2.42.4.1 Analyze Variability

Contents

Introduction

Analyze Variability in DOE examines how experimental factors influence not just the average response (location), but the spread or consistency of that response (dispersion). Standard DOE optimizes mean performance; variability analysis ensures that optimum is also stable and robust.

Use this analysis when your design includes replicates (multiple observations per run) and you suspect that some factors affect consistency rather than just the average.

Supported design types

Input Data and Summarizing

The input data for DOE variability analysis requires replicate observations — multiple independent measurements taken at each combination of factor settings.

The data can be arranged in two ways:

Replicates Stored in Separate Adjacent Columns

  1. Activate the worksheet containing your factorial design data (generated via Generate Factorial Design or Define Custom Design), in which the replicate measurements stored in separate adjacent columns
    DOE Analyze Variability Input Exp.png
  2. Select Statistics: Quality Improvement: Design of Experiment from the Origin menu
  3. Click the Analyze Variability icon and choose Summarize Response from the context menu
    DOE Analyze Variability.png
  4. In the opened dialog, select Compute for repeat responses across rows and select the responses, then click OK.
    DOE Analyze Variability Summarized Input O1.png
  5. This generates the SD, N and Mean column
    DOE Analyze Variability Summarized Input.png

Replicates Stacked inside Individual Columns

  1. Activate the worksheet containing your factorial design data (generated via Generate Factorial Design or Define Custom Design).
    DOE Analyze Variability Input Exp2.png
  2. Select Statistics: Quality Improvement: Design of Experiment from the Origin menu
  3. Click the Analyze Variability icon and choose Summarize Response from the context menu
  4. In the opened dialog, select Compute for repeat responses across rows and select the responses, then click OK .
    DOE Analyze Variability Summarized Input O2.png
  5. This generates the SD and N columns
    DOE Analyze Variability Summarized Result2.png

Run the Analysis

  1. Select Statistics: Quality Improvement: Design of Experiment from the Origin menu
  2. Click the Analyze Variability icon and choose Analyze Variability from the context menu
    DOE Analyze Variability.png
  3. In the Model tab of the dialog, specify the Response(Standard Deviation) column, and Number of Repeats/Replicates column.
    DOE Analyze Variability Input Dlg.png

The remaining options in the analysis dialog are the same as Analyze Factorial Design dialog

Results of Analyze Variability

Analyze Variability fits a model to the natural log of the standard deviation (or variance). The session-window tables parallel those from standard factorial analysis, with two adaptations: the response is log-transformed spread rather than the mean, and the coefficients table includes Ratio Effect columns. The output tables are otherwise largely similar, with the following exceptions.

For detailed guidance on interpreting general DOE results, See the Interpreting DOE Results

Coded Coefficients

The table, available on the report sheet, shows how each factor affects the log-standard deviation.

Effect Change in ln(SD) when the factor moves from its low (-1) to high (+1) level.
Ratio Effect exp(Effect). The multiplicative factor by which the actual standard deviation changes at the high level versus the low level.
Value The regression coefficient
Prob>|t| P-value. Values below 0.05 indicate a statistically significant dispersion effect.
VIF Variance inflation factor. Values much larger than 1 suggest multicollinearity among model terms.
Means Table

This table, available on the report sheet, displays the marginal fitted means for each factor level in the variability model. Because the analysis models the natural log of the standard deviation, the "Fitted Mean" column is in ln(SD) units, while "Fit (Original)" back-transforms that value into the predicted standard deviation in original measurement units.

Value The actual factor level setting (uncoded units).
Fitted Mean Predicted ln(SD) at that factor level, averaged across all other factors.
SE Mean Standard error of the fitted mean.
Fit (Original) exp(Fitted Mean) - the predicted standard deviation in original units.
Diagnostics

The diagnostics are displayed in fitted result worksheet, named DOEFittedResultItalic text

Fitted Values

Fitted Values (Ln Units) Predictions in the transformed scale
Fitted Values (Original) exp(fitted ln value), giving the predicted SD in the original measurement units.

Residuals

Ln Residuals computed in the log-transformed scale: observed ln(SD)-fitted ln(SD)
Ratio The ratio of observed to fitted standard deviation in original units, equivalent to exp(Ln residual)
  • A ratio of 1.0 means perfect prediction.
  • Ratios > 1 indicate the run was more variable than predicted; ratios < 1 indicate less variable.
Standardized Ln The Ln residuals divided by their standard error (studentized or standardized form). Use these to identify outliers objectively.
  • Values beyond +-3 flag runs where the model poorly explains the observed variability, warranting further investigation.