Please Note: the code on this page has been updated to Stata 12
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 5 56 3.05 0.0361
|
a | 112 2 56 3.05 0.0721
b | 24 1 24 1.31 0.2675
a#b | 144 2 72 3.93 0.0384
|
Residual | 330 18 18.3333333
-----------+----------------------------------------------------
Total | 610 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.
contrast {a 1 0 -1}, effects
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df F P>F
-------------+----------------------------------
a | 1 5.45 0.0313
|
Residual | 18
------------------------------------------------
------------------------------------------------------------------------------
| Contrast Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
a |
(1) | -5 2.140872 -2.34 0.031 -9.497805 -.5021946
------------------------------------------------------------------------------
On page 241, Keppel shows how to perform tests of simple main effects testing the effect of A at b1 and b2.
contrast a@b,effects
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df F P>F
-------------+----------------------------------
a@b |
1 | 2 6.76 0.0064
2 | 2 0.22 0.8061
Joint | 4 3.49 0.0281
|
Residual | 18
------------------------------------------------
--------------------------------------------------------------------------------
| Contrast Std. Err. t P>|t| [95% Conf. Interval]
---------------+----------------------------------------------------------------
a@b |
(2 vs base) 1 | 7 3.02765 2.31 0.033 .6391426 13.36086
(2 vs base) 2 | 1 3.02765 0.33 0.745 -5.360857 7.360857
(3 vs base) 1 | 11 3.02765 3.63 0.002 4.639143 17.36086
(3 vs base) 2 | -1 3.02765 -0.33 0.745 -7.360857 5.360857
--------------------------------------------------------------------------------
Page 246 shows how to do a simple comparison.
* means of a @ b1
margins a, at(b=1)
Adjusted predictions Number of obs = 24
Expression : Linear prediction, predict()
at : b = 1
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
a |
1 | 3 2.140872 1.40 0.161 -1.196032 7.196032
2 | 10 2.140872 4.67 0.000 5.803968 14.19603
3 | 14 2.140872 6.54 0.000 9.803968 18.19603
------------------------------------------------------------------------------
contrast {a 1 -1 0}@1.b, effects
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df F P>F
-------------+----------------------------------
a@b |
(1) 1 | 1 5.35 0.0328
|
Residual | 18
------------------------------------------------
------------------------------------------------------------------------------
| Contrast Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
a@b |
(1) 1 | -7 3.02765 -2.31 0.033 -13.36086 -.6391426
------------------------------------------------------------------------------
means of a @ b2
margins a, at(b=2)
Adjusted predictions Number of obs = 24
Expression : Linear prediction, predict()
at : b = 2
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
a |
1 | 11 2.140872 5.14 0.000 6.803968 15.19603
2 | 12 2.140872 5.61 0.000 7.803968 16.19603
3 | 10 2.140872 4.67 0.000 5.803968 14.19603
------------------------------------------------------------------------------
contrast {a 1 -1 0}@2.b, effects
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df F P>F
-------------+----------------------------------
a@b |
(1) 2 | 1 0.11 0.7450
|
Residual | 18
------------------------------------------------
------------------------------------------------------------------------------
| Contrast Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
a@b |
(1) 2 | -1 3.02765 -0.33 0.745 -7.360857 5.360857
------------------------------------------------------------------------------
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