The Unscrambler Methods

The Unscrambler User Manual

Camo Software AS

The Unscrambler

Methods

By CAMO Software AS



Camo Software AS

The Unscrambler User Manual

This manual was produced using ComponentOne Doc-To-Help? 2005 together with Microsoft? Word. Visio and Excel were used to make some of the illustrations. The screen captures were taken with Paint Shop Pro.

Trademark Acknowledgments Doc-To-Help? is a trademark of ComponentOne LLC. Microsoft? is a registered trademark and Windows? 95, Windows? 98, Windows? NT, Windows? 2000, Windows? ME, Windows? XP, Excel and Word are trademarks of Microsoft Corporation. PaintShop Pro is a trademark of JASC, Inc. Visio is a trademark of Shapeware Corporation.

Restrictions Information in this manual is subject to change without notice. No part of the documents that build it up may be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of CAMO Software AS.

Software Version This manual is up to date for version 9.6 of The Unscrambler?. Document last updated on June 5, 2006.

Copyright ? 1996-2006 CAMO Software AS. All rights reserved.

The Unscrambler User Manual

Camo Software AS

Contents

What Is New in The Unscrambler 9.6?

1

If You Are Upgrading from Version 9.5 ............................................................................................. 1 If You Are Upgrading from Version 9.2 ............................................................................................. 2 If You Are Upgrading from Version 9.1 ............................................................................................. 3 If You Are Upgrading from Version 8.0.5.......................................................................................... 4 If You Are Upgrading from Version 8.0 ............................................................................................. 5

If You Are Upgrading from Version 7.8 ............................................................................................. 5 If You Are Upgrading from Version 7.6............................................................................................. 6 If You Are Upgrading from Version 7.5 ............................................................................................. 7 If You Are Upgrading from Version 7.01...........................................................................................8

What is The Unscrambler?

11

Make Well-Designed Experimental Plans ........................................................................................ 11

Reformat, Transform and Plot your Data.......................................................................................... 12 Study Variations among One Group of Variables ............................................................................ 12 Study Relations between Two Groups of Variables ......................................................................... 13 Validate your Multivariate Models with Uncertainty Testing .......................................................... 13 Make Calibration Models for Three-way Data ................................................................................. 13

Estimate New, Unknown Response Values ...................................................................................... 14 Classify Unknown Samples .............................................................................................................. 14 Reveal Groups of Samples ................................................................................................................ 14

Data Collection and Experimental Design

15

Principles of Data Collection and Experimental Design................................................................... 15 Data Collection Strategies ..................................................................................................... 15 What Is Experimental Design? .............................................................................................. 16

Various Types of Variables in Experimental Design............................................................. 16 Investigation Stages and Design Objectives .......................................................................... 18 Designs for Unconstrained Screening Situations................................................................... 19 Designs for Unconstrained Optimization Situations.............................................................. 23 Designs for Constrained Situations, General Principles ........................................................ 25

Designs for Simple Mixture Situations.................................................................................. 30 Introduction to the D-Optimal Principle ................................................................................ 35 D-Optimal Designs Without Mixture Variables .................................................................... 37 D-Optimal Designs With Mixture Variables ......................................................................... 38 Various Types of Samples in Experimental Design .............................................................. 39

Sample Order in a Design ...................................................................................................... 43 Extending a Design................................................................................................................ 44 Building an Efficient Experimental Strategy ......................................................................... 47 Advanced Topics for Unconstrained Situations .................................................................... 48 Advanced Topics for Constrained Situations ........................................................................ 49 Three-Way Data: Specific Considerations........................................................................................ 52

What Is A Three-Way Data Table? ....................................................................................... 52

The Unscrambler Methods

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Camo Software AS

The Unscrambler User Manual

Logical organization Of Three-Way Data Arrays ................................................................. 52 Unfolding Three-Way Data ................................................................................................... 53

Experimental Design and Data Entry in Practice.............................................................................. 55 Various Ways To Create A Data Table ................................................................................. 55 Build A Non-designed Data Table ........................................................................................ 56 Build An Experimental Design.............................................................................................. 57 Import Data............................................................................................................................ 57 Save Your Data...................................................................................................................... 57

Work With An Existing Data Table ...................................................................................... 57 Print Your Data...................................................................................................................... 57

Represent Data with Graphs

59

The Smart Way To Display Numbers ............................................................................................... 59 Various Types of Plots...................................................................................................................... 59

Line Plot ................................................................................................................................ 60

2D Scatter Plot....................................................................................................................... 61 3D Scatter Plot....................................................................................................................... 61 Matrix Plot............................................................................................................................. 62 Normal Probability Plot......................................................................................................... 62 Histogram Plot....................................................................................................................... 63

