Half-normal plots (Daniel plots) of effects

The hnplot function constructs a (half-) normal plot of effects (see Daniel 1959) that is traditionally used to identify active effects in a screening experiment. Reference lines and various other options and extensions are supported.

Usage

hnplot(effects, ref = TRUE, half = TRUE, horiz = TRUE, method = "Zahn", 
       a = 0.375, col = half, pch = 16, ID = FALSE, alpha, ...)

Arguments

effects

Numeric vector of effects or contrasts to be explored.

ref

Logical value. If TRUE, a reference line is added to the plot determined by method. If FALSE, no reference is shown.

half

Logical value. If TRUE, a plot based on the absolute effects is constructed. If FALSE (not recommended: see Details), the original signed effects are used.

horiz

Logical value. If TRUE, the (absolute) effects are plotted on the horizontal scale and the (half-) normal scores or labels are plotted on the vertical scale. If FALSE, these axes are reversed.

method

Character value. When ref is TRUE, the method to use in determining the reference line, curve, and/or critical values. This must be the name of a provided pseudo-standard-error method (see PSE), or a compatible user-supplied one.

a

The adjustment used in scaling and centering ranks in the interval (0, 1). The \(i\)th ordered (half-) normal score is computed as the \((i - a) / (n + 1 - 2*a)\) quantile of the reference distribution.

col

Scalar or vector of colors; or a logical value. If logical, a value of TRUE colors the positive effects blue, the negative effects red, and any zeros as black. A logical value of FALSE colors them all black.

pch

Plotting character(s) to use.

alpha

Numeric value. If specified, a null reference distribution for method is used (see ref.dist) to determine a margin of error (labeled ‘ME’) and simultaneous margin of error (labeled ‘SME’) corresponding to a significance level of alpha, and reference lines are added to the plot at those positions as an aid to assessing the statistical significance of the effects. This is based on a suggestion in Mee (2015). These reference lines are omitted when alpha is left unspecified.

ID

Logical or numeric value. If logical and TRUE, then after the plot is contructed, the plot is put in identify mode, where the user may click on points to be labeled on the plot. If a numeric value is supplied, it is used as a threshold by which all effects greater than ID[1] in absolute value are labeled.

...

Additional graphical parameters (see par) used in constructing the plot.

Details

Use of half = FALSE is not recommended because it can be misleading to the user. Inactive effects are those that are close to zero, and a regular normal plot displays deviations from normality rather than deviations from zero.

References

Daniel, C (1959) Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments. Technometrics, 1(4), 311-341

Mee, R (2015) Discussion: Better, not Fewer, Plots. Journal of Quality Technology, 47(2), 107-109

Author

Russell V. Lenth

See also

Other ways of assessing active effects include a dot plot with a reference curve (refplot), a pareto plot of effects (see parplot), and a tabular style of presenting effects and \(P\) values (see eff.test). For more information on methods, see PSE and ref.dist.

Examples

require("unrepx")

hnplot(pdEff, ID = ME(pdEff))