Post Hoc Tests - Agricultural Statistical Data Analysis Using Stata - page 156

You can see that, as the number of comparisons increases, the chosen
probability quickly becomes very small. With 10 varieties and 45 pos-
sible comparisons, the 5% probability is now actually 0.001.
Šidák's adjustment uses the following formula to determine the
probability at which the difference should be declared significant:

1

a =− − 11 ( α )

n

Again using the absorbance data with 10 possible comparisons and
wishing to use a 5% level of significance, the new probability level
would be

1 10

0 005 . =− − 11005 ( .)

Scheffé's approach is to calculate a multiplier ( S ), which then is
multiplied against the standard error and this value then is used as the
minimum difference for significance. This multiplier is calculated as

S =− ( t 1 ) F

( )

α , t − 1 , errordf

where t is the number of treatments and F is the critical value often
available in the F distribution table in the back of statistics textbooks.
he S value can be easily calculated and displayed in Stata. Enter the
following command to display the S multiplier:

display sqrt (4*i nvFtail (4,50,0.05))

This also can be displayed by entering the following command imme-
diately after calculating the ANOVA. The oneway command saves
several scalars in r(), which can be viewed with ereturn list .
Enter the following to calculate the S value:

display sqrt (r(df_m)* invFtail (r(df_m),r(df_r),0.05))

S, which is 3.1982365 in this case, is then multiplied with the stan-
dard error of the difference between two means. The SE value is cal-
culated as

11

2

SE = s +

nn

a b