Two and More Factors ANOVA - Agricultural Statistical Data Analysis Using Stata - page 116

Table 6.3 Source of variation and degrees of freedom for ANOVA for experiment over seasons

and years

ANALYSIS OF VARIANCE OVER SEASONS

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

Seasons
( season )

s - 1 2 - 1 = 1

Replications within seasons
( replseason )

s ( r - 1) 2(4 - 1) = 6

Treatments
( var )

( t - 1) 7 - 1 = 6

Season x treatment
( season#var )

( s - 1)( t - 1) (2 - 1)(7 - 1) = 6

Pooled error
( rep#varl season )

s ( r - 1)( t - 1) 2(4 - 1)(7 - 1) = 36

ANALYSIS OF VARIANCE OVER YEARS

Years
( year )

y - 1 3 - 1 = 2

Replications within years
( repl year )

y ( r - 1) 3(6 - 1) = 15

Treatments
( var )

( t - 1) 8 - 1 = 7

Years × treatments
( year#var )

( y - 1)( t - 1) (3 - 1)(8 - 1) = 14

Replications × treatment within years
( rep#varl year )

y ( r - 1)( t - 1) 3(6 - 1)(8 - 1) = 105

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

anova wt season / rep | season var season # var / rep # var | season

Number of obs = 84 R-squared = 0.9634
Root MSE = 13.4639 Adj R-squared = 0.8916
Source | Partial SS df MS F Prob > F
--------------+---------------------------------------------------
Model | 133692.817 55 2430.77849 13.41 0.0000
|
season | 812.240238 1 812.240238 2.14 0.1935
rep|season | 2273.86821 6 378.978036
--------------+---------------------------------------------------
var | 106106.946 6 17684.4911 45.30 0.0000
season#var | 5842.9131 6 973.818849 2.49 0.0403
rep#var|season| 14053.6693 36 390.379702
--------------+---------------------------------------------------
|
Residual | 5075.75 28 181.276786
--------------+---------------------------------------------------
Total | 138768.567 83 1671.91045