Plotting Raw Data ............................................................................................................................. 63 Line Plot of Raw Data ........................................................................................................... 63 2D Scatter Plot of Raw Data.................................................................................................. 65 3D Scatter Plot of Raw Data.................................................................................................. 65 Matrix Plot of Raw Data........................................................................................................ 66 Normal Probability Plot of Raw Data.................................................................................... 66

Histogram of Raw Data ......................................................................................................... 67 Special Cases .................................................................................................................................... 69

Special Plots .......................................................................................................................... 69 Table Plot............................................................................................................................... 69

Re-formatting and Pre-processing

71

Principles of Data Pre-processing ..................................................................................................... 71

Filling Missing Values........................................................................................................... 72 Computation of Various Functions........................................................................................ 72 Smoothing.............................................................................................................................. 72 Normalization........................................................................................................................ 74 Spectroscopic Transformations ............................................................................................. 76

Multiplicative Scatter Correction...........................................................................................77 Adding Noise.........................................................................................................................78 Derivatives............................................................................................................................. 78 Standard Normal Variate .......................................................................................................81 Averaging .............................................................................................................................. 82 Transposition .........................................................................................................................82

Shifting Variables.................................................................................................................. 82 User-Defined Transformations .............................................................................................. 82 Centering ............................................................................................................................... 82 Weighting .............................................................................................................................. 83 Pre-processing of Three-way Data ........................................................................................ 85

Re-formatting and Pre-processing in Practice................................................................................... 85 Make Simple Changes In The Editor..................................................................................... 85 Organize Your Samples And Variables Into Sets .................................................................. 87 Change the Layout or Order of Your Data ............................................................................ 87 Apply Transformations.......................................................................................................... 87

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The Unscrambler Methods

The Unscrambler User Manual

Camo Software AS

Undo and Redo...................................................................................................................... 88 Re-formatting and Pre-processing: Restrictions for 3D Data Tables..................................... 88 Re-formatting and Pre-processing: Restrictions for Mixture and D-Optimal Designs .......... 89

Describe One Variable At A Time

91

Simple Methods for Univariate Data Analysis ................................................................................. 91 Descriptive Statistics ............................................................................................................. 91 First Data Check .................................................................................................................... 91 Descriptive Variable Analysis ............................................................................................... 92 Plots For Descriptive Statistics.............................................................................................. 92

Univariate Data Analysis in Practice ................................................................................................ 92 Display Descriptive Statistics In The Editor.......................................................................... 92 Study Your Variables Graphically.........................................................................................92 Compute And Plot Detailed Descriptive Statistics ................................................................ 93

Describe Many Variables Together

95

Principles of Descriptive Multivariate Analysis (PCA) .................................................................... 95

Purposes Of PCA................................................................................................................... 95 How PCA Works (In Short) .................................................................................................. 95 Calibration, Validation and Related Samples ........................................................................ 97 Main Results Of PCA ............................................................................................................ 97 More Details About The Theory Of PCA.............................................................................. 99 How To Interpret PCA Results............................................................................................ 100

PCA in Practice............................................................................................................................... 102 Run A PCA.......................................................................................................................... 103 Save And Retrieve PCA Results.......................................................................................... 103 View PCA Results ............................................................................................................... 103 Run New Analyses From The Viewer................................................................................. 104

Extract Data From The Viewer............................................................................................ 105 How to Run an Analysis on 3-D Data ................................................................................. 106

Combine Predictors and Responses In A Regression Model

107

Principles of Predictive Multivariate Analysis (Regression) .......................................................... 107 What Is Regression? ............................................................................................................ 107 Multiple Linear Regression (MLR) ..................................................................................... 109

Principal Component Regression (PCR) ............................................................................. 109 PLS Regression ................................................................................................................... 110 Calibration, Validation and Related Samples ...................................................................... 110 Main Results Of Regression ................................................................................................ 111 More Details About Regression Methods............................................................................ 114 How To Interpret Regression Results.................................................................................. 115

Multivariate Regression in Practice ................................................................................................ 116 Run A Regression................................................................................................................116 Save And Retrieve Regression Results................................................................................117 View Regression Results .....................................................................................................117 Run New Analyses From The Viewer................................................................................. 118

Extract Data From The Viewer............................................................................................ 119

Validate A Model

121

Principles of Model Validation.......................................................................................................121 What Is Validation? ............................................................................................................. 121 Test Set Validation .............................................................................................................. 121 Cross Validation .................................................................................................................. 122

The Unscrambler Methods

Contents v

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