Factorial experiment in beans

Factorial experiment in beans

data("cochran.factorial")

Format

A data frame with 32 observations on the following 4 variables.

rep

rep factor

block

block factor

trt

treatment factor, 16 levels

yield

yield (pounds)

Details

Conducted by Rothamsted Experiment Station in 1936. The treatments are listed below.

d = dung: None, 10 tons/acre.

n = nitrochalk: None, 0.4 hundredweight nitrogen per acre.

p = Superphosphate: None, 0.6 hundredweight per acre

k = muriate of potash: None, 1 hundredweight K20 per acres.

The response variable is the yield of beans.

Source

Cochran, W.G. and Cox, G.M. (1957), Experimental Designs, 2nd ed., Wiley and Sons, New York, p. 160.

Examples

# \dontrun{

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

# Split treatment into individual factors
dat <- transform(dat,
                 d = -1 + 2 * grepl('d',trt),
                 n = -1 + 2 * grepl('n',trt),
                 p = -1 + 2 * grepl('p',trt),
                 k = -1 + 2 * grepl('k',trt))
dat <- transform(dat, d=factor(d), n=factor(n), p=factor(p), k=factor(k))

# Cochran table 6.5.
m1 <- lm(yield ~ rep * block + (d+n+p+k)^3, data=dat)
anova(m1)
#> Analysis of Variance Table
#> 
#> Response: yield
#>           Df Sum Sq Mean Sq F value   Pr(>F)   
#> rep        1   3.12    3.12  0.1288 0.725064   
#> block      1  78.13   78.13  3.2193 0.094393 . 
#> d          1   2.00    2.00  0.0824 0.778258   
#> n          1 325.12  325.12 13.3974 0.002572 **
#> p          1   6.12    6.12  0.2524 0.623205   
#> k          1   4.50    4.50  0.1854 0.673303   
#> rep:block  1  45.12   45.12  1.8595 0.194213   
#> d:n        1  32.00   32.00  1.3186 0.270083   
#> d:p        1 242.00  242.00  9.9720 0.006982 **
#> d:k        1   6.13    6.13  0.2524 0.623205   
#> n:p        1  78.13   78.13  3.2193 0.094393 . 
#> n:k        1  32.00   32.00  1.3186 0.270083   
#> p:k        1  24.50   24.50  1.0096 0.332058   
#> d:n:p      1   2.00    2.00  0.0824 0.778258   
#> d:n:k      1  10.13   10.13  0.4172 0.528774   
#> d:p:k      1  15.13   15.13  0.6233 0.443007   
#> n:p:k      1  32.00   32.00  1.3186 0.270083   
#> Residuals 14 339.75   24.27                    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


libs(FrF2)
#> Loading required package: DoE.base
#> Loading required package: conf.design
#> 
#> Attaching package: 'conf.design'
#> The following object is masked from 'package:lme4':
#> 
#>     factorize
#> Registered S3 method overwritten by 'DoE.base':
#>   method           from       
#>   factorize.factor conf.design
#> 
#> Attaching package: 'DoE.base'
#> The following objects are masked from 'package:stats':
#> 
#>     aov, lm
#> The following object is masked from 'package:graphics':
#> 
#>     plot.design
#> The following object is masked from 'package:base':
#> 
#>     lengths
aliases(m1)
#> [1] no aliasing in the model
MEPlot(m1, select=3:6,
       main="cochran.factorial - main effects plot")

# }