SigmaXl Features

Taguchi L9 (3 Level) Four Factor - Paper Airplane Example
L4, L8, L9, L12, L16, L18, L27
Signal-to-Noise Ratios: Nominal is Best, Nominal is Best (Variance Only), Nominal is Best (Mean Square Deviation with Target), Larger is Better, Smaller is Better
Pareto of Deltas (Effects) and ANOVA SS (Sum-of-Squares) % Contribution (for Main Effects and Two-Way Interactions)
Main Effects and Interaction Plots

Control Chart Templates

Individuals, C-Chart

Graphical Tools:

Interval Plots and Multiple X Interval Plots

Interaction Plot **

Multiple Normal Probability Plots (with 95% confidence intervals to ease interpretation of normality/non-normality)

Empirical/Normal CDF Plots

Run Charts (with Nonparametric Runs Test allowing you to test for Clustering, Mixtures, Lack of Randomness, Trends and Oscillation)

Overlay Run Chart

Multi-Vari Charts

Scatter Plots (with linear regression and optional 95% confidence intervals and prediction intervals)

Scatter Plot Matrix

XYZ Contour/Surface Plot

Analysis of Means (ANOM) Charts

Statistical Tools:

P-Values turn red when results are significant (P-Value < alpha)
Descriptive Statistics including Anderson-Darling Normality test, Skewness and Kurtosis with P-Values
Descriptive Statistics Options:

Percentile Report and Percentile Ranges
Percentile Confidence and Tolerance Intervals
Additional Descriptive Statistics and Normality Tests (Shapiro-Wilk and Doomik-Hansen Normality)
Outlier (Boxplot and Grubbs) and Randomness (Nonparametric Runs) Tests

Reports AD Normality, F-test and Levene's for variance, t-test assuming equal and unequal variance, Mann-Whitney test for medians

One-Way ANOVA and Means Matrix

Multiple Comparison of Means Probability Methods (Post-Hoc): Fisher, Tukey, Dunnett With Control

Automatic Assumptions Check for One Sample, Two-Sample, Paired T-tests and One-Way ANOVA

Test report with color highlight: Green (OK), Yellow (Warning) and Red (Serious Violation)
Test each sample for Normality. If not, check minimum sample size of robustness of test
Check each sample for Outliers: Potential (Tukey's Boxplot 1.5*IQR); Likely (2.2*IQR); Extreme (3*IQR)
Randomness (Nonparametric Runs Test)
Equal Variance (for 2 or more samples)

Two-Way ANOVA (Balanced and Unbalanced)

Equal Variance Tests (Bartlett, Levene and Welch's ANOVA)

Multiple Comparison of Variances Probability Methods (Post-Hoc): F-Test (with Bonferroni Correction), Levene, Tukey ADM (Absolute Deviation for Medians)
Welch Multiple Comparison of Means Probability Methods (Post-Hoc): Welch Pairwise, Games Howell

Correlation Matrix (Pearson and Spearman's Rank Correlation)

Automatic normality check for correlation utilizing the powerful Doornik-Hansen bivariate normality test
Yellow highlight to recommend significant Pearson or Spearman correlation - Pearson is highlighted if the data are bivariate normal, otherwise Spearman is highlighted

General Linear Model:

Extends Advanced Multiple Regression to include:

Fixed and Random Factors

Nested Factors

Covariates (can be Nested)

For Random or Mixed Random/Fixed Factors with a balanced design, the ANOVA and Variance Components (VC) report is given based on Expected Mean Squares. VC confidence intervals using Restricted Maximum Likelihood (REML) are included.

If the design is unbalanced or model is non-hierarchical, REML is used to compute the VC values and confidence intervals. Fixed Effects Tests are based on Satterthwaite approximation degrees of freedom.

Main Effects with Confidence Intervals and Interaction Plots of Fitted Means for Non-Nested Fixed Factors

Tukey and Fisher Pairwise Comparison of Means for Non-Nested Fixed Factors

Predicted Response Calculator

Multiple Response Optimization for Nested or Non-Nested Fixed Factors

Advanced Multiple Regression:

Standardization and coding of continuous predictors

Option to display regression equation with unstandardized coefficients

(1, 0) or (-1,0,+1) coding of categorical predictors

Box-Cox Transformation

Specify confidence level

Residual Plots (Regular, Standardized, Studentized – Deleted t)

Main Effects and Interaction Plots (Fitted Means)

Contour and Surface Plots

Optimization with optional constraints

Automatic removal of extreme VIF or collinear terms (with alias and removal report)

Specify interactions, quadratic and higher orders (all interactions or up to 3-Way)

ANOVA Type I and/or Type III Sum-of-Squares with Pareto of Percent Contribution and Standardized Effects

Lenth Pseudo Standard Error for Saturated Models (Orthogonal or Non-Orthogonal) with Monte Carlo or Student T P-Values

Specify Test/Withhold Sample for R-square Test & StDev Test Validation

R-Square Predicted (Leave-One-Out Cross Validation)

R-Square K-Fold & StDev K-Fold (K-Fold Cross Validation)

Test for Constant Variance: Breusch-Pagan. Anderson-Darling Normality test is applied to residuals in order to automatically select Normal or Koenker (Robust) version. Report includes the Overall test and Individual predictors as well.

