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

## DOE Youden Plot

DOE Youden Plot: Introduction The DOE (Design of Experiments) Youden plot is a specialized Youden plot used in the analysis of full and fractional experiment designs. In particular, it is used in conjunction with the Yates algorithm. These designs may have a low level, coded as "-1" or "-", and a high level, coded as "+1" or "+", for each factor. In addition, there can optionally be one or more center points. Center points are at the midpoint between the low and high levels for each factor and are coded as "0".

The Yates agorithm and the the DOE Youden plot only use the "-1" and "+1" points. The Yates agorithm is used to estimate factor effects. The DOE Youden plot can be used to help determine the approriate model to based on the effect estimates from the Yates algorithm.

Construction of DOE Youden Plot The following are the primary steps in the construction of the DOE Youden plot.

1. For a given factor or interaction term, compute the mean of the response variable for the low level of the factor and for the high level of the factor. Any center points are omitted from the computation.

2. Plot the point where the y-coordinate is the mean for the high level of the factor and the x-coordinate is the mean for the low level of the factor. The character used for the plot point should identify the factor or interaction term (e.g., "1" for factor 1, "13" for the interaction between factors 1 and 3).

3. Repeat steps 1 and 2 for each factor and interaction term of the data.

The high and low values of the interaction terms are obtained by multiplying the corresponding values of the main level factors. For example, the interaction term X13 is obtained by multiplying the values for X1 with the corresponding values of X3. Since the values for X1 and X3 are either "-1" or "+1", the resulting values for X13 are also either "-1" or "+1".

In summary, the DOE Youden plot is a plot of the mean of the response variable for the high level of a factor or interaction term against the mean of the response variable for the low level of that factor or interaction term.

For unimportant factors and interaction terms, these mean values should be nearly the same. For important factors and interaction terms, these mean values should be quite different. So the interpretation of the plot is that unimportant factors should be clustered together near the grand mean. Points that stand apart from this cluster identify important factors that should be included in the model.

Sample DOE Youden Plot The following is a DOE Youden plot for the data used in the Eddy current case study. The analysis in that case study demonstrated that X1 and X2 were the most important factors.

Interpretation of the Sample DOE Youden Plot From the above DOE Youden plot, we see that factors 1 and 2 stand out from the others. That is, the mean response values for the low and high levels of factor 1 and factor 2 are quite different. For factor 3 and the 2 and 3-term interactions, the mean response values for the low and high levels are similar.

We would conclude from this plot that factors 1 and 2 are important and should be included in our final model while the remaining factors and interactions should be omitted from the final model.

Case Study The Eddy current case study demonstrates the use of the DOE Youden plot in the context of the analysis of a full factorial design.
Software DOE Youden plots are not typically available as built-in plots in statistical software programs. However, it should be relatively straightforward to write a macro to generate this plot in most general purpose statistical software programs.