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In chapter 10 Keppel shows how to perform a two-way factorial anova on page 217. We use the xi3 command as shown below to get the analysis for the two-way anova. The a*b term requests the main effects of a and b and interaction effect of a by b. You can download the xi3 command by typing findit xi3 (see How can I use the findit command to search for programs and get additional help? for more information about using findit).
use http://www.ats.ucla.edu/stat/stata/examples/da/chap10, clear
xi3: regress errors g.a*g.b
g.a _Ia_1-3 (naturally coded; _Ia_1 omitted)
g.b _Ib_1-2 (naturally coded; _Ib_1 omitted)
Source | SS df MS Number of obs = 24
-------------+------------------------------ F( 5, 18) = 3.05
Model | 280 5 56 Prob > F = 0.0361
Residual | 330 18 18.3333333 R-squared = 0.4590
-------------+------------------------------ Adj R-squared = 0.3087
Total | 610 23 26.5217391 Root MSE = 4.2817
------------------------------------------------------------------------------
errors | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ia_2 | 4 2.140872 1.87 0.078 -.4978054 8.497805
_Ia_3 | 5 2.140872 2.34 0.031 .5021946 9.497805
_Ib_2 | 2 1.748015 1.14 0.268 -1.672443 5.672443
_Ia2Xb2 | -6 4.281744 -1.40 0.178 -14.99561 2.995611
_Ia3Xb2 | -12 4.281744 -2.80 0.012 -20.99561 -3.004389
_cons | 10 .8740074 11.44 0.000 8.163779 11.83622
------------------------------------------------------------------------------
Below we use the test command to get the main effect of a, the main effect of b and the interaction of a by b.
test _Ia_2 _Ia_3
( 1) _Ia_2 = 0.0
( 2) _Ia_3 = 0.0
F( 2, 18) = 3.05
Prob > F = 0.0721
test _Ib_2
( 1) _Ib_2 = 0.0
F( 1, 18) = 1.31
Prob > F = 0.2675
test _Ia2Xb2 _Ia3Xb2
( 1) _Ia2Xb2 = 0
( 2) _Ia3Xb2 = 0
F( 2, 18) = 3.93
Prob > F = 0.0384
On page 222, Keppel shows how to compute Omega Squared for the a*b effect. We do not know how to compute this via regression so we have not done that.
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