1.
Exploratory Data Analysis
1.3.
EDA Techniques
1.3.3.
Graphical Techniques: Alphabetic
1.3.3.13.
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DEX Standard Deviation Plot
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Purpose:
Detect Important Factors with Respect to Scale
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The dex standard deviation plot is appropriate for analyzing
data from a designed experiment, with respect to important
factors, where the factors are at two or more levels and there
are repeated values at each level. The plot
shows standard deviation values for the two or more levels of
each factor plotted by factor. The standard deviations for a
single factor are connected by a straight line. The dex
standard deviation plot is a complement to the traditional
analysis of variance
of designed experiments.
This plot is typically generated for the standard deviation.
However, it can also be generated for other scale statistics
such as the range, the median absolute deviation, or the
average absolute deviation.
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Sample Plot
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This sample dex standard deviation plot shows that:
- factor 1 has the greatest difference in standard
deviations between factor levels;
- factor 4 has a significantly lower average standard
deviation than the average standard deviations of
other factors (but the level 1 standard deviation
for factor 1 is about the same as the level 1
standard deviation for factor 4);
- for all factors, the level 1 standard deviation is
smaller than the level 2 standard deviation.
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Definition:
Response Standard Deviations Versus Factor Variables
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Dex standard deviation plots are formed by:
- Vertical axis: Standard deviation of the response
variable for each level of the factor
- Horizontal axis: Factor variable
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Questions
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The dex standard deviation plot can be used to answer the
following questions:
- How do the standard deviations vary across factors?
- How do the standard deviations vary within a factor?
- Which are the most important factors with respect to
scale?
- What is the ranked list of the important factors with
respect to scale?
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Importance:
Assess Variability
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The goal with many designed experiments is to determine
which factors are significant. This is usually determined
from the means of the factor levels (which can be
conveniently shown with a dex mean plot). A secondary goal
is to assess the variability of the responses both within
a factor and between factors. The dex standard deviation plot
is a convenient way to do this.
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Related Techniques
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Dex scatter plot
Dex mean plot
Block plot
Box plot
Analysis of
variance
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Case Study
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The dex standard deviation plot is demonstrated in the
ceramic strength
data case study.
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Software
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Dex standard deviation plots are not available in most general purpose
statistical software programs. It may be feasible to write macros for
dex standard deviation plots in some statistical software programs
that do not support them directly.
Dataplot supports
a dex standard deviation plot.
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