1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.3. Graphical Techniques: Alphabetic

## DOE Standard Deviation Plot

Purpose:
Detect Important Factors With Respect to Scale
The DOE 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 DOE 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.

Sample Plot

This sample DOE standard deviation plot of the BOXBIKE2.DAT data set shows that:

1. factor 1 has the greatest difference in standard deviations between factor levels;
2. 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);
3. for all factors, the level 1 standard deviation is smaller than the level 2 standard deviation.
Definition:
Response Standard Deviations Versus Factor Variables
DOE standard deviation plots are formed by:
• Vertical axis: Standard deviation of the response variable for each level of the factor
• Horizontal axis: Factor variable
Questions The DOE standard deviation plot can be used to answer the following questions:
1. How do the standard deviations vary across factors?
2. How do the standard deviations vary within a factor?
3. Which are the most important factors with respect to scale?
4. What is the ranked list of the important factors with respect to scale?
Importance:
Assess Variability
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 DOE mean plot). A secondary goal is to assess the variability of the responses both within a factor and between factors. The DOE standard deviation plot is a convenient way to do this.
Related Techniques DOE scatter plot
DOE mean plot
Block plot
Box plot
Analysis of variance
Case Study The DOE standard deviation plot is demonstrated in the ceramic strength data case study.
Software DOE standard deviation plots are not available in most general purpose statistical software programs. It may be feasible to write macros for DOE standard deviation plots in some statistical software programs that do not support them directly.