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Russ Lenth advocates that we abandon normal and half-normal plots of effects as a tool for analyzing 2^sup k^ and 2^sup k-p^ experiments. Whether or not we decide to bury these plots, let me begin by praising them.
The half-normal plot for two-level factorial designs was introduced by Daniel (1959) and henceforth, like Lenth, I will use the term Daniel plots to refer to both the normal and half-normal versions. Considering the tools available for data analysis in the 1950s, Daniel's ingenuity produced a remarkably successful method with a number of noteworthy properties:
* It is easy to produce.
* It gives a quick visual summary of which effects are the most important.
* Effects can be compared to a reference-the contrasts on a line through the origin-to assess whether or not they stand out from background noise.
* Outliers leave a distinguishing fingerprint and can often be detected.
* The plot may suggest the need for a transformation of the response data.
* The analysis adapts to split-plot experiments and can be used as a diagnostic tool to detect inadvertent split-plotting.
* All the orthogonal contrasts from the design are plotted, so the analysis is not dependent on specifying a particular model.
All the points above (with the exception of the last) were noted and explored by Daniel in his original paper and further elaborated in his book (Daniel (1976)).
More than 50 years have passed since Daniel's paper was published. Modern software offers many analysis and visualization alternatives for factorial experiments. Has the Daniel plot outlived its usefulness? On this basic question, I disagree with Lenth and will explain in what follows why I think that Daniel plots remain useful.
The greatest single advantage of the Daniel plot is its ability to stimulate discussion of the results of an experiment by encapsulating, in a single display, such a variety of information. In a Daniel plot, the experimenter can see how large are the factor effects, if they stand out from noise (including an automatic adjustment for multiple testing) and indicators of problems like outliers or need for transformation.
Lenth recommends the screening summary from JMP©, which includes an effect plot, estimates and p-values using Lenth's method (1989) (see his Figure 5). I agree...