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In chapter 11 Keppel shows how to perform comparisons of main effects and simple effects in a two way factorial anova based on the example from chapter 10. Let's start by running the basic anova from chapter 10.
use http://www.ats.ucla.edu/stat/stata/examples/da/chap10, clear
anova errors a b a*b
Number of obs = 24 R-squared = 0.4590
Root MSE = 4.28174 Adj R-squared = 0.3087
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 280.00 5 56.00 3.05 0.0361
|
a | 112.00 2 56.00 3.05 0.0721
b | 24.00 1 24.00 1.31 0.2675
a*b | 144.00 2 72.00 3.93 0.0384
|
Residual | 330.00 18 18.3333333
-----------+----------------------------------------------------
Total | 610.00 23 26.5217391
On page 234 Keppel shows a comparison comparing group a1 with group a3 We create a variable acomp1 that compares group a1 with group a3.
gen acomp1=a recode acomp1 1=1 2=0 3=-1
We also create a variable acomp2 that is orthogonal to acomp1.
gen acomp2=a recode acomp2 1=1 2=-2 3=1
We now run the anova, replacing a with acomp1 acomp2, and adding contin(acomp1 acomp2). We see the effect acomp1 is the same as shown on page 234.
anova errors acomp1 acomp2 b acomp1*b acomp2*b , contin(acomp1 acomp2)
Number of obs = 24 R-squared = 0.4590
Root MSE = 4.28174 Adj R-squared = 0.3087
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 280.00 5 56.00 3.05 0.0361
|
acomp1 | 100.00 1 100.00 5.45 0.0313
acomp2 | 12.00 1 12.00 0.65 0.4291
b | 24.00 1 24.00 1.31 0.2675
acomp1*b | 144.00 1 144.00 7.85 0.0118
acomp2*b | 0.00 1 0.00 0.00 1.0000
|
Residual | 330.00 18 18.3333333
-----------+----------------------------------------------------
Total | 610.00 23 26.5217391
On page 241, Keppel shows how to perform tests of simple main effects testing the effect of A at b1 and b2. Stata does not have a built in command for computing simple main effects, however UCLA Academic Technology Services has created a command sme which will compute this for you and can be downloaded by typing findit sme in the command line and proceed with the installation (see How can I use the findit command to search for programs and get additional help? for more information about using findit).
Now, we rerun the original anova as shown below.
anova errors a b a*b
Number of obs = 24 R-squared = 0.4590
Root MSE = 4.28174 Adj R-squared = 0.3087
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 280.00 5 56.00 3.05 0.0361
|
a | 112.00 2 56.00 3.05 0.0721
b | 24.00 1 24.00 1.31 0.2675
a*b | 144.00 2 72.00 3.93 0.0384
|
Residual | 330.00 18 18.3333333
-----------+----------------------------------------------------
Total | 610.00 23 26.5217391
Now we get the simple effects of A at b1 and b2.
sme a b Test of a at b(1): F(2/18) = 6.7636364 Test of a at b(2): F(2/18) = .21818182 Critical value of F for alpha = .05 using ... -------------------------------------------------- Dunn's procedure = 4.2877197 Marascuilo & Levin = 4.9000978 per family error rate = 4.5596361 simultaneous test procedure = 4.6736374
Page 246 shows how to do a simple comparison. We have skipped this for now, as we are not sure how to do this in Stata.
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