Activity 5:
Twoway ANOVA
With two factors, there is an additional question beyond whether each factor separately is
significant:
Is there an interaction between the two factors?
That is, does the effect of
one factor depend on the level of the other factor?
I.
To illustrate this, let’s consider the effects of ethanolic NaOH concentration and coal
type on total acidity.
Each of these factors has three levels.
Open the data from the
website.
1.
First, let’s look at an interaction plot.
Go to
Stat > ANOVA > Interactions
Plot….
Enter Acidity as the response and NaOH and Coal Type as the factors (in
that order).
Copy and paste the interaction plot below.
For Morwell coal, what
concentration of NaOH gives the highest mean acidity?
for Yallourn?
for
Maddingley?
Since the lines (for each concentration of NaOH) are roughly parallel, it appears that the
effect of NaOH concentration does not depend on the type of coal.
This suggests that
there is
NO INTERACTION
between the factors.
Thus, when we perform a twoway
ANOVA, the interaction term will probably not be significant.
(Check but do not
answer:
Do you get a different intuition if you produce an interaction plot with the
factors in the other order?)
2.
So let’s look at the results.
Go to
Stat > ANOVA > Twoway…
.
Enter Acidity as
the response, NaOH as the row factor and Coal Type as the column factor.
Copy and
paste the ANOVA table (and ONLY the table) below.
What are the test statistic and p
value for the interaction term?
What can you conclude?
If the interaction term is not significant, then we can focus on the main effects…the
effects of the individual factors.
3.
Since the interaction term isn’t significant, let’s not waste those 4 degrees of freedom
on the interaction when they could be used to give a more accurate estimate of the mean
square error.
Refit the model without the interaction term by clicking the “Fit additive
model” box in
Stat > ANOVA > Twoway…
.
Paste the new ANOVA table below.
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 Fall '00
 Akritas
 Statistics, interaction term

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