Click on the following links - please note these will open in a new window
A defining feature of ANOVA procedures as they were introduced in Chapter 13 was the attention given to two quantities: the sum of squares between and the sum of squares within. Often times, it is difficult to understand these quantities without some sort of visual aid. This web exercise attempts to provide such an aid.
Navigate to the following URL: http://www.ruf.rice.edu/~lane/stat_sim/one_way/index.html.
Once there, click on the "Begin" button in the upper left of your screen. A new window will have opened for you. Maximize this window. You should see three bars on the screen in front of you, one for each of three groups. For the sake of simplicity, let's say that our sample consists of all students who took a statistics class in the fall of 2008 at the University of Wisconsin Milwaukee. Group 1 consists of sophomores. Group 2 consists of juniors. And Group 3 consists of seniors.
Suppose that all students were given a statistics readiness assessment at the start of the semester worth 10 points. Underneath the "Choose dataset" label, use the dropdown menu and select "Sample set 1." Upon doing so, you will see that a small red cross appears on each of the group bars. Take this cross to be the mean score for each group on the statistics readiness assessment. As such, we can see that sophomores scored the lowest and seniors scored the highest.
Where ANOVA procedures are concerned, the pie chart on the right of your screen shows the relative contribution of the sum squares between and the sum squares within to the value of the F statistic. As you can see from the three group mean scores, there is much variation between groups. Suppose, however, that each group scored a 7.5 of the statistics readiness assessment. With you cursor, navigate to each of the small red crosses. Click and hold your mouse button, and then drag the cross up to a score of 7.5. (Note: you may have to click and drag multiple times to achieve this). Do this for all three groups. Notice what happens in the pie chart on the right of your screen to the relative share of the sum squares between.
Once you have completed the above warm-up, click the "Clear All" button on the right side of your screen. Then, use the dropdown menu to select another sample set, e.g., "Sample set 4." How do these results compare to what you tried earlier. Continue to repeat the steps above, trying different sample sets, as well as adjusting the location of the small red crosses with your cursor. Try as many different examples as possible to give you a better grasp of the relationship between the sum of squares between and the sum of squares within.