Generates Full or Half-Normal Plots

DESCRIPTION:

Full-normal or half-normal plots of the effects estimated from the analysis of a fractional factorial design.

USAGE:

qqnorm(x, method=<<see below>>, sig=.05, omit=F, slope, label="sig",  
          datax=T, full=F, legend.loc, ...) 

REQUIRED ARGUMENTS:

x
object of class "fac.aov".

OPTIONAL ARGUMENTS:

method
character string specifying the method used to estimate the standard error of the effects for drawing significance limits and slope lines on the plot.
`"mse"'

uses an estimate of the standard error of the factorial effects based on mean squared error.

`"pse"'
uses a pseudo standard error estimate.
`"tse"'
uses a 60% trimmed standard error of the effects.
`"ase"'
uses an adaptive standard error estimate.
`"all"'
all the available methods are used.

The default is "pse", unless "mse" is available, in which case both "pse" and "mse" are used.
sig
value giving significance level for significance lines. Default is .05.
omit
integer or "sig", giving how many large effects to omit from plot. If omit is an integer, that many largest effects are omitted. If omit = "sig" all significant effects are omitted. A half-normal plot of effects should "straighten out" when significant effects are removed. By default, no effects are omitted from the plot.
slope
logical value for whether to plot slope lines and significance lines for the standard error estimates. If TRUE, lines with intercept=0 and slope=1/(standard error) are plotted for each method given in the method parameter (if datax = F, slope = standard error). If full = F, significance limits are also plotted at level given by sig.
label
logical integer or "sig" for labelling of points. If FALSE, no labelling is done. If TRUE, the user is prompted to identify the points to label. If a single number, n, the n largest effects will be labeled. If "sig", all of the significant effects are labeled, with significance determined by sig and method. If more than one method is used, the method which results in the most significant effects is used to label the effects.
datax
logical value for which axis the data goes on: if TRUE, data goes on the x-axis; if FALSE data goes on the y-axis. Default is TRUE.
full
logical variable: TRUE produces a full-normal plot, FALSE a half-normal plot. When full=TRUE, the defaults become slope=FALSE, and label=FALSE. This creates a plot which is useful for identifying possible outliers.
legend.loc
vector of length 2 giving the x and y coordinates for the upper left hand corner of the legend.
...
arguments passed to the plot function.

VALUE:

NULL

SIDE EFFECTS:

a half or full normal plot is produced on the current graphics device.

METHOD:

The underlying assumption of the normal and half-normal plot is that the inactive or unimportant effects will be normally distributed with zero mean and an unknown standard deviation. Thus, the line drawn on the normal or half-normal plot has zero intercept and slope equal to an estimate of the standard deviation of the "inactive" effects. In general, points on a half-normal plot falling off a line (i.e., below the line on the right) drawn through the "center" of the data are considered to be possibly important effects. This function will draw a line with intercept 0 and slope determined by one of several methods. Drawing the line on the plot is equivalent to estimating the standard error of the inactive effects. The following methods are available for drawing lines on the plot:

ARGUMENTS:

(1) "mse": an estimate of the standard error of the effects calculated from root mean squared error,
(2) "pse": a psuedo standard error estimate (Lenth, 1989, Haaland and O'Connell, 1994),
(3) "tse": a 60% trimmed standard error of the effects (Berk and Picard, 1991, Haaland and O'Connell, 1994), and
(4) "ase": an adaptive estimate of the standard error of the effects (Dong, 1993, Haaland and O'Connell, 1994).

See Nair (1984) for more general information about estimating location and scale parameters by drawing lines on normal probability plots.

REFERENCES:

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., W. G. Hunter, J. S. Hunter (1978), Statistics for Experimenters, New York: Wiley.

Daniel, C. (1959), Use of half-normal plots in interpreting factorial two-level experiments, Technometrics, 1, 311-341.

Dong, F. (1993). "On the Idendification of Active Contrasts in Unreplicated Fractional Factorials." Statistica Sinica, 3, 209-217.

Haaland, P. D. (1989), Experimental Design in Biotechnology, New York: Marcel Dekker.

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 factorials, Technometrics, 31, 469-473.

Nair, V. J. (1984), On the behavior of some estimators from probability plots, Journal of the American Statistical Association, 79, 823-831.

SEE ALSO:

, , , , , , , .

EXAMPLES:

buffer.fac <- fac.aov(buffer.df) 
qqnorm(buffer.fac)  # use all defaults 
qqnorm(buffer.fac, label=T)  # interactively identify effects to label 
# specify different methods for plotting lines: 
qqnorm(buffer.fac, "ase", .10) 
qqnorm(buffer.fac, method="all") 
# omit certain significant effects from plot: 
qqnorm(buffer.fac, omit="sig", method="all") 
qqnorm(buffer.fac, omit=4, method="all") 
# put data on y axis: 
qqnorm(buffer.fac, datax=F) 
qqnorm(buffer.fac, datax=F, method="all") 
# produce full-normal plots with various options: 
qqnorm(buffer.fac, full=T) 
qqnorm(buffer.fac, full=T, datax=F, method="all")