# aovSufficient

##### 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 `vcovSufficient`

.

- Keywords
- htest

##### Usage

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

##### Arguments

- formula, data, projections, qr, contrasts, ...
- See#ifndef S-Plus
`aov`

. #endif #ifdef S-Plus`aov`

. #endif - weights
- See#ifndef S-Plus
`lm`

. #endif #ifdef S-Plus`lm`

. #endif - sd
- vector of within-group standard deviations.
- object
`"aov"`

object constructed by`aovSufficient`

. It also works with regular`aov`

objects.

##### Value

- For
`aovSufficient`

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

, 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 `aovSufficient`

in `glht`

requires the `vcov.`

and `df`

arguments.

##### See Also

##### Examples

```
## This example is from Hsu and Peruggia
## This is the R version
## See ?mmc.mean for S-Plus
if.R(s={},
r={
data(pulmonary)
pulmonary
pulmonary.aov <- aovSufficient(FVC ~ smoker,
data=pulmonary)
summary(pulmonary.aov)
pulmonary.mmc <- mmc(pulmonary.aov,
linfct=mcp(smoker="Tukey"),
df=pulmonary.aov$df.residual,
vcov.=vcovSufficient)
old.omd <- par(omd=c(.0,.95,0,1))
plot(pulmonary.mmc, ry=c(2.5, 3.4), x.offset=.05)
## tiebreaker plot, with contrasts ordered to match MMC plot,
## with all contrasts forced positive and with names also reversed,
## and with matched x-scale.
plotMatchMMC(pulmonary.mmc$mca)
## orthogonal contrasts
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)
pulm.lmat
pulmonary.mmc <- mmc(pulmonary.aov,
linfct=mcp(smoker="Tukey"),
df=pulmonary.aov$df.residual,
vcov.=vcovSufficient,
focus.lmat=pulm.lmat)
plot(pulmonary.mmc, ry=c(2.5, 3.4), x.offset=.05)
plotMatchMMC(pulmonary.mmc$lmat, col.signif='blue')
## pairwise and orthogonal contrasts on the same plot
plot(pulmonary.mmc, ry=c(2.5, 3.4), x.offset=.05,
print.mca=TRUE, print.lmat=TRUE)
par(old.omd)
})
```

*Documentation reproduced from package HH, version 2.3-37, License: GPL (>= 2)*