Balanced lattice experiment in cotton

data("cochran.lattice")

Format

A data frame with 80 observations on the following 5 variables.

y: percent of affected flower buds
rep: replicate
row: row
col: column
trt: treatment factor

Details

The experiment is a balanced lattice square with 16 treatments in a 4x4 layout in each of 5 replicates. The treatments were applied to cotton plants. Each plot was ten rows wide by 70 feet long (about 1/18 of an acre). (Estimated plot width is 34.5 feet.) Data were collected from the middle 4 rows. The data are the percentages of squares showing attack by boll weevils. A 'square' is the name given to a young flower bud.

The plot orientation is not clear.

Source

William G. Cochran, Gertrude M. Cox. Experimental Designs, 2nd Edition. Page 490.

Originally from: F. M. Wadley (1946). Incomplete block designs in insect population problems. J. Economic Entomology, 38, 651--654.

References

Walter Federer. Combining Standard Block Analyses With Spatial Analyses Under a Random Effects Model. Cornell Univ Tech Report BU-1373-MA. https://hdl.handle.net/1813/31971

Examples

# \dontrun{

library(agridat)
data(cochran.lattice)
dat <- cochran.lattice

libs(desplot)
desplot(dat, y~row*col|rep,
        text=trt, # aspect unknown, should be 2 or .5
         main="cochran.lattice")


# Random rep,row,column model often used by Federer
libs(lme4)
dat <- transform(dat, rowf=factor(row), colf=factor(col))
m1 <-  lmer(y ~ trt + (1|rep) + (1|rep:row) + (1|rep:col), data=dat)
#> boundary (singular) fit: see ?isSingular
summary(m1)
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: y ~ trt + (1 | rep) + (1 | rep:row) + (1 | rep:col)
#>    Data: dat
#> 
#> REML criterion at convergence: 433.9
#> 
#> Scaled residuals: 
#>     Min      1Q  Median      3Q     Max 
#> -2.1384 -0.5057 -0.0117  0.4584  2.2629 
#> 
#> Random effects:
#>  Groups   Name        Variance Std.Dev.
#>  rep:col  (Intercept)  3.17    1.781   
#>  rep:row  (Intercept) 10.92    3.304   
#>  rep      (Intercept)  0.00    0.000   
#>  Residual             23.86    4.885   
#> Number of obs: 80, groups:  rep:col, 20; rep:row, 20; rep, 5
#> 
#> Fixed effects:
#>             Estimate Std. Error t value
#> (Intercept)    6.090      2.566   2.373
#> trtT02         7.641      3.451   2.214
#> trtT03         2.403      3.451   0.696
#> trtT04         5.254      3.451   1.522
#> trtT05         3.472      3.451   1.006
#> trtT06         1.206      3.451   0.350
#> trtT07         1.208      3.451   0.350
#> trtT08         3.323      3.451   0.963
#> trtT09         4.024      3.451   1.166
#> trtT10         9.094      3.451   2.635
#> trtT11        11.815      3.451   3.423
#> trtT12         6.756      3.451   1.958
#> trtT13         4.942      3.451   1.432
#> trtT14         8.160      3.451   2.364
#> trtT15         3.205      3.451   0.929
#> trtT16         4.537      3.451   1.315
#> 
#> Correlation matrix not shown by default, as p = 16 > 12.
#> Use print(x, correlation=TRUE)  or
#>     vcov(x)        if you need it
#> convergence code: 0
#> boundary (singular) fit: see ?isSingular
#> 

# }