ANOVA (Day 2)
OneWay or SingleFactor ANOVA (review) One manipulation or one factor to see if
means are different
Practice Problem from Day 1 notes. OneWay (or SingleFactor) ANOVA:
Does custodial parenting
arrangement affect children’s behavior problems?
Additional Notes/Questions:
•
Assumptions
•
Power
Sampling distribution of
F
•
Minimum value of F is 0
o
Ratio of variances; variances are never negative
•
F distribution is positively skewed
o
F =t squared
•
Distribution of F varies by df
Just like we have done with z and t tests, we need to compare our obtained value to something else to
see the likelihood of obtaining such a result by chance alone.
•
We use the
sampling distribution
of
F
to determine the probability of an obtained value of
F
.
•
The sampling distribution of
F
shows the frequency of each
possible value of
F
when 1) H
0
is true, and 2) the population
is sampled randomly with replacement until all possible
samples have been taken.

Lowest possible value of F = 0. F is never negative
because variance is a squared value.

If H
0
is true, then the center of the distribution will
be over approximately 1.00.

The F distribution is positively skewed.

The exact shape of the F distribution depends on
df
within
and df
between
•
Use the table of critical values of
F
to identify critical value and mark critical region of the
F
distribution.
A oneway ANOVA divides variance into two sources and produces an F Statistic:
1)
Between group variance
•
Differences between group means
F =
pVariance
WithinGrou
upVariance
BetweenGro
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•
Caused by the independent variable plus some error
2)
Within group variance
•
Spread or dispersion of scores within each group
•
Caused by error (individual differences, sampling error, uncontrolled variables, etc.)
Assumptions in ANOVA
The F and the t test are very closely related. In fact, when there are only 2 groups F = t
2
. As such the
assumptions for a oneway ANOVA are the same as those for the t test for independent samples.
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 Fall '08
 Burns
 Dr. Viji Sathy

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