Stat 421, Fall 2008
Fritz Scholz
Homework 5
Due: October 31, 2008
Problem 1: Using the Flux data set, assume that for some reason we
received less data, say 5 for flux X and 5 for flux Y. In particular,
work with the flux data set, where the rows/boards 1,5,6,9,10,13,14,15
have been removed. Explain line by line what the following function does,
by embedding comment lines # ......
Note that there is a function fun0 defined within pval.delta. That works as long as
you define the function before you call it. See what happens if you define the function
after you first call it.
pval.delta = function (delta=0)
{
fun0=function(ind,y){mean(y[ind])-mean(y[-ind])}
# The following assumes that the original data set
# flux is in your work space.
flux0=flux[-c(1,5,6,9,10,13,14,15),]
SIR=flux0$SIR
FLUX=flux0$FLUX
sir.delta=SIR
sir.delta[FLUX=="Y"]=sir.delta[FLUX=="Y"]-delta
ybar.xbar.observed=mean(SIR[FLUX=="Y"])-delta-
mean(SIR[FLUX=="X"])
ybar.xbar.ref.dist=combn(1:10,5,FUN=fun0,y=sir.delta)
pval=mean(abs(ybar.xbar.ref.dist)>=.999999*abs(ybar.xbar.obs
erved))
pval
}
Think of delta as a possible effect due to flux difference.
By subtracting out that delta from all SIR values that were
treated with Y we remove such a difference effect. The test
of the null hypothesis (no difference in flux) should then lead
to acceptance (high p-values) as long as we remove the
right amount delta from the SIR values obtained under FLUX Y.
In effect we test the hypothesis that the effect of FLUX=Y is a
delta shift in the SIR values relative to the SIR values under FLUX=X.
After removing such a delta shift from SIR under FLUX Y we treat
