pbperr: Distribution of F statistics corrected for back-projection...

In bbolker/cpcbp: common principal components/back-projection analysis

Description

Computes (by random simulation) the null F statistic (ratio of mean squares) for a back-projection ANOVA with a specified level of back-projection error

Usage

rbperr(n, df1, df2, bpms, atab, scaled, dvar=FALSE)
pbperr(x, df1, df2, bpms, atab, nsim = 20000,
lower.tail= TRUE, ...)
qbperr(q, df1, df2, bpms, atab, nsim = 20000, ...)
dbperr(x, df1, df2, bpms, atab, nsim = 20000, ...)

Arguments

x	An observed value
n	Number of deviates
q	Quantile
df1	Numerator (treatment) degrees of freedom
df2	Denominator (error) degrees of freedom
bpms	Estimated scaled mean square associated with back-projection error: if s2 is the back-projection variance, then bpms = s2*(N/df1)/ms.err
atab	an anova object: if specified, df1, df2, and s2.err will be extracted from it
nsim	Number of simulations
lower.tail	Return lower tail of cumulative distribution?
scaled	interpret bpms as scaled mean square or as back-projection variance? (default is TRUE if atab is provided, otherwise FALSE)
dvar	incorporate variance of MSE in the simulation? (I'm not yet sure which way is right)
...	additional arguments to rbperr

Details

The statistic returned is like an F(df1,df2) statistic, but the numerator adds an additional term c*bp.ms, where c is a chi-squared deviate with 1 df. The p, q, and d functions work by simulating values and finding the empirical cumulative density, quantile, or density (all three of these could be quite crude).

Value

Random deviates, estimated quantiles or cumulative densities as appropriate.

Note

A "p value" of 0 should best be interpreted as a p-value of (<1/nsim). WARNING: the functions are not completely vectorized.

Author(s)

Ben Bolker

See Also

bp.anova

Examples

  curve(df(x,5,10),from=0,to=10,lwd=2,col=1,n=200,
    xlab="Probability density")
  bvec = c(0,0.5,1,2)
  for (i in seq(along=bvec)) {
     curve(dbperr(x,5,10,bpms=bvec[i]),col=i+1,add=TRUE,n=200)
  }
  legend("topright",c("F(5,10)",paste("bperr (bpms=",bvec,")",sep="")),
     col=1:(length(bvec)+1),lty=1)

bbolker/cpcbp documentation built on May 11, 2019, 9:28 p.m.