Copyright 1998, 2000 Tom Malloy
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.
ANOVA is a simple little program that lets you put all
this theory we've been describing into a simple visual
whole. It assumes that you've read the Meanings and
Intuitions section and have have understood the the
general ideas at least. Even if your understanding of
the previous section is incomplete at this time, it
is worth playing with Visual ANOVA since that may clear
up the big picture for you. You can go back and forth
between the Meanings and Intuitions section and Visual
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 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
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.
ON THE YELLOW BUTTONS.
Click on the + and - buttons for each group. Doing so
will increase or decrease the variability within each
conceptual formula for F is shown below the graph. We'll
talk about it in the next graphics.
BETWEEN AND HI WITHIN
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.
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.
MEAN. You also can see a long green line across
the whole graph. It represents the mean of the groups
means (the Grand Mean).
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.
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.
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
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.
BETWEEN AND LO WITHIN
current graphic is pretty much the same as the previous
one, except that the variability within the groups has
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
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.
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.
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