Today we

1
Today were going to work through a computational
example of ANOVA.
Subject Treatment group Depressive symptoms
A placebo 5
B placebo 6
C placebo 4
D cog-behav 3
E cog-behav 4
F cog-behav 2
G psychoanalytic 2
H psychoanalytic 2
I psychoanalytic 5
2
Lets find the estimated population mean for each
group.
Subject Treatment group Depressive symptoms
A placebo 5
B placebo 6
C placebo 4
D cog-behav 3
E cog-behav 4
F cog-behav 2
G psychoanalytic 2
H psychoanalytic 2
I psychoanalytic 5
3
Subject Treatment group Depressive symptoms
A placebo 5
B placebo 6
C placebo 4
D cog-behav 3
E cog-behav 4
F cog-behav 2
G psychoanalytic 2
H psychoanalytic 2
I psychoanalytic 5
Lets find the estimated population variance for
each group.
4
Recall that, if the null hypothesis is true, then
these three population variance estimates are
estimates of the same value. Thus, we can pool
them to obtain a single estimate of the
population variance, under the assumption that
the null hypothesis is true. This quantity is our
within-groups estimate of the population
variance.
5
To obtain our between-groups estimate of the
population variance, we recognize that, if the
null hypothesis is true, our three group means
can be viewed as being three samples drawn from
the same population. As a consequence, by finding
the variance of these three means, we can
estimate the variance of the corresponding
sampling distribution, and, hence, estimate the
population variance.
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• Our estimate of the population variance
  within-groups is 1.66
• Out estimate of the population variance
  between-groups is 4.00
• The F-ratio, then is 4.00/1.66 or 2.4.
• The p-value associated with this F-ratio, given
  the sample size and number of groups involved is
  about .17.