Two and More Factors ANOVA - Agricultural Statistical Data Analysis Using Stata - page 122

Table 6.4 Source of variation and degrees of freedom for a split-split plot design

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

Replication (rep) r - 1 3 - 1 = 2

Main plot (nitro) a - 1 5 - 1 = 4

Main-plot error (rep#nitro) ( r - 1)( a - 1) (3 - 1)(5 - 1) = 8

Subplot factor (manage) b - 1 3 - 1 = 2

Nitrogen × management interaction (nitro#manage) ( r - 1)( b - 1) (5 - 1)(3 - 1) = 8

Subplot error nitro(rep - 1)(manage - 1) a ( r - 1)( b - 1) 5(3 - 1)(3 - 1) = 20

Sub-subplot factor (var) ( c - 1) (3 - 1) = 2

Nitrogen × variety (nitro#var) ( a - 1)( c - 1) (5 - 1)(3 - 1) = 8

Management × variety (mange#var) ( b - 1)( c - 1) (3 - 1)(3 - 1) = 4

Nitrogen × management × variety (nitro#mange#var) ( a - 1)( b - 1)( c - 1) (5 - 1)(3 - 1)(3 - 1) = 16

Sub-subplot error nitro#manage(rep - 1)(var - 1) ab ( r - 1)( c - 1) 5*3(3 - 1)(3 - 1) = 60

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