Two and More Factors ANOVA - Agricultural Statistical Data Analysis Using Stata - page 131

trt | 25292.9333 2 12646.4667 2.48 0.1447
rep | 58169.0667 4 14542.2667 2.86 0.0964
|
Residual | 40713.7333 8 5089.21667
---------+----------------------------------------------------
Total | 124175.733 14 8869.69524
Because there was a missing value, the degrees of freedom for the
residual or error is lowered from 8 to 7, and a new residual mean
square calculated. Thus, the mean square error is now 5,816.2476
(40,713.7333/7) and the F value for treatments (trt) is 2.1743343
(12,646.4667/5,816.2476). To calculated and display the new prob-
ability after this adjustment, the Fden( n1,n2,f ) density function can
be used. The n1 is the degrees of freedom for the numerator (i.e., 2)
and the n2 is the degrees of freedom for the denominator (i.e., 7). The
f is the calculated F (i.e., 2.1743343) value.
display Fden (2,7, 2.1743343)
which results in
.11368131
This procedure can be used for more than one missing value. A new
dummy variable would be created for each additional missing value
and the process repeated, including reducing the error degrees of free-
dom by one for each missing value. Obviously, there is a limit to the
number of missing values you should replace. In a planned experiment
such as this, you would expect very few missing values, but it does
happen. The decision to continue an analysis with multiple missing
values is a judgment call. Remember, statistics is a tool to help you
understand your data, not a crutch to hold up an experiment with
problems.