Chapter 13
TwoWay Analysis of Variance:
Twoway ANOVA compares the means of populations that are classified
two ways or the mean responses in twofactor experiments.
Examples:
1. The strength of concrete depends upon the formula used to prepare it.
An experiment compares six different mixtures.
Nine specimens of
concrete are poured from each mixture.
Three of these specimens are
subjected to 0 cycles of freezing and thawing, three are subjected to
100 cycles, and three specimens are subjected to 500 cycles.
The
strength of each specimen is then measured.
2. Four methods for teaching sign language are to be compared.
Sixteen
students in special education and sixteen students majoring in other
areas are the subjects for the study.
Within each group they are
randomly assigned to the methods.
Scores on a final exam are
compared.
Why is it better to do a TwoWay ANOVA than to just do 2 separate
OneWay ANOVAs:
•
It is more efficient to study two factors simultaneously rather than
separately.
Your sample size does not have to be as large so
experiments with several factors are an efficient use of resources.
•
We can reduce the residual variation in a model by including a second
factor thought to influence the response variable (lurking variable).
We are reducing σ and increasing the power of the test.
•
We can investigate the interactions between factors.
Assumptions for TwoWay ANOVA:
1.
We have two factors.
We have
I
factor levels for the first factor (call
it factor A) and
J
factor levels for the second factor (call it factor B).
We have
I
x
J
combinations of individual factor levels.
2.
We have independent SRSs of size
ij
n
from each of
I
x
J
populations.
3.
Each of the
I
x
J
populations are normally distributed.
4.
Each of the
I
x
J
populations have the same standard deviation σ.
Lecture 9, Chapter 13
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 Spring '08
 Staff
 Standard Deviation, Variance, GPi, twoway anova

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