Free Form Folio: Analysis Results

When accessed from a free form folio, the Analysis Summary window will contain detailed information about analysis results, including information that describes how each factor and factorial interaction affects the response that is currently selected on the control panel.

Analysis Results

The following tables provide general information about the effects of the factors and factorial interactions on the selected response. This information may be presented for individual factors and interactions or for groups of factors and interactions, depending on your analysis setting on the control panel.

The Analysis of Variance (ANOVA) table includes the following columns:

Source of Variation is the source that caused the difference in the observed output values. This can be a factor, factorial interaction, curvature, block, error, etc. If your design includes more than one factor and you have selected to use grouped terms in the analysis (specified on the Analysis Settings page of the control panel), the effects will be grouped by order (i.e., main effects, two-way interactions, etc.). Sources displayed in red are considered to be significant.
The number of Degrees of Freedom for the Model is the number of regression coefficients for the effects included in the analysis (e.g., two coefficients might be included in the regression table for a given main effect). The number of degrees of freedom for the Residual is the total number of observations minus the number of parameters being estimated.
Sum of Squares is the amount of difference in observed output values caused by this source of variation.
Mean Squares is the average amount of difference caused by this source of variation. This is equal to Sum of Squares/Degrees of Freedom.
F Ratio is the ratio of Mean Squares of this source of variation and Mean Squares of pure error. A large value in this column indicates that the difference in the output caused by this source of variation is greater than the difference caused by noise (i.e., this source affects the output).
P Value (alpha error or type I error) is the probability that an equal amount of variation in the output would be observed in the case that this source does not affect the output. This value is compared to the risk level (alpha) that you specify on the Analysis Settings page of the control panel. If the p value is less than alpha, this source of variation is considered to have a significant effect on the output. In this case, the term and its p value will be displayed in red.
The following values are shown underneath the ANOVA table, and they indicate how well the model fits the data:

S is the standard error of the noise. It represents the magnitude of the response variation that is caused by noise. Lower values indicate better fit.
R-sq is the percentage of total difference that is attributable to the factors under consideration. It is equal to Sum of Squares(factor)/Total Sum of Squares. Higher values usually indicate better fit.
R-sq(adj) is an R-sq value that is adjusted for the number of parameters in the model. Higher values indicate better fit.

PRESS is the prediction error sum of squares, which provides a measure of the model’s validity. The lower the PRESS value, the better the model’s predictive ability.
R-sq(pred) is a measure of how well the model predicts new observations. It is equal to 1-PRESS/Total Sum of Squares. The larger the value, the more accurate the model’s predictions are likely to be.

This table includes the following columns:

- Model displays the model for which the results apply.
- - Reduced assumes that the product life is the same at different levels of the factor.
  - Full assumes that the product life is different at different levels of the factor.
- Degrees of Freedom is the degrees of freedom of this source of variation. This is also the number of parameters in the model for this source.
- Ln(Likelihood Value) is the logarithm transformation of the likelihood value for this source of variation.
- Likelihood Ratio is the likelihood ratio value for this source of variation.
- P Value is the probability that LR is from a chi-squared distribution, which would indicate that the factor has no effect on product life. This value is compared to the risk level (alpha) that you specify on the Analysis Settings page of the control panel. If the p value is less than alpha, then the factor is considered to have a significant effect on product life. In this case, the effect and its p value will be displayed in red.

The following tables provide specific information on the contribution of each predictor to the variation in the response and an analysis of the significance of this contribution.

This table includes the following columns:

Term is the factor, factorial interaction, curvature, block, etc. under consideration. Terms displayed in red are considered to be significant. In cases where there is no error in the model, significant effects are determined according to Lenth’s method and the term names are displayed in red and followed by an asterisk (*).

Coefficient is the regression coefficient of the term, which represents the contribution of the term to the variation in the response.
Standard Error is the standard deviation of the regression coefficient.
Low Confidence and High Confidence are the lower and upper confidence bounds on the regression coefficient.
T Value is the normalized regression coefficient, which is equal to Coefficient/Standard Error.
P Value (alpha error or type I error) is the probability that an equal amount of variation in the output would be observed in the case that this term does not affect the output. This value is compared to the risk level (alpha) that you specify on the Anaysis Settings page of the control panel. If the p value is less than alpha, this source of variation is considered to have a significant effect on the output. In this case, the term and its p value will be displayed in red.

This table includes the following columns:

- Term is the factor, factorial interaction, etc. under consideration. Terms displayed in red are considered to be significant.
- Effect is a measure of how much the response value (Y) changes when the value of the corresponding term in the model (using coded values) changes from -1 to 1.
- Coefficient is the regression coefficient of the term, which represents the contribution of the term to the variation in the response.
- Standard Error is the standard deviation of the regression coefficient.
- Low Confidence is the lower confidence bound of the regression coefficient, using Fisher bounds.
- High Confidence is the upper confidence bound of the regression coefficient, using Fisher bounds.
- Z Value is the normalized regression coefficient, which is equal to Coefficient/Standard Error.
- P Value is the probability that an equal amount of variation in the output would be observed in the case that this source does not affect the output. This value is compared to the risk level (alpha) that you specify on the Analysis Settings page of the control panel. If the p value is less than alpha, this source of variation is considered to have a significant effect on the output. In this case, the term and its p value will be displayed in red.

This information is presented using multiple tables.

The Response table displays the response that the regression equation applies to and the units of measurement that were entered for the response (if any).
The Additional Settings table shows the transformation and risk level you entered for the response.

The Significant Terms table is applicable only when at least one term was found to be significant. It shows the significant terms in the Name column and the associated regression coefficients in the Coefficient column.
The Equation tables show the regression coefficients for the model of the selected response. For example, consider this table:

The corresponding model for this table is y = 9.3903 - 0.8467x1 + 1.2813x2 + 0.7303x1x2.

The first Equation table shows the coefficients for a model that uses coded values for the factors.
The second Equation table shows the coefficients for a model that uses the actual factor values.

Additional Results

All of the following tables provide information that was generated from the main calculations. The available tables will vary depending on design type you are working with. The results that could be available include:

Alias Structure

Var/Cov Matrix

Diagnostic Information

Least Squares Means

What's Changed? In DOE++ 1, diagnostic information (e.g., the residual for each run) was accessed by clicking an icon on the control panel to open the Diagnostics window. In the current version, this information is placed together with other analysis results in the Analysis Summary window.

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	Free Form Folio