ase(x) pase(q,k) qase(p,k)
k
must be between 5 and 31, inclusive.
ase
returns the estimated adaptive standard error of a set of estimated
effects.
pase
and
qase
return probability and quantile vectors for the
distribution of the ASE based statistic.
Elements of
q
or
p
that are missing will cause the corresponding
elements of the result to be missing. Values of the
pase
and
qase
are available for
k
= 5 to 31. The quantiles of the empirical cdf are
stored in a matrix
cdf.ase
for the values .70 to .99 by .01.
Thus the quantile associated with
p
between .70 and .99
is found in the
k
th row and
floor(p*100)-69
th column of
cdf.ase
.
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.
Dong (1993) proposes the adaptive standard error (ASE) as a robust scale
estimator for this problem.
Haaland and O'Connell (1994) studied the properties of this and
several related tests. The ASE based test is recommended when there
is a priori reason to believe that there will be only a few significant
effects, say 0 to 3. However, the PSE (pseudo standard error -- Lenth,
1989) is recommended as an all around good test for identifying significant
effects in a saturated fractional factorial design.
The value of the ASE 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 ASE is equal to
1/slope of the line through the null effects on the half-normal plot.
Tests based on the ASE 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.
Dong, F. (1993). "On the Idendification of Active Contrasts in
Unreplicated Fractional Factorials." Statistica Sinica 3, 209-217.
Haaland, P. D. and M. A. O'Connell (1994), "Inference
for Effect Saturated Fractional Factorials", to apear 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$ase$ ase(buffer.fac$feffects$) qase(.95,15) summary(buffer.fac,method="ase") pareto(buffer.fac,method="ase") qqnorm(buffer.fac,method="ase") ebplot(buffer.fac,method="ase")