White robust standard errors for non-constant variance (Heteroskedasticity-Consistent)

Durbin-Watson test for autocorrelation in residuals with P-Values

Newey-West robust standard errors for non-constant variance with autocorrelation (Heteroskedasticity and Autocorrelation-Consistent)

White or Newey-West automatically selected based on Durbin-Watson P-Values

Stepwise/Best Subsets Regression:

Forward/Backward with alpha-to-enter, alpha-to-remove

Forward Selection with alpha-to-enter

Backward Elimination with alpha-to-remove

Forward, Backward Criterion: Minimize AICc, BIC; Maximize R-Square Adjusted, R-Square Predicted, R-Square K-Fold

Best Subsets utilizes the powerful MIDACO Solver (Mixed Integer Distributed Ant Colony Optimization) to solve best subsets with up to hundreds of continuous or categorical variables, including interactions and higher order terms. This feature gives SigmaXL a significant advantage over competitors with Best Subsets limited to 30 continuous variables.

Best Subsets Criterion: Minimize AICc, BIC; Maximize R-Square Adjusted

Hierarchical option

Detailed report with additional statistics such as Condition Number and Mallows’ Cp.

Box-Tidwell Test and Power Transformation Recommendation for Continuous Predictors (New in Version 10.02)

Multiple Response Optimization:

Multiple Response Optimization with Desirability

Multistart Nelder-Mead Simplex
MIDACO

Binary and Ordinal Logistic Regression:

Powerful and user-friendly logistic regression.

Report includes a calculator to predict the response event probability for a given set of input X values

Categorical (discrete) predictors can be included in the model in addition to continuous predictors

Model summary and goodness of fit tests include Likelihood Ratio Chi-Square, Pseudo R-Square, Pearson Residuals Chi-Square, Deviance Residuals Chi-Square, Observed and Predicted Outcomes - Percent Correctly Predicted

Stored data includes Event Probabilities, Predicted Outcome, Observed-Predicted, Pearson Residuals, Standardized Pearson Residuals, and Deviance Residuals

Multiple Linear Regression:

Accepts continuous and/or categorical (discrete) predictors
Interactive Predicted Response Calculator with 95% Confidence Interval and 95% Prediction Interval
Residual Plots: histogram, normal probability plot, residuals vs. time, residuals vs. predicted and residuals vs. X factors
Residual types include Regular, Standardized, Studentized (Deleted t) and Cook's Distance (Influence), Leverage and DFITS
Highlight of significant outliers in residuals
Durbin-Watson Test for Autocorrelation in Residuals with p-value
ANOVA report for categorical predictors
Pure Error and Lack-of-Fit report
Collinearity Variance Inflation Factor (VIF) and Tolerance report
Fit Intercept is optional

Chi-Square Test (Stacked Column data and Two-Way Table data)

With Fisher Exact (utilizing permutations and fast networks algorithms) and Monte Carlo P-Values
Options: Advanced Tests and Measures of Association for Nominal & Ordinal Categories

Nonparametric Tests:

1 Sample Sign and 1 Sample Wilcoxon
2 Sample Mann-Whitney
Kruskal-Wallis and Mood's Median Test (With graph of Group Medians and 95% Median Confidence Intervals)

Runs Test
With Exact and Monte Carlo P-Value

Nonparametric Tests - Exact:

Runs Test - Exact

Power and Sample Size Calculators for:

1 and 2 Sample t-Test
One-Way ANOVA
1 Proportion Test , 2 Proportions Test
The Power and Sample Size Calculators allow you to solve for Power (1 - Beta), Sample Size, or Difference (specify two, solve for the third)

Power and Sample Size Chart. Quickly create a graph showing the relationship between Power, Sample Size and Difference

Measurement System Analysis:

Create Gage R&R (Crossed) Worksheet:

Generate worksheet with user specified number of parts, operators, replicates

Analyze Gage R&R (Crossed)

ANOVA, %Total, %Tolerance (with upper and/or lower specifications), %Process, Variance Components, Number of Distinct Categories
Gage R&R Multi-Vari and X-bar R Charts
Confidence Intervals for %Total, %Tolerance, %Process and Standard Deviations
Handles unbalanced data

Attribute MSA (Binary, Ordinal, Nominal)

Process Capability:

Histogram, Normal Probability Plot and Normality Test

Capability Report (Cp, Cpk, Pp, Ppk, Cpm, ppm, %)

Control Charts

Distribution Fitting Report

All valid distributions and transformations reported with histograms, curve fit and probability plots
Sorted by AD P-value

Capability Combination Report for Nonnormal Data (Individuals)

