### Stata FAQ How can I compute effect size in Stata after an ANOVA?

After you perform an ANOVA, it is important to report effect size in addition to statistical significance. Here is a user written developed a program called effectsize that you can download and use to compute omega squared and eta squared after running an ANOVA. You can download the omega2 command by typing findit effectsize (see How can I use the findit command to search for programs and get additional help? for more information about using findit).

Once installed, you can use effectsize after running an ANOVA.  Below, we run an ANOVA using the hsb2 dataset.

use http://www.ats.ucla.edu/stat/data/hsb2, clear

anova write prog##female

Number of obs =     200     R-squared     =  0.2590
Root MSE      = 8.26386     Adj R-squared =  0.2399

Source |  Partial SS    df       MS           F     Prob > F
------------+----------------------------------------------------
Model |  4630.36091     5  926.072182      13.56     0.0000
|
prog |  3274.35082     2  1637.17541      23.97     0.0000
female |  1261.85329     1  1261.85329      18.48     0.0000
prog#female |  325.958189     2  162.979094       2.39     0.0946
|
Residual |  13248.5141   194  68.2913097
------------+----------------------------------------------------
Total |   17878.875   199   89.843593


We can now run effectsize on the significant prog and female maine effects.
effectsize prog

anova effect size for prog with dep var = write

total variance accounted for
omega2         = .17483363
eta2           = .18314076
Cohen's f      = .46030079

partial variance accounted for
partial omega2 = .18681606
partial eta2   = .19817089

effectsize female

anova effect size for female with dep var = write

total variance accounted for
omega2         = .0665042
eta2           = .07057789
Cohen's f      = .26691216

partial variance accounted for
partial omega2 = .08036467
partial eta2   = .08696219
Remarks

Eta2 is interpreted as percent of dv accounted for by the effect in the sample. While omega2 is interpreted as percent of dv accounted for by the effect in the population.

Very rough guidelines for effect size:

omega2 and eta2: .01 small; .06 medium; .14 large
Cohen's f:       .10 small; .25 medium; .40 large

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