Read Instructions for using Visual ANOVA
Read an online, printable lecture about One-way ANOVA
Do Computer-graded Online Homework
Do Handwritten Homework with Answer Key
Copyright 1998, 2000 Tom Malloy
Note: These instructions are abstracted from and can be supplemented by the full web lecture on the one-way ANOVA for independent groups available through another link on this page.
You may print this web page on your local printer if you wish.
Right below the "Understanding ANOVA Visually" title are three little buttons labeled MS between, MSwithin, and Instructions. Running your mouse over each of these button will bring up brief text to remind you of various concepts or to tell you the point of the Visual ANOVA tool.
The tool interface is a graph representing a four group study. The length of the red jelly bean icons represents how much variability there is within each of the four groups.
DRAG THE RED JELLY BEANS. You can click and drag the red jelly bean icons on the graph. Doing so will allow you to move each group mean up or down. That way you can increase the variability between the four group means.
CLICK ON THE YELLOW BUTTONS. Click on the + and - buttons for each group. Doing so will increase or decrease the variability within each group.
The conceptual formula for F is shown below the graph. We'll talk about it in the next graphics.
HI BETWEEN AND HI WITHIN
The current graphic shows a case where the Visual ANOVA tool has been set so that the differences between the means are large. The variability within the groups is also set to be large.
GROUP MEANS. Notice that now you can see a green line in the middle of the red group icons. The green line represents the group mean.
GRAND MEAN. You also can see a long green line across the whole graph. It represents the mean of the groups means (the Grand Mean).
MSbg DIVIDED BY MSwg. Just below the yellow within group variability buttons, you can see a conceptual formula for F. Conceptually, the F ratio is variability between groups divided by variability within groups or MSbg divided by MSwg. This F ratio is represented visually as length of a gold bar divided by the length of a purple bar.
F RATIO. At the very bottom of the tool, the value of F is represented by a large blue bar. There is a scale from 0 to 10 above the blue bar so you can have some sense of how large the F value is.
NO NUMBERS. Other than the scale above the blue bar there are no numbers. The purpose of this tool is to get away from all the convoluted words and complex calculations and get you some experience playing visually with the holistic ideas which give all these numbers and words meaning.
Notice that for the way the Visual ANOVA tool is set in this graphic, the gold MSbg bar is about the same length as the purple MSwg bar. So the blue F bar extends out to about 1 on the scale.
HI BETWEEN AND LO WITHIN
The current graphic is pretty much the same as the previous one, except that the variability within the groups has been decreased.
Now you'll notice that the gold bar representing MSbg is longer by about 3 or 4 times as the purple bar representing MSwg. Consequently, blue bar is now out to about 3 on the scale.
These lecture graphics are just static snapshots. Play with the Visual ANOVA tool to get a feel for how variability between groups and variability within groups interact to change the value of the F ratio.
DISCLAIMERS AND COMMENTS. As we said, this tool is meant to direct your attention to relationships among the components of ANOVA by representing them visually. It is not meant to be a calculation device. In the programming, we have scaled various values so that they can be presented on the screen in a way that looks good rather than in a way that is highly accurate computationally. For example, F can can actually vary from 0 to infinity. But on the tool F can only vary from 0 to 10. We placed similar restrictions on MSbg and MSwg.
Also, the red icons represent VARIABILITY as a concept. Their lengths are a transformation of actual variance values. These transformations are simply to make the graph work as a visual whole. Variance is a squared value and its length is very long compared the distance between means. The standard deviation was visually unappealing because it was too short. So the length of the red bars while an accurate representation of variability in general is not specifically the range nor the variance nor the standard deviation.
© Dr Thomas Malloy 2000