Rich Gonzalez's Statistics Animations

 

Here are some animations that I use when I teach Psychological Statistics (Psychology 613/614) at the University of Michigan.

Each animation includes a description of the concept, instructions for how to run the animation or demo, and clues for what you should be see.

This website also includes links to programs written in Excel, R, Maple and Matlab that show additional demonstrations of statistical concepts.

 

Web Animations

  1. t-distribution to Normal Animation
  2. Unfolding Animation
  3. Distance Matrix Animation
  4. Eigenvalues & Picture Pixelation
  5. Indscal Animation
  6. Isotonic Animations
    1. Animation 1: monotonic order
    2. Animation 2: data with few order violations
    3. Animation 3: data with more order violations
  7. Minkowski Animation
  8. Polynomial Animation
  9. Power Family Animation
  10. Power Series Animation
  11. Correlation Animation
  12. PCA in action
  13. Regression by clicking

Excel Spreadsheets

  1. two sample t-test: the effect of an outlier
  2. one way ANOVA: decomposing sum of squares
  3. two way ANOVA: all possible patterns
  4. Fisher r to Z transformation for correlations

R Examples and Animations

  1. Pending: 3D representation of the Actor-Partner Model

Maple Examples and Animations

  1. Pending: 3D scatterplots

Matlab Examples and Animations

  1. 3d Scatterplot: visualizing multicolinearity (support file)

Self-Paced Quizzes

  1. Basic statistics
  2. ANOVA
  3. Regression

Sample Animation: Constraints Placed by Distance Information

This animation shows how the arrangement of three points in a two dimensional space is constrained by their distances. Say the distances are

AB=5, AC=3, and BC=4.

The animation places the points A and B a distance of 5 units. C can be placed anywhere along a radius of 3 from A and a radius 4 from B, but only two positions are possible. We arbitrarily pick one (so the final arrangement is unique up to reflection).

This shows how it is possible to capture a dimensional represenation merely from the distances and an assumption about the number of dimensions (in this case two). We know that if we have distances between cities we can compute distances between them, but this animation shows that it is possible to go in the other direction--from distances one can compute their spatial arrangement.

This intuition forms the basis for many multivariate techniques including factor analysis, multidimensional scaling and clustering analysis.

Thanks to Sandra Becker for programming help with many of these animations.

 

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