Box-Cox Transformation (includes an automatic threshold option so that data with negative values can be transformed)
Johnson Transformation
Distributions supported: Half-Normal, Lognormal (2 & 3 parameter), Exponential (1 & 2), Weibull (2 & 3), Beta (2 & 4), Gamma (2 & 3), Logistic, Loglogistic (2 & 3), Largest Extreme Value, Smallest Extreme Value
Automatic Best Fit based on AD p-value
Nonnormal Process Capability indices: Z-Score (Cp, Cpk, Pp, Ppk) and Percentile (ISO) Method (Pp, Ppk)

Basic Design of Experiments:

Generate 2-Level Factorial and Plackett-Burman Screening Designs

User-friendly dialog box

2 to 19 Factors; 4,8,12,16,20 Runs

Unique "view power analysis as you design"

Randomization, Replication, Blocking and Center Points

Basic DOE Templates

2 to 5 Factors, 2-Level Full and Fractional-Factorial designs

Automatic update to Pareto of Coefficients

Easy to use, ideal for training

2 to 5 Factors

Central Composite and Box-Behnken Designs

Easy to use design selection sorted by number of runs

Analyze 2-Level Factorial and Plackett-Burman Screening Designs

Used in conjunction with Recall Last Dialog, it is very easy to iteratively remove terms from the model

Interactive Predicted Response Calculator with 95% Confidence Interval and 95% Prediction Interval.

ANOVA report for Blocks, Pure Error, Lack-of-Fit and Curvature

Collinearity Variance Inflation Factor (VIF) and Tolerance report

Residual plots: histogram, normal probability plot, residuals vs. time, residuals vs. predicted and residuals vs. X factors

Highlight of significant outliers in residuals

Durbin-Watson Test for Autocorrelation

Advanced Design of Experiments **:

Extends DOE functionality to include:

Improved 2-Level Factorial/Screening Designs:
- Expanded catalog with up to 128 design runs
- Up to 19 Continuous and/or Categorical Factors
- Aliasing of Effects Report with Interactions to Specified Order
Augment 2-Level Factorial/Screening Design:
- Foldover Design
- Add Center/Axial Points
- Replicate Design
General Full Factorial Designs:
- 1 to 10 Categorical Factors with 10 Levels
- Use 1 Categorical Factor with Block on Replicates for Randomized Complete Block Design
Improved Response Surface Designs:
- Expanded catalog with up to 128 design (cube) runs
- Up to 8 Continuous Factors and 10 Categorical Factors with 8 Levels
- Central Composite Designs with minimum of 2 center points, Uniform Precision or Orthogonal Blocks
- Box-Behnken Designs for 3 to 7 Continuous Factors
Definitive Screening Designs:
- Up to 19 Continuous and/or Categorical Factors (minimum of 2 Continuous)

Optimal Designs:
- D-Optimal (recommended as an efficient general purpose alternative to classical screening and two-level factorial designs)
- I-Optimal (recommended for response surface designs)
- A-Optimal (recommended for screening designs)
- 1 to 19 Continuous and/or Categorical Factors (maximum of 10 Categorical Factors with 10 Levels)
- Continuous Factor Linear Constraint formulas
- Report of Optimal Design Diagnostic Metrics and Model Term SE and VIF values
Improved power calculator with detailed power information (2-Level Factorial/Screening, Augment and General Full Factorial Designs)
Fraction of Design Space (FDS) Plots (Augment 2-Level Factorial/Screening for Add Center/Axial Points, Definitive Screening, Response Surface and Optimal Designs)
Option for randomized or equally spaced center points (2-Level Factorial/Screening, Definitive Screening and Response Surface Designs)
Randomize runs with Seed (Base) as Clock or Specified Value
Analysis (for all designs) uses Advanced Multiple Regression, with options such as Stepwise/Best Subsets and includes Multiple Response Optimization

Control Charts:

Control Chart Selection Guide
Individuals, Individuals & Moving Range
X-Bar & R , X-Bar & S
I-MR-R , I-MR-S (Between/Within)
P, NP, C, U
P' and U' (Laney) to handle overdispersion
Control charts include a report on tests for special causes. Special causes are also labeled on the control chart data point. Set defaults to apply any or all of Tests 1-8
Process Capability report (Pp, Ppk, Cp, Cpk) is available for I, I-MR, X-Bar & R, X-bar & S charts
Add data to existing charts for operator ease of use!
Scroll through charts with user defined window size

Advanced Control Limit options: Subgroup Start and End; Historical Groups (e.g. split control limits to demonstrate before and after improvement)
Exclude data points for control limit calculation
Add comment to data point for assignable cause
± 1, 2 Sigma Zone Lines
Control charts for Nonnormal data (Individuals)

Box-Cox and Johnson Transformations
16 Nonnormal distributions supported (see Process Capability)
Individuals chart of original data with percentile based control limits
Individuals/Moving Range chart for normalized data with optional tests for special causes