R: Examples for 'stats::aov'

### ** Examples

## From Venables and Ripley (2002) p.165.

## Set orthogonal contrasts.
op <- options(contrasts = c("contr.helmert", "contr.poly"))
( npk.aov <- aov(yield ~ block + N*P*K, npk) )

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 are balanced

## No test: 
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

## End(No test)
coefficients(npk.aov)

(Intercept)      block1      block2      block3      block4      block5 
 54.8750000   1.7125000   1.6791667  -1.8229167  -1.0137500   0.2950000 
         N1          P1          K1       N1:P1       N1:K1       P1:K1 
  2.8083333  -0.5916667  -1.9916667  -0.9416667  -1.1750000   0.1416667

## to show the effects of re-ordering terms contrast the two fits
aov(yield ~ block + N * P + K, npk)

Call:
   aov(formula = yield ~ block + N * P + K, data = npk)

Terms:
                   block        N        P        K      N:P Residuals
Sum of Squares  343.2950 189.2817   8.4017  95.2017  21.2817  218.9033
Deg. of Freedom        5        1        1        1        1        14

Residual standard error: 3.954232
Estimated effects are balanced

aov(terms(yield ~ block + N * P + K, keep.order = TRUE), npk)

Call:
   aov(formula = terms(yield ~ block + N * P + K, keep.order = TRUE), 
    data = npk)

Terms:
                   block        N        P      N:P        K Residuals
Sum of Squares  343.2950 189.2817   8.4017  21.2817  95.2017  218.9033
Deg. of Freedom        5        1        1        1        1        14

Residual standard error: 3.954232
Estimated effects are balanced

## as a test, not particularly sensible statistically
npk.aovE <- aov(yield ~  N*P*K + Error(block), npk)
npk.aovE

Call:
aov(formula = yield ~ N * P * K + Error(block), data = npk)

Grand Mean: 54.875

Stratum 1: block

Terms:
                    N:P:K Residuals
Sum of Squares   37.00167 306.29333
Deg. of Freedom         1         4

Residual standard error: 8.750619
Estimated effects are balanced

Stratum 2: Within

Terms:
                        N         P         K       N:P       N:K       P:K
Sum of Squares  189.28167   8.40167  95.20167  21.28167  33.13500   0.48167
Deg. of Freedom         1         1         1         1         1         1
                Residuals
Sum of Squares  185.28667
Deg. of Freedom        12

Residual standard error: 3.929447
Estimated effects are balanced

## IGNORE_RDIFF_BEGIN
summary(npk.aovE)

Error: block
          Df Sum Sq Mean Sq F value Pr(>F)
N:P:K      1   37.0   37.00   0.483  0.525
Residuals  4  306.3   76.57               

Error: Within
          Df Sum Sq Mean Sq F value  Pr(>F)   
N          1 189.28  189.28  12.259 0.00437 **
P          1   8.40    8.40   0.544 0.47490   
K          1  95.20   95.20   6.166 0.02880 * 
N:P        1  21.28   21.28   1.378 0.26317   
N:K        1  33.14   33.14   2.146 0.16865   
P:K        1   0.48    0.48   0.031 0.86275   
Residuals 12 185.29   15.44                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## IGNORE_RDIFF_END
options(op)  # reset to previous

Examples for 'stats::aov'

Fit an Analysis of Variance Model