Latin square design in wheat

Six wheat plots were sampled by six operators and shoot heights measured. The operators sampled plots in six ordered sequences. The dependent variate was the difference between measured height and true height of the plot.

Format

A data frame with 36 observations on the following 4 variables.

row

row

col

column

operator

operator factor

diff

difference between measured height and true height

Source

Cochran, W.G. and Cox, G.M. (1957), Experimental Designs, 2nd ed., Wiley and Sons, New York.

Examples

library(agridat)

data(cochran.latin)
dat <- cochran.latin

libs(desplot)
desplot(dat, diff~col*row,
        text=operator, cex=1, # aspect unknown
        main="cochran.latin")


dat <- transform(dat, rf=factor(row), cf=factor(col))
aov.dat <- aov(diff ~ operator + Error(rf*cf), dat)
summary(aov.dat)
#> 
#> Error: rf
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> Residuals  5   28.6    5.72               
#> 
#> Error: cf
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> Residuals  5  78.87   15.77               
#> 
#> Error: rf:cf
#>           Df Sum Sq Mean Sq F value   Pr(>F)    
#> operator   5 155.60  31.119    9.35 0.000103 ***
#> Residuals 20  66.56   3.328                     
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
model.tables(aov.dat, type="means")
#> Tables of means
#> Grand mean
#>          
#> 4.758333 
#> 
#>  operator 
#> operator
#>     a     b     c     d     e     f 
#> 6.067 5.583 6.117 6.917 2.667 1.200