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11

Goodness-of-Fit Tests

for Normality

L. C. Tang and S. W. Lam

One of the basic model assumptions in statistical procedures used in Six Sigma ap-
plications is that of normality of data. Statistical ‘goodness-of-fit’ (GOF) techniques
have been developed in the past decades to assess the adequacy of using the normal
distribution to model real-world data so as to limit the risk against severe departures
from normality. These GOF techniques have been widely used in Six Sigma projects
with the help of statistical software packages such as JMP and MINITAB. This chap-
ter presents the theoretical concepts together with the operational procedures (coded
in Microsoft Excel) for a collection of commonly used GOF tests for normality. The
limitations of some of these GOF tests are discussed and compared.

11.1 INTRODUCTION

A systematic and highly disciplined data-driven approach which leverages on rig-
orous statistical analysis procedures for continuous quality improvements has al-
ways been the cornerstone for success in Six Sigma projects. 1,2 Only through care-
fully designed sampling procedures and the rigorous assessment of information can
breakthrough Six Sigma improvement results be achieved and objectively justified.
Statistical techniques which are built on firm scientific thinking and mathematical
foundations provide convenient tools to achieve this in Six Sigma projects.
Central to the practical application of statistical procedures is the statistical model-
ing of data obtained from real-world processes. For Six Sigma projects to effectively
leverage on the strengths of rigorous statistical procedures for quality improvement,
theappropriatedepictionofreal-worlddatathroughstatisticalmodelsiscriticalbefore
all other data-analysis and optimization procedures can be undertaken. Appropriate

Six Sigma: Advance 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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