Post Hoc Tests - Agricultural Statistical Data Analysis Using Stata - page 157

where s 2 is the residual mean square or mean square error and n a and
n b are the number of replications for treatments a and b . This can be
calculated and displayed within Stata for our example with
display sqrt (.001659631*2/11)
Using the scalars from the ANOVA, it also can be displayed with
display sqrt (r(rss)/r(df_r)*2/(r(N)/(r(df_m)+1)))
Multiplying S by SE (0.01737098) results in 0.0556, which is then
used as the minimum value to compare any two means. If the dif-
ference between the means exceeds this value, then the difference is
considered significant at the specified probability level.
Programming Scheffé's Test
Stata offers a wide variety of post hoc multiple range tests that can
list the probabilities of all pairwise comparisons. However, results are
rarely, if ever, presented in this format in the agricultural literature. It
is more common to present these results with means followed by letters
where any means having the same letters are not considered signifi-
cantly different at the chosen probability level (usually 0.05 or 0.01).
To develop your programming skills further and develop programs
that present these results in a more table-friendly format do-files of
several of these multiple range tests have been developed. You should
have already read the previous chapter on programming to help
understand this process. We will be using the Strontium.dta dataset.
This is a dataset of strontium levels found in various lakes (Zar, 1974,
p. 152). Load the dataset and open the Do-file scheffe.do.
The scheffe.do program calculates the Scheffé's multiple contrasts
test and presents the results as a list of means followed by letters
indicating which means differ. Means followed by the same letter
are not significantly different at the 5% level. This program assumes
the experiment is an RCBD. The significance level and the experi-
mental design, however, can be easily changed within the program.
Remember, to use the program, first it must be run. This can be
accomplished by selecting the Run or Do buttons on the top right of
the Do-File Editor.