An EDA approach to experimental design
This section presents an
exploratory data analysis (EDA)
approach to analyzing the data from a designed experiment. This
material is meant to complement, not replace, the more model-based
approach for analyzing experiment designs given in
section 4 of this chapter.
Choosing an appropriate design is discussed in detail in
section 3 of this chapter.
The problem category we will address is the screening problem.
Two characteristics of screening problems are:
- There are many factors to consider.
- Each of these factors may be either continuous or
The desired output from the analysis of a screening problem is:
- A ranked list (by order of importance) of factors.
- The best settings for each of the factors.
- A good model.
The essentials of the screening problem are:
- There are k factors with n observations.
- The generic model is:
Y = f(X1,
Xk) + ε
In particular, the EDA approach is applied to 2k
full factorial and
fractional factorial designs.
An EDA approach is particularly applicable to screening designs
because we are in the preliminary stages of understanding our
EDA is not a single technique. It is an approach to analyzing
- EDA is data-driven. That is, we do not assume an initial
model. Rather, we attempt to let the data speak for
- EDA is question-based. That is, we select a technique
to answer one or more questions.
- EDA utilizes multiple techniques rather than depending on a
single technique. Different plots have a different basis,
focus, and sensitivities, and therefore may bring out different
aspects of the data. When multiple
techniques give us a redundancy of conclusions, this increases
our confidence that our conclusions are valid. When they give
conflicting conclusions, this may be giving us a clue as
to the nature of our data.
- EDA tools are often graphical. The primary objective is
to provide insight into the data, which graphical
techniques often provide more readily than quantitative
The following is a 10-step EDA process for analyzing the data
from 2k full factorial and
2k-p fractional factorial designs.
Each of these plots will be presented with the following format:
- Ordered data plot
- DOE scatter plot
- DOE mean plot
- Interaction effects matrix plot
- Block plot
- DOE Youden plot
- |Effects| plot
- Half-normal probability plot
- Cumulative residual standard
- DOE contour plot
- Purpose of the plot
- Output of the plot
- Definition of the plot
- Motivation for the plot
- An example of the plot using the defective springs data
- A discussion of how to interpret the plot
- Conclusions we can draw from the plot for the defective springs
Defective springs data
The plots presented in this section are demonstrated with
a data set from
Box and Bisgaard (1987).
These data are from a 23 full factorial data set that
contains the following variables:
- Response variable Y = percentage of springs without
- Factor 1 = oven temperature (2 levels: 1450 and 1600 F)
- Factor 2 = carbon concentration (2 levels: 0.5% and 0.7%)
- Factor 3 = quench temperature (2 levels: 70 and 120 F)
Y X1 X2 X3
Percent Oven Carbon Quench
Acceptable Temperature Concentration Temperature
67 -1 -1 -1
79 +1 -1 -1
61 -1 +1 -1
75 +1 +1 -1
59 -1 -1 +1
90 +1 -1 +1
52 -1 +1 +1
87 +1 +1 +1