A Conceptual View
of ANOVA

Goals:
Conceptually, the goal of ANOVA is to
 determine the amount of variability in groups of data
 to determine where it comes from
 to see if the variability is greater between groups
than within groups.
Visual Demonstration
We can demonstrate how this works visually with three hypothetical
sets of data.
 In each set of data there are 3 groups sampled from
3 populations.
 The populations have means of 15, 30 and 45. We have
colored the data to show the groups. We use
 Red for the group with population mean=15
 Green for the group with population mean=30
 Blue for the group with population mean=45
 The three sets of data differ according to the variances
of the 3 populations:
 Dataset 1 sampled from populations with variances
of 4, 4, and 4.
 Dataset 2 sampled from populations with variances
of 4, 64, and 4.
 Dataset 3 sampled from populations with variances
of 64, 64, and 64.
 With each visualization we present the corresponding
FTest value and its p value.
Example 1
Population Means = 15, 30, 45
Population variances = 4, 4, 4
F=854.24, p<.0001

Example 2
Population Means = 15, 30, 45
Population variances = 4, 64, 4
F=11.66, p<.0001

Example 3
Population Means = 15, 30, 45
Population variances = 64, 64, 64
F=1.42, p=.2440

Note that in these examples, the means of the three groups
haven't varied, but the variances have. We see that when the
groups are well separated, the F value is very significant.
On the other hand, when they overlap a lot, the F is much
less significant.
