Latin Square Design

library(agridat)

dat = depalluel.sheep

#my version loaded in
dat = read.csv("~/Downloads/sheep.csv")
attach(dat)

print(dat)

##        Food          Breed  Month Weight.difference
## 1  Potatoes Isle de France  First             10.00
## 2  Potatoes         Beauce Fourth             24.25
## 3  Potatoes      Champagne  Third             14.75
## 4  Potatoes        Picardy Second             13.00
## 5   Turnips Isle de France Second             18.00
## 6   Turnips         Beauce  First             15.00
## 7   Turnips      Champagne Fourth             16.00
## 8   Turnips        Picardy  Third             18.50
## 9     Beets Isle de France  Third             22.00
## 10    Beets         Beauce Second             15.25
## 11    Beets      Champagne  First             13.25
## 12    Beets        Picardy Fourth             21.00
## 13     Corn Isle de France Fourth             32.00
## 14     Corn         Beauce  Third             22.50
## 15     Corn      Champagne Second             22.00
## 16     Corn        Picardy  First             16.00

#latin square ANOVA
model = lm(Weight.difference ~ Food + Breed + Month)

#anova table
anova(model)

## Analysis of Variance Table
## 
## Response: Weight.difference
##           Df  Sum Sq Mean Sq F value  Pr(>F)  
## Food       3 133.297  44.432  4.0955 0.06703 .
## Breed      3  41.422  13.807  1.2727 0.36538  
## Month      3 201.547  67.182  6.1925 0.02875 *
## Residuals  6  65.094  10.849                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

At alpha = .05, there is no significant effect of grain diet on weight difference for sheep.