Switchback experiment on dairy cattle, milk yield for 4 treatments

data("patterson.switchback")

Format

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

y: response, milk FCM
trt: treatment factor, 4 levels
period: period factor, 3 levls
cow: cow factor, 12 levels

Details

There are three periods. Each cow is assigned to one treatment cycle like T1-T2-T1, where T1 is the treatment in period P1 and P3, and T2 is the treatment in period P2.

There are four treatments.

All 4*3 = 12 treatment cycles are represented.

Data were extracted from Lowry, page 70.

Source

Patterson, H.D. and Lucas, H.L. 1962. Change-over designs. Technical Bulletin 147, North Carolina Agricultural Experimental Station.

References

Lowry, S.R. 1989. Statistical design and analysis of dairy nutrition experiments to improve detection of milk response differences. Proceedings of the Conference on Applied Statistics in Agriculture, 1989. https://newprairiepress.org/agstatconference/1989/proceedings/7/

Examples

# \dontrun{

library(agridat)
data(patterson.switchback)
dat <- patterson.switchback

# Create groupings for first treatment, second treatment
datp1 <- subset(dat, period=="P1")
datp2 <- subset(dat, period=="P2")
dat$p1trt <- datp1$trt[match(dat$cow, datp1$cow)]
dat$p2trt <- datp2$trt[match(dat$cow, datp2$cow)]
                     
libs(latticeExtra)
useOuterStrips(xyplot(y ~ period|p1trt*p2trt, data=dat,
                      group=cow, type=c('l','r'),
                      auto.key=list(columns=5),
                      main="patterson.switchback",
                      xlab="First/Third period treatment", 
                      ylab="Second period treatment"))


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

# Need to use 'terms' to preserve the order of the model terms
m1 <- aov(terms(y ~ cow + per:cow + period + trt, keep.order=TRUE), data=dat)
anova(m1) # Match table 2 of Lowry
#> Analysis of Variance Table
#> 
#> Response: y
#>           Df Sum Sq Mean Sq F value    Pr(>F)    
#> cow       11 3466.0 315.091 57.1773 2.258e-06 ***
#> cow:per   12  953.5  79.455 14.4182 0.0004017 ***
#> period     1   19.7  19.740  3.5821 0.0950382 .  
#> trt        3   58.3  19.418  3.5237 0.0685092 .  
#> Residuals  8   44.1   5.511                      
#> ---
#> 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)
## cow       11 3466.0 315.091 57.1773 2.258e-06 ***
## cow:per   12  953.5  79.455 14.4182 0.0004017 ***
## period     1   19.7  19.740  3.5821 0.0950382 .
## trt        3   58.3  19.418  3.5237 0.0685092 .
## Residuals  8   44.1   5.511

# }