Two and More Factors ANOVA - Agricultural Statistical Data Analysis Using Stata - page 111

Table 6.2 Source of variation and degrees of freedom for a split-block design experiment

SOURCE OF VARIATION DEGREES OF FREEDOM (DF) RESULTS OF DF

Replication
( rep )

r - 1 3 - 1 = 2

Horizontal factor
( var )

a - 1 6 - 1 = 5

Horizontal factor error
( rep#var )

( r - 1)( a - 1) (3 - 1)(6 - 1) = 10

Vertical factor
( fert )

b - 1 3 - 1 = 2

Vertical factor error
( rep#fert )

( r - 1)( b - 1) (3 - 1)(3 - 1) = 4

Variety × fertilizer interaction
( var#fert )

( a - 1)( b - 1) (6 - 1)(3 - 1) = 10

Variety × fertilizer error
( rep#var#fert )

( r - 1)( a - 1)( b - 1) (3 - 1)(6 - 1)(3 - 1) = 20

Note: Arrows indicate the ratio of mean squares for calculating F values.

-------------+----------------------------------------------------
fert | 50676061.4 2 25338030.7 34.07 0.0031
fert#rep | 2974907.89 4 743726.972
-------------+----------------------------------------------------
var#fert | 23877979.4 10 2387797.94 5.80 0.0004
rep#var#fert | 8232917.22 20 411645.861
-------------+----------------------------------------------------
|
Residual | 0 0
-------------+----------------------------------------------------
Total | 167005649 53 3151049.98

Looking at the results, we see that variety ( var ) and fertility ( fert )
rates are significant. In addition, the variety by fertility interaction is
significant as well.
Because the fertilizer was applied at equally spaced rates, it is pos-
sible to examine this factor as a linear effect (regression and correla-
tion will be discussed more fully in Chapter 10). Examine the dataset
and you will see the fertilizer rates are entered as they were applied: 0,
60, and 120 kg/ha. Entering a c. prior to a variable tells Stata to treat
this variable as continuous rather than as discrete values. Enter the
following command:

anova yield rep var/var#rep c.fert/c.fert#rep
var#c.fert/rep#var#c.fert