npk.RdA classical N, P, K (nitrogen, phosphate, potassium) factorial experiment on the growth of peas conducted on 6 blocks. Each half of a fractional factorial design confounding the NPK interaction was used on 3 of the plots.
npkThe npk data frame has 24 rows and 5 columns:
blockwhich block (label 1 to 6).
Nindicator (0/1) for the application of nitrogen.
Pindicator (0/1) for the application of phosphate.
Kindicator (0/1) for the application of potassium.
yieldYield of peas, in pounds/plot (the plots were (1/70) acre).
This dataset is also contained in R 3.0.2 and later.
Imperial College, London, M.Sc. exercise sheet.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.
options(contrasts = c("contr.sum", "contr.poly"))
npk.aov <- aov(yield ~ block + N*P*K, npk)
## IGNORE_RDIFF_BEGIN
npk.aov
#> Call:
#> aov(formula = yield ~ block + N * P * K, data = npk)
#>
#> Terms:
#> block N P K N:P N:K P:K Residuals
#> Sum of Squares 343.29 189.28 8.40 95.20 21.28 33.14 0.48 185.29
#> Deg. of Freedom 5 1 1 1 1 1 1 12
#>
#> Residual standard error: 3.9294
#> 1 out of 13 effects not estimable
#> Estimated effects may be unbalanced
summary(npk.aov)
#> Df Sum Sq Mean Sq F value Pr(>F)
#> block 5 343 68.7 4.45 0.0159 *
#> N 1 189 189.3 12.26 0.0044 **
#> P 1 8 8.4 0.54 0.4749
#> K 1 95 95.2 6.17 0.0288 *
#> N:P 1 21 21.3 1.38 0.2632
#> N:K 1 33 33.1 2.15 0.1686
#> P:K 1 0 0.5 0.03 0.8628
#> Residuals 12 185 15.4
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
alias(npk.aov)
#> Model :
#> yield ~ block + N * P * K
#>
#> Complete :
#> (Intercept) block1 block2 block3 block4 block5 N1 P1 K1 N1:P1 N1:K1
#> N1:P1:K1 0 1 -1 -1 -1 1 0 0 0 0 0
#> P1:K1
#> N1:P1:K1 0
#>
coef(npk.aov)
#> (Intercept) block1 block2 block3 block4 block5
#> 54.87500 -0.85000 2.57500 5.90000 -4.75000 -4.35000
#> N1 P1 K1 N1:P1 N1:K1 P1:K1
#> -2.80833 0.59167 1.99167 -0.94167 -1.17500 0.14167
options(contrasts = c("contr.treatment", "contr.poly"))
npk.aov1 <- aov(yield ~ block + N + K, data = npk)
summary.lm(npk.aov1)
#>
#> Call:
#> aov(formula = yield ~ block + N + K, data = npk)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -6.408 -2.144 0.204 2.329 7.075
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 53.21 2.28 23.38 8.5e-14 ***
#> block2 3.42 2.79 1.23 0.237
#> block3 6.75 2.79 2.42 0.028 *
#> block4 -3.90 2.79 -1.40 0.181
#> block5 -3.50 2.79 -1.26 0.227
#> block6 2.32 2.79 0.83 0.416
#> N1 5.62 1.61 3.49 0.003 **
#> K1 -3.98 1.61 -2.48 0.025 *
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 3.94 on 16 degrees of freedom
#> Multiple R-squared: 0.716, Adjusted R-squared: 0.592
#> F-statistic: 5.77 on 7 and 16 DF, p-value: 0.00181
#>
se.contrast(npk.aov1, list(N=="0", N=="1"), data = npk)
#> [1] 1.6092
model.tables(npk.aov1, type = "means", se = TRUE)
#> Tables of means
#> Grand mean
#>
#> 54.875
#>
#> block
#> block
#> 1 2 3 4 5 6
#> 54.03 57.45 60.78 50.13 50.53 56.35
#>
#> N
#> N
#> 0 1
#> 52.07 57.68
#>
#> K
#> K
#> 0 1
#> 56.87 52.88
#>
#> Standard errors for differences of means
#> block N K
#> 2.787 1.609 1.609
#> replic. 4 12 12
## IGNORE_RDIFF_END