Instructions for using Visual ANOVA

One Way ANOVA Independent: An online, printable lecture.

Visual
ANOVA Instructions

**Visual 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 ANOVA tool. **

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.**

**PRINT:
You may print this web page on your local printer if you wish.
**

INSTRUCTIONS

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.**

**Have fun.**

**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*