pse(x) ppse(q,k) qpse(p,k)
pse
returns the estimated pseudo standard error of a set of estimated
effects.
ppse
and
qpse
return probabilities and quantiles for the
distribution of the PSE based statistic.
Elements of
q
or
p
that are missing will cause the corresponding
elements of the result to be missing. Values of the
ppse
and
qpse
are available for k = 5 to 31. The quantiles of the empirical cdf are
stored in a matrix
cdf.pse
for the values .70 to .99 by .01.
Thus the quantile associated with
p
between .70 and .99
is found in the kth row and
floor(p*100)-69
th column of
cdf.pse
.
Due to cost and time restrictions, industrial experimentation is often
geared toward the use of highly fractionated, unreplicated factorial
designs. These designs typically allow no degrees of freedom for the
estimation of error and are referred to by Box and Meyer (1986) as effect
saturated designs. Because there is no independent estimate of the
error, identification of important effects lies outside the range of
classical methods (Haaland and O'Connell 1994).
An approach to this problem which motivates the use of robust
estimators of scale is as follows: think of the estimated effects as a
sample from a zero mean normal distribution (the null effects)
contaminated by the non-null effects. Use robust methods to find an
estimate of the scale of the null effects that is insensitive to the
non-null effects. Then the estimated effects that are large compared to
this scale estimate correspond to the non-null effects.
The value of the PSE is included in the fac.aov object created in the
standard analysis of a fractional factorial design in S+DOX. The
reference distribution is used to provide approximate p-values in the
summary procedure and to draw a cut-off line for significant effects
on the pareto and half-normal plots. The estimated PSE is equal to
1/slope of the line through the null effects on the half-normal plot.
Tests based on the PSE are also used in the empirical bayes plot.
Box, G.E.P. and Meyer, R.D. (1986). "An Analysis for Unreplicated
Fractional Factorials." Technometrics, 28, 1-18.
Haaland, P. D. and M. A. O'Connell (1994), "Inference
for Effect Saturated Fractional Factorials,"
to appear in Technometrics.
Lenth, R. V. (1989), "Quick and Easy Analysis of
Unreplicated Fractional Factorials." Technometrics, 31, 469-473.
Zahn, D. A. (1975). "An Empirical Study of the Half-Normal Plot."
Technometrics, 17, 201-211.
buffer.fac <- fac.aov(buffer.df) buffer.fac$pse pse(buffer.fac$feffects) qpse(.95,15) summary(buffer.fac) pareto(buffer.fac) qqnorm(buffer.fac) ebplot(buffer.fac)