9867

Likelihood-Based Goodness of Fit in Two-Way Contingency Tables

Models of contingency tables are based on the counts by category. In a two-way table, models can depend on either, neither, or both of the categories. The likelihood ratio statistic provides a measure of how well a particular model fits the original counts. The null hypothesis is that the chosen model fits the data well. The alternative hypothesis is that the saturated model (the model with predicted counts equal to the actual counts) is needed. A small -value for the statistic indicates the chosen model does not fit the data well. As the counts in the table get large, follows a distribution, and a approximation can be used to obtain a -value provided the predicted counts in the table are not very small.
Use the sliders to adjust the original counts. Select between the four models to get the predicted counts and test statistic for that model of the contingency table.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The underlying model is a log-linear Poisson model. The categories are treated as nominal predictor variables.
The mean count model fits the case where each cell is equally likely. This model predicts an equal number for each cell in the table.
The choice effect model fits the case where the count differs across choice, but is constant across group. The group effect model predicts that counts differ across group, but not across choice.
Choice and group have an additive effect on predicted counts for the additive model. The total predicted counts by choice and the total predicted counts by group for this model match those totals for the original contingency table.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+