Classical N, P, K Factorial Experiment

Description

A 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.

Usage

npk

Format

The npk data frame has 24 rows and 5 columns:

block

which block (label 1 to 6).

N

indicator (0/1) for the application of nitrogen.

P

indicator (0/1) for the application of phosphate.

K

indicator (0/1) for the application of potassium.

yield

Yield of peas, in pounds/plot (the plots were (1/70) acre).

Source

Imperial College, London, M.Sc. exercise sheet.

References

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

Examples

options(contrasts = c("contr.sum", "contr.poly"))
npk.aov <- aov(yield ~ block + N*P*K, npk)
npk.aov
summary(npk.aov)
coef(npk.aov)
options(contrasts = c("contr.treatment", "contr.poly"))
npk.aov1 <- aov(yield ~ block + N + K, data = npk)
summary.lm(npk.aov1)
se.contrast(npk.aov1, list(N=="0", N=="1"), data = npk)
model.tables(npk.aov1, type = "means", se = TRUE)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> library(datasets)
> png(filename="/home/ddbj/snapshot/RGM3/R_rel/result/datasets/npk.Rd_%03d_medium.png", width=480, height=480)
> ### Name: npk
> ### Title: Classical N, P, K Factorial Experiment
> ### Aliases: npk
> ### Keywords: datasets
> 
> ### ** Examples
> ## No test: 
> options(contrasts = c("contr.sum", "contr.poly"))
> npk.aov <- aov(yield ~ block + N*P*K, npk)
> npk.aov
Call:
   aov(formula = yield ~ block + N * P * K, data = npk)

Terms:
                   block        N        P        K      N:P      N:K      P:K
Sum of Squares  343.2950 189.2817   8.4017  95.2017  21.2817  33.1350   0.4817
Deg. of Freedom        5        1        1        1        1        1        1
                Residuals
Sum of Squares   185.2867
Deg. of Freedom        12

Residual standard error: 3.929447
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  343.3   68.66   4.447 0.01594 * 
N            1  189.3  189.28  12.259 0.00437 **
P            1    8.4    8.40   0.544 0.47490   
K            1   95.2   95.20   6.166 0.02880 * 
N:P          1   21.3   21.28   1.378 0.26317   
N:K          1   33.1   33.14   2.146 0.16865   
P:K          1    0.5    0.48   0.031 0.86275   
Residuals   12  185.3   15.44                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> coef(npk.aov)
(Intercept)      block1      block2      block3      block4      block5 
 54.8750000  -0.8500000   2.5750000   5.9000000  -4.7500000  -4.3500000 
         N1          P1          K1       N1:P1       N1:K1       P1:K1 
 -2.8083333   0.5916667   1.9916667  -0.9416667  -1.1750000   0.1416667 
> 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 
-6.4083 -2.1438  0.2042  2.3292  7.0750 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   53.208      2.276  23.381  8.5e-14 ***
block2         3.425      2.787   1.229  0.23690    
block3         6.750      2.787   2.422  0.02769 *  
block4        -3.900      2.787  -1.399  0.18082    
block5        -3.500      2.787  -1.256  0.22723    
block6         2.325      2.787   0.834  0.41646    
N1             5.617      1.609   3.490  0.00302 ** 
K1            -3.983      1.609  -2.475  0.02487 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.942 on 16 degrees of freedom
Multiple R-squared:  0.7163,	Adjusted R-squared:  0.5922 
F-statistic: 5.772 on 7 and 16 DF,  p-value: 0.001805

> se.contrast(npk.aov1, list(N=="0", N=="1"), data = npk)
[1] 1.609175
> 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 60.77 50.12 50.52 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
> ## End(No test)
> 
> 
> 
> 
> dev.off()
null device 
          1 
>