Statistics Review - Mathematics and Statistics for the Environment - page 157

3. For the difference between two minor treatments within a single major treatment:

D = 2(Subplot errormean square

s

R

where the degrees of freedom for t is equal to the degrees of freedom for the subplot
error.

4. For the difference between the means of two major treatments at a single level of a minor
treatment, or between the means of two major treatments at different levels of a minor
treatment:

( m − 1 )(Subplot errormean square) Major plot errormean square

( ()

+

s

D =

2

mR

In this case, t will not follow the t distribution. A close approximation to the value of t
required for significance at the a level is given by

( m − )1Subplot errormean square) t m + (Majorploterrormean square) t

M

t =

( m −1 )( Subplot er rormean square) Majorploterrormean sq + uare)

where
t m = Tabular value of t at the α level for degrees of freedom equal to the degrees of freedom
for the subplot error.
t M = Tabular value of t at the α level for degrees of freedom equal to the degrees of freedom
for the major plot error.

Other symbols are as previously defined.

7.16.7 m issing p lots
A mathematician who had developed a complex electronic computer program for analyzing a wide
variety of experimental designs was asked how he handled missing plots. His disdainful reply was,
“We tell our research workers not to have missing plots.” This is good advice. But it is sometimes
hard to follow, and particularly so in forest, environmental, and ecological research, where close
control over experimental material is difficult and studies may run for several years. The likelihood
of plots being lost during the course of a study should be considered when selecting an experimental
design. Lost plots are least troublesome in the simple designs. For this reason, complete randomiza-
tion and randomized blocks may be preferable to the more intricate designs when missing data can
be expected.
In the complete randomization design, loss of one or more plots causes no computational difficul-
ties. The analysis is made as though the missing plots never existed. Of course, a degree of freedom
will be lost from the total and error terms for each missing plot and the sensitivity of the test will
be reduced. If missing plots are likely, the number of replications should be increased accordingly.
In the randomized block design, completion of the analysis will usually require an estimate of the
values for the missing plots. A single missing value can be estimated by