# npk: Classical N, P, K Factorial Experiment In MASS: Support Functions and Datasets for Venables and Ripley's MASS

## 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

 `1` ```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).

## Note

This dataset is also contained in R 3.0.2 and later.

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```options(contrasts = c("contr.sum", "contr.poly")) npk.aov <- aov(yield ~ block + N*P*K, npk) npk.aov summary(npk.aov) alias(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) ```

### Example output

```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
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
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

(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

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

[1] 1.609175
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
```

MASS documentation built on April 30, 2018, 9:03 a.m.