Methods?

Yes. An example of superior power of exact parametric methods and results of a simulation study on size performance of exact methods compared to asymptotic methods is provided in the XPro demonstration page .

Other software products claim to employ exact statistic. How is XPro different from these programs?

XPro is the world's only software package specializing in Exact Parametric Methods such as those in ANOVA, Mixed Models, Repeated Measures, Growth Curves, MANOVA, and Regression. XPro procedures are complimentary to such program as StatXact which specialize in exact non-parametric methods, such as those dealing with contingency tables and categorical data. Most programs provides exact parametric methods only under assumptions such as the assumption of equal variances in ANOVA. In addition to such classical procedures, XPro provides procedures based on milder assumptions.

To make this possible XPro performs high dimensional numerical integrations and solve highly nonlinear equations. The complexities of the underlying formulas make the problem of computing exact p-values and confidence limits very tedious. XPro makes use of efficient algorithms tailor made for exact inferences in linear models and provides an easy to use interface that facilitates all necessary analyses without passing the burden of any such numerical methods to the user.

What are some of the main procedures available from XPro?

Two-Sample Inferences

  • Testing and intervals for variance differences and ratios
  • Testing and intervals for means - equal variances - unequal variances

    One-Way ANOVA

  • Testing the equality of means under - equal variances - unequal variances
  • Exact likelihood ratio test for testing the equality of variances
  • Planned multiple comparisons with or without equal variances
  • Post hoc multiple comparisons with or without equal variances

    Two-Way ANOVA

    Inference in Mixed Models


    Repeated Measures and Growth Curves

    Multivariate Analysis


    Who uses XPro?

    XPro has been placed into everyday use by many commercial, academic and government statisticians to perform the most powerful parametric statistical inference in applications, such as Regression, ANOVA Fixed/Mixed Effects Models, Repeated Measures Models, and Growth Curve Models.

    Is XPro easy to use?

    Yes. XPro was initially designed by a team of statisticians for their own use. Their specific design objectives were to develop an easy to use, and yet a powerful menu driven tool. XPro employs a convenient and simple GUI that supports pull-down menus, hot keys, resizable/dragable windows, and complete context-sensitive help.

    Further, recent versions of XPro provide "one-step plotting" that adds real-time graphing capabilities to further improve user productivity. To perform any XPro analysis, you simply enter (or import) data into the spreadsheet, choose the type of analysis to perform from the dialog box, and press "Enter". To obtain help in completing XPro dialogs simply press the F1 key.

    Let's see an example. With the simple One-Way ANOVA (random) dialog box shown below, you can: 1) test the significance of the variance component, 2) test any hypothesized percent variance due to factor, 3) test any hypothesized factor variance, 4) construct confidence intervals for percent variance due to factor and 5) construct confidence intervals for the factor variance by Healy, Tukey-Williams and generalized Wald methods.

    How about another example? With the One-Way ANOVA (Fixed) dialog box shown below, you can test the equality of all means, the equality of the variances, or perform multiple comparisons.

    What are XPro's system requirements?

    - IBM PC or compatible system

    - Windows (should work on most versions)

    - 2MB disk space and 512K MB RAM

    - Math coprocessor