Switchback experiment on dairy cattle, milk yield for 3 treatments

data("lucas.switchback")

Format

A data frame with 36 observations on the following 5 variables.

cow: cow factor, 12 levels
trt: treatment factor, 3 levels
period: period factor, 3 levels
yield: yield (FCM = fat corrected milk), pounds/day
block: block factor

Details

Lucas says "because no data from feeding trials employing the present designs are yet available, uniformity data will be used".

Six cows were started together in block 1, then three cows in block 2 and three cows in block 3.

Source

Lucas, HL. 1956. Switchback trials for more than two treatments. Journal of Dairy Science, 39, 146-154. https://doi.org/10.3168/jds.S0022-0302(56)94721-X

References

Sanders, WL and Gaynor, PJ. 1987. Analysis of Switchback Data Using Statistical Analysis System. Journal of Dairy Science, 70, 2186-2191. https://doi.org/10.3168/jds.S0022-0302(87)80273-4

Examples


library(agridat)

data(lucas.switchback)
dat <- lucas.switchback

# Create a numeric period variable
dat$per <- as.numeric(substring(dat$period,2))

libs(lattice)
xyplot(yield ~ period|block, data=dat, group=cow, type=c('l','r'),
       auto.key=list(columns=6),
       main="lucas.switchback - (actually uniformity data)")

# Need to use 'terms' to preserve the order of the model terms
# Really, cow(block), per:cow(block), period(block)
m1 <- aov(terms(yield ~ block + cow:block + per:cow:block +
                period:block + trt, keep.order=TRUE), data=dat)
anova(m1) # Match Sanders & Gaynor table 3
#> Analysis of Variance Table
#> 
#> Response: yield
#>               Df  Sum Sq Mean Sq F value    Pr(>F)    
#> block          2   30.93  15.464  55.345 5.132e-05 ***
#> block:cow      9 1700.97 188.997 676.426 1.907e-09 ***
#> block:cow:per 12  120.47  10.040  35.932 4.137e-05 ***
#> block:period   3   14.85   4.950  17.717  0.001194 ** 
#> trt            2    1.58   0.789   2.825  0.126048    
#> Residuals      7    1.96   0.279                      
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Variance Table
##               Df  Sum Sq Mean Sq F value    Pr(>F)
## block          2   30.93  15.464  55.345 5.132e-05 ***
## block:cow      9 1700.97 188.997 676.426 1.907e-09 ***
## block:cow:per 12  120.47  10.040  35.932 4.137e-05 ***
## block:period   3   14.85   4.950  17.717  0.001194 **
## trt            2    1.58   0.789   2.825  0.126048
## Residuals      7    1.96   0.279

coef(m1) # trtT2 and trtT3 match Sanders table 3 trt diffs
#>        (Intercept)            blockB2            blockB3     blockB3:cowC10 
#>         37.5833333         -4.1750000        -14.7250000         18.0083333 
#>     blockB3:cowC11      blockB1:cowC2      blockB1:cowC3      blockB1:cowC4 
#>          4.6041667        -12.5375000         -1.1416667         14.9402778 
#>      blockB1:cowC5      blockB1:cowC6      blockB2:cowC7      blockB2:cowC8 
#>        -15.1555556        -10.9305556         -1.0291667          5.7416667 
#>  blockB1:cowC1:per blockB3:cowC10:per blockB3:cowC11:per blockB3:cowC12:per 
#>         -3.0500000         -2.1500000         -1.1500000         -1.0000000 
#>  blockB1:cowC2:per  blockB1:cowC3:per  blockB1:cowC4:per  blockB1:cowC5:per 
#>         -2.1000000         -2.7000000         -3.4500000         -0.0500000 
#>  blockB1:cowC6:per  blockB2:cowC7:per  blockB2:cowC8:per  blockB2:cowC9:per 
#>         -0.7500000         -1.8500000         -3.4000000         -2.2000000 
#>   blockB1:periodP2   blockB2:periodP2   blockB3:periodP2              trtT2 
#>          1.4833333          1.1166667          1.3333333         -0.5333333 
#>              trtT3 
#>         -0.5541667