Pseudo Standard Error
DESCRIPTION:
Returns an estimate of the pseudo standard error (PSE) of estimated effects from a fractional factorial design and the cumulative probabilities and quantiles for the distribution of the PSE based statistic described below.
USAGE: 
pse(x)
ppse(q,k)
qpse(p,k)
REQUIRED ARGUMENTS:
x:
vector of estimated effects. Missing values (NAs) are not allowed.
p:
vector of probabilities. Missing values (NAs) are allowed.
q:
vector of quantiles. Missing values (NAs) are allowed.
k:
number of estimated effects. k must be between 5 and 31, inclusive.
VALUE:
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.
DETAILS:
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 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.
BACKGROUND:
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.

REFERENCES:
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.

SEE ALSO:
ase , tse , fac.aov , summary.fac.aov , pareto.fac.aov , qqnorm.fac.aov , ebplot .
EXAMPLES: 
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)