tse(x) ptse(q,k) qtse(p,k)
tse
returns the estimated trimmed standard error of a set of estimated
effects.
ptse
and
qtse
return probabilities and quantiles for the
distribution of the TSE based statistic.
Elements of
q
or
p
that are missing will cause the corresponding
elements of the result to be missing. Values of the
ptse
and
qtse
are available for k = 5 to 31. The quantiles of the empirical cdf are
stored in a matrix
cdf.tse
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.tse
.
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.
Berk and Picard (1991) proposes the trimmed standard error (TSE) as a
robust scale estimator for this problem.
Haaland and O'Connell (1994) studied the properties of this and
several related tests. The TSE based test is not as powerful as
the PSE (pseudo standard error, Lenth, 1989) based test but is an
acceptable alternative as long as there aren't too many non-null effects.
The value of the TSE 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 TSE is equal to
1/slope of the line through the null effects on the half-normal plot.
Tests based on the tse are also used in the empirical bayes plot.
Berk, K.N. and Picard, R.R. (1991). "Significance Tests for Saturated
Orthogonal Arrays." Journal of Quality Technology 23, 174-178.
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$tse tse(buffer.fac$feffects) qtse(.95,15) summary(buffer.fac,method="tse") pareto(buffer.fac,method="tse") qqnorm(buffer.fac,method="tse") ebplot(buffer.fac,method="tse")