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12

Introduction to the Analysis

of Categorical Data

L. C. Tang and S. W. Lam

Effective statistical analysis hinges upon the use of appropriate techniques for differ-
ent types of data. As Six Sigma evolves from its original applications in manufacturing
environments to new-found applications in transactional operations, categorical re-
sponses increasingly become the norm rather than the exception. In this chapter two
basic schemes, contingency tables and logistic regression, for the analysis of cate-
gorical data are presented. These techniques can easily be implemented in Excel or
statistical software such as MINITAB. Two case studies, one for each of these methods,
are also given to illustrate their application.

12.1 INTRODUCTION

An important statistical procedure in Six Sigma implementation is the statistical mod-
eling of relationships between the key process input variables (KPIVs) and key pro-
cess output variables (KPOVs). Linear regression techniques based on ordinary least
squares (OLS) have always been the tool of choice in most Six Sigma applications
for manufacturing processes. Generally, when the KPOVs are continuous random
variables, the usual OLS regression assumptions are embedded in the analysis. How-
ever, when the KPOVs are not continuous but measured on scales comprising distinct
categories, these OLS assumptions are violated. Such situations are relatively more
pervasive in the modeling of relationships between KPIVs and KPOVs for transac-
tional processes. Fortunately, a broad family of statistical tools and techniques has
been specially developed to deal with such cases. These techniques are applicable
regardless of whether the associated KPIVs are measured on discrete categorical or

Six Sigma: Advanced Tools for Black Belts and Master Black Belts L. C. Tang, T. N. Goh, H. S. Yam and T. Yoap
C 2006 John Wiley & Sons, Ltd
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