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Single Factor Analysis of Variance

​
blue population
_
x
1
18
s
1
1
purple population
_
x
2
20
s
2
1
green population
_
x
3
21
s
3
1
set
s
1
=
s
2
=
s
3
to:
0.75
1
1.25
reset
Means
SDs
shading
On
Off
Source
Sum of Squares
df
Mean Square
F Value
P Value
Between Groups
46.667
2
23.333
23.333
< .01
Within Groups
27.000
27
1.000
​
​
Total
73.667
29
​
​
​
This Demonstration shows how a single factor analysis of variance (ANOVA) works. There are three groups, each with sample size 10. You can change the mean or standard deviation of each group separately and observe the changes in the ANOVA table of results. The black line represents the grand mean and its value is at the top of the line. The significance of
F
is provided as
p<0.01
,
p<0.05
, or
p>0.05
based on a regular table for the distribution of
F
at 2 and 27 degrees of freedom.
You can set the standard deviations to be equal across the groups at 0.75, 1, and 1.25. The reset buttons set the means or standard deviations back to the default values. The shading buttons turn the shading of the curves on and off.

Details

The formulas underlying this Demonstration are based on the method for estimating an ANOVA with summary data as found in[1].
Reference
[1] D. A. Larson, "Analysis of Variance with Just Summary Statistics as Input," American Statistician, 46, 1992 pp. 151–152.

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