# aov.sufficient

##### Analysis of variance from sufficient statistics for groups.

Analysis of variance from sufficient statistics for groups.
For each group, we need the factor level, the response mean, the
within-group standard deviation, and the sample size.
The correct ANOVA table is produced. The residuals are fake.
The generic `vcov`

and `summary.lm`

don't work for the
variance of the regression coefficients in this case.
Use `vcov.sufficient`

.

- Keywords
- htest

##### Usage

```
aov.sufficient(formula, data = NULL,
projections = FALSE, qr = TRUE, contrasts = NULL,
weights = data$n, sd = data$s,
...)
```vcov.sufficient(object, ...)

##### Arguments

##### Value

- For
`aov.sufficient`

, an object of class c("aov", "lm"). For`vcov.sufficient`

, a function that returns the covariance matrix of the regression coefficients.

##### Note

The residuals are fake. They are all identical and equal to the MLE
standard error (`sqrt(SumSq.res/df.tot)`

). They give the right
ANOVA table. They may cause confusion or warnings in other programs.
The standard errors and t-tests of the coefficients are not calculated
by `summary.lm`

.
Using the `aov`

object from `aov.sufficient`

in `glht`

requires the `vcov.`

and `df`

arguments.

##### See Also

##### Examples

```
## This example is from Hsu and Peruggia
## This is the R version
## See ?aov.sufficient for S-Plus
if.R(s={},
r={
pulmonary <- read.table(hh("datasets/pulmonary.dat"), header=TRUE,
row.names=NULL)
names(pulmonary)[3] <- "FVC"
names(pulmonary)[1] <- "smoker"
pulmonary$smoker <- factor(pulmonary$smoker, levels=pulmonary$smoker)
row.names(pulmonary) <- pulmonary$smoker
pulmonary
pulmonary.aov <- aov.sufficient(FVC ~ smoker,
data=pulmonary)
summary(pulmonary.aov)
pulmonary.mca <- glht(pulmonary.aov,
linfct=mcp(smoker="Tukey"),
df=pulmonary.aov$df.residual,
vcov.=vcov.sufficient)
plot(pulmonary.mca)
pulm.lmat <- cbind("npnl-mh"=c( 1, 1, 1, 1,-2,-2), ## not.much vs lots
"n-pnl" =c( 3,-1,-1,-1, 0, 0), ## none vs light
"p-nl" =c( 0, 2,-1,-1, 0, 0), ## {} arbitrary 2 df
"n-l" =c( 0, 0, 1,-1, 0, 0), ## {} for 3 types of light
"m-h" =c( 0, 0, 0, 0, 1,-1)) ## moderate vs heavy
dimnames(pulm.lmat)[[1]] <- row.names(pulmonary)
if.R(r=pulm.lmat <- rbind(Int=0, pulm.lmat[-1,]),
s={})
pulm.lmat
pulmonary.mmc <- glht.mmc(pulmonary.aov,
linfct=mcp(smoker="Tukey"),
df=pulmonary.aov$df.residual,
vcov.=vcov.sufficient,
lmat=pulm.lmat,
calpha=attr(confint(pulmonary.mca)$confint,"calpha"))
plot(pulmonary.mmc, print.mca=TRUE, print.lmat=FALSE)
## tiebreaker plot, with contrasts ordered to match MMC plot,
## with all contrasts forced positive and with names also reversed,
## and with matched x-scale.
plot(confint(as.glht(pulmonary.mmc$mca)),
xlim=par()$usr[1:2], xaxs="i",
main="", xlab="")
## orthogonal contrasts
plot(pulmonary.mmc, print.lmat=TRUE, col.lmat.signif='blue', col.iso='gray')
## pairwise and orthogonal contrasts on the same plot
plot(pulmonary.mmc, print.mca=TRUE, print.lmat=TRUE,
col.mca.signif='red', col.lmat.signif='blue', col.iso='gray',
lty.lmat.not.signif=2)
})
```

*Documentation reproduced from package HH, version 1.18-1, License: GPL version 2 or newer*