Data from an Oats Field Trial

The yield of oats from a split-plot field trial using three varieties and four levels of manurial treatment. The experiment was laid out in 6 blocks of 3 main plots, each split into 4 sub-plots. The varieties were applied to the main plots and the manurial treatments to the sub-plots.

oats

Format

This data frame contains the following columns:

B

Blocks, levels I, II, III, IV, V and VI.

V

Varieties, 3 levels.

N

Nitrogen (manurial) treatment, levels 0.0cwt, 0.2cwt, 0.4cwt and 0.6cwt, showing the application in cwt/acre.

Y

Yields in 1/4lbs per sub-plot, each of area 1/80 acre.

Source

Yates, F. (1935) Complex experiments, Journal of the Royal Statistical Society Suppl. 2, 181--247.

Also given in Yates, F. (1970) Experimental design: Selected papers of Frank Yates, C.B.E, F.R.S. London: Griffin.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

oats$Nf <- ordered(oats$N, levels = sort(levels(oats$N)))
oats.aov <- aov(Y ~ Nf*V + Error(B/V), data = oats, qr = TRUE)
summary(oats.aov)
#> 
#> Error: B
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> Residuals  5  15875    3175               
#> 
#> Error: B:V
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> V          2   1786   893.2   1.485  0.272
#> Residuals 10   6013   601.3               
#> 
#> Error: Within
#>           Df Sum Sq Mean Sq F value   Pr(>F)    
#> Nf         3  20020    6673  37.686 2.46e-12 ***
#> Nf:V       6    322      54   0.303    0.932    
#> Residuals 45   7969     177                     
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
summary(oats.aov, split = list(Nf=list(L=1, Dev=2:3)))
#> 
#> Error: B
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> Residuals  5  15875    3175               
#> 
#> Error: B:V
#>           Df Sum Sq Mean Sq F value Pr(>F)
#> V          2   1786   893.2   1.485  0.272
#> Residuals 10   6013   601.3               
#> 
#> Error: Within
#>             Df Sum Sq Mean Sq F value   Pr(>F)    
#> Nf           3  20020    6673  37.686 2.46e-12 ***
#>   Nf: L      1  19536   19536 110.323 1.09e-13 ***
#>   Nf: Dev    2    484     242   1.367    0.265    
#> Nf:V         6    322      54   0.303    0.932    
#>   Nf:V: L    2    168      84   0.475    0.625    
#>   Nf:V: Dev  4    153      38   0.217    0.928    
#> Residuals   45   7969     177                     
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
par(mfrow = c(1,2), pty = "s")
plot(fitted(oats.aov[[4]]), studres(oats.aov[[4]]))
abline(h = 0, lty = 2)
oats.pr <- proj(oats.aov)
qqnorm(oats.pr[[4]][,"Residuals"], ylab = "Stratum 4 residuals")
qqline(oats.pr[[4]][,"Residuals"])

par(mfrow = c(1,1), pty = "m")
oats.aov2 <- aov(Y ~ N + V + Error(B/V), data = oats, qr = TRUE)
model.tables(oats.aov2, type = "means", se = TRUE)
#> Warning: SEs for type 'means' are not yet implemented
#> Tables of means
#> Grand mean
#>          
#> 103.9722 
#> 
#>  N 
#> N
#> 0.0cwt 0.2cwt 0.4cwt 0.6cwt 
#>  79.39  98.89 114.22 123.39 
#> 
#>  V 
#> V
#> Golden.rain  Marvellous     Victory 
#>      104.50      109.79       97.63