Instructions

A "Begin" button will appear on the left when the applet is finished loading. This may take a minute or two depending on the speed of your internet connection and computer. Please be patient. If no begin button appears, it is probably because your browser does not support Java 1.1.

This applet demonstrates the partioning of sums of squares in analysis of variance (ANOVA). After you press the "Begin" button, you will be shown a display of the first sample dataset. There are three groups of subjects and four scores per subject. Each score is represented by a dot; the mean is represented as a red horizontal line. The values range from 0 to 10. The Y-axis ticks represent values of 0, 2.25, 5, 7.75, and 10. The means of the three groups are 2.50, 5.50, and 8.50.

The table in the lower left-hand portion of the window displays, for each group, the sample size, the mean, the sum of squared deviations of individual scores from the mean, and the squared difference between the group mean and the grand mean multiplied by the sample size. The bottom row shows the the sums of these quantities. The sum of the last column is the sums of squares between and the sum of the second-to-last column is the sum of squares within. The ANOVA summary table based on these values is shown to the right. The sum of squares between and within are depicted graphically above the ANOVA summary table.

You can choose other datasets using the pop-up menu. You can also enter your own data by clicking on the data display. If you click in a blank area, an new datapoint is created (if you hold the mouse down after you click you can position the point by moving the mouse). You can modify the data by clicking on a point and moving it to another location. Finally, you can delete a data point by dragging it outside the colored region.

Credits

The simulations were developed as part of a grant from NSF to David Lane of Rice University. Partial support for this work was provided by the National Science Foundation's Division of Undergraduate Education through grant DUE 9751307. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.