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On page 349, table 16-4, Keppel shows the results of a one way within subjects anova. We show this analysis in Stata below.
use http://www.ats.ucla.edu/stat/stata/examples/da/chap16n, clear
anova score a s, repeated(a)
Number of obs = 18 R-squared = 0.5789
Root MSE = 3.95811 Adj R-squared = 0.2841
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 215.333333 7 30.7619048 1.96 0.1608
|
a | 148.00 2 74.00 4.72 0.0360
s | 67.3333333 5 13.4666667 0.86 0.5396
|
Residual | 156.666667 10 15.6666667
-----------+----------------------------------------------------
Total | 372.00 17 21.8823529
Between-subjects error term: s
Levels: 6 (5 df)
Lowest b.s.e. variable: s
Repeated variable: a
Huynh-Feldt epsilon = 1.6280
*Huynh-Feldt epsilon reset to 1.0000
Greenhouse-Geisser epsilon = 0.9875
Box's conservative epsilon = 0.5000
------------ Prob > F ------------
Source | df F Regular H-F G-G Box
-----------+----------------------------------------------------
a | 2 4.72 0.0360 0.0360 0.0367 0.0818
Residual | 10
-----------+----------------------------------------------------
When you specify the repeated(a) that tells Stata that a is a within subjects variable and that it should pick the appropriate error term. It also includes the H-F and G-G adjusted probabilities. You can also manually specify the error term as shown below. The "/" indicates to Stata that s a should be tested against s|a (i.e., s nested within a). This way, we are telling Stata to test a against s nested within a (we also indicate to test s against s nested within a, but we are not as interested in that test).
anova score s a / s|a
Number of obs = 18 R-squared = 1.0000
Root MSE = 0.00 Adj R-squared =
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 372.00 17 21.8823529
|
s | 67.3333333 5 13.4666667 0.86 0.5396
a | 148.00 2 74.00 4.72 0.0360
s|a | 156.666667 10 15.6666667
-----------+----------------------------------------------------
|
Residual | 0.00 0
-----------+----------------------------------------------------
Total | 372.00 17 21.8823529
You might ask why you would use this second syntax instead of the first, since the first is easier. Well, on page 358, table 16-6, Keppel shows a contrast on the repeated factor. We accomplish the contrast by creating acomp1 which shows the comparison of interest.
generate acomp1 = a recode acomp1 1=-1 2=2 3=-1
As Keppel shows in table 16-6 Acomp is compared against Acomp x S. We use acomp1 s / acomp1*s to indicate to Stata.
anova score acomp1 s / acomp1*s, contin(acomp1)
Number of obs = 18 R-squared = 0.6989
Root MSE = 4.32049 Adj R-squared = 0.1470
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 260.00 11 23.6363636 1.27 0.4038
|
acomp1 | 121.00 1 121.00 8.44 0.0336
s | 67.3333333 5 13.4666667 0.94 0.5264
acomp1*s | 71.6666667 5 14.3333333
-----------+----------------------------------------------------
|
Residual | 112.00 6 18.6666667
-----------+----------------------------------------------------
Total | 372.00 17 21.8823529
On page 363, table 16-8, Keppel shows a similar analysis which also includes the position p (trial number) for removing practice effects. Since all of the factors to be tested are tested against the residual, we can test this simply by the following anova test.
anova score a s p
Number of obs = 18 R-squared = 0.8217
Root MSE = 2.87953 Adj R-squared = 0.6211
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 305.666667 9 33.962963 4.10 0.0298
|
a | 148.00 2 74.00 8.92 0.0092
s | 67.3333333 5 13.4666667 1.62 0.2580
p | 90.3333333 2 45.1666667 5.45 0.0321
|
Residual | 66.3333333 8 8.29166667
-----------+----------------------------------------------------
Total | 372.00 17 21.8823529
We should note that when doing tests that involve repeated measures in Stata, you need to often manually specify error terms, and because of this you have to be very careful with such analyses. If you would like more information, you can see the Stata FAQ about this at http://www.stata.com/support/faqs/stat/anova2.html.
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