Fit an Analysis of Variance Model

Description

Fit an analysis of variance model by a call to lm for each stratum.

Usage

aov(formula, data = NULL, projections = FALSE, qr = TRUE,
    contrasts = NULL, ...)

Arguments

Details

This provides a wrapper to lm for fitting linear models to balanced or unbalanced experimental designs.

The main difference from lm is in the way print, summary and so on handle the fit: this is expressed in the traditional language of the analysis of variance rather than that of linear models.

If the formula contains a single Error term, this is used to specify error strata, and appropriate models are fitted within each error stratum.

The formula can specify multiple responses.

Weights can be specified by a weights argument, but should not be used with an Error term, and are incompletely supported (e.g., not by model.tables).

Value

An object of class c("aov", "lm") or for multiple responses of class c("maov", "aov", "mlm", "lm") or for multiple error strata of class c("aovlist", "listof"). There are print and summary methods available for these.

Note

aov is designed for balanced designs, and the results can be hard to interpret without balance: beware that missing values in the response(s) will likely lose the balance. If there are two or more error strata, the methods used are statistically inefficient without balance, and it may be better to use lme in package nlme.

Balance can be checked with the replications function.

The default ‘contrasts’ in R are not orthogonal contrasts, and aov and its helper functions will work better with such contrasts: see the examples for how to select these.

Author(s)

The design was inspired by the S function of the same name described in Chambers et al (1992).

References

Chambers, J. M., Freeny, A and Heiberger, R. M. (1992) Analysis of variance; designed experiments. Chapter 5 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

See Also

lm, summary.aov, replications, alias, proj, model.tables, TukeyHSD

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) )
summary(npk.aov)
coefficients(npk.aov)

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


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

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)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(stats)
> png(filename="/home/ddbj/snapshot/RGM3/R_rel/result/stats/aov.Rd_%03d_medium.png", width=480, height=480)
> ### Name: aov
> ### Title: Fit an Analysis of Variance Model
> ### Aliases: aov print.aov print.aovlist Error
> ### Keywords: models regression
> 
> ### ** 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
> 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
> options(op)  # reset to previous
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>