Statistics Toolbox

The aoctool Demo

The aoctool demo is an interactive graphical environment for fitting and prediction with analysis of covariance (anocova) models. It is similar to the polytool demo.

Analysis of covariance is a technique for analyzing grouped data having a response (y, the variable to be predicted) and a predictor (x, the variable used to do the prediction). Using analysis of covariance, you can model y as a linear function of x, with the coefficients of the line possibly varying from group to group. The aoctool function fits the following models for the ith group:

same mean
separate means
same line
parallel lines
separate lines

In the fourth model, for example, the intercept varies from one group to the next, but the slope is the same for each group. In the first model, there is a common intercept and no slope. In order to make the group coefficients well determined, we impose the constraints _i=_i = 0.

The aoctool demo displays the results of the fit in three figure windows. One window displays estimates of the coefficients (, _i, , _i). A second displays an analysis of variance table that you can use to test whether a more complex model is significantly better than a simpler one. The third, main graphics window has the following features:

• A graph of the data with superimposed fitted lines and optional confidence bounds.
• y-axis text to display the predicted y-value and its uncertainty at the current x-value for the current group, if a group is currently selected.
• A data entry box to evaluate the fit at a specific x-value.
• A list box to evaluate the fit for a specific group or to display fitted lines for all groups.
• A draggable vertical reference line to do interactive evaluation of the fit at varying x-values.
• A Close button to end the demonstration.
• An Export list box to store fit results into variables.

The following section provides an illustrative example.

Overfitting

Example: aoctool with Sample Data