ISO/TR 22914:2020

TECHNICAL ISO/TR
REPORT 22914
First edition
2020-10
Statistical methods for
implementation of Six Sigma —
Selected illustration of analysis of
variance
Méthodes statistiques pour la mise en œuvre du Six Sigma - Exemples
choisis d'application de l'analyse de la variance
Reference number
©
ISO 2020
© ISO 2020
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ii © ISO 2020 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and abbreviated terms . 4
5 General description of one-way and two-way classifications . 4
5.1 General . 4
5.2 Stating objectives . 5
5.3 Data collection plan . 6
5.4 Variables description . 6
5.5 Measurement system considerations . 6
5.6 Performing data collection . 6
5.7 Verification of ANOVA assumptions . 7
5.7.1 General. 7
5.7.2 Test of normality . 7
5.7.3 Test of homogeneity of variance . 7
5.7.4 Test of independence . 7
5.7.5 Outliers identification . 7
5.7.6 How to deal with non-standard cases . 8
5.8 Undertaking ANOVA analysis . 8
5.8.1 State hypotheses H and H . 8
0 1
5.8.2 Graphical analysis . 8
5.8.3 Generate analysis results . 8
5.8.4 Residual analysis . 8
5.9 Further analysis . 9
5.10 Conclusion . 9
6 Description of Annexes A through E . 9
Annex A (informative) Bond strength .11
Annex B (informative) Effect of script and training on income per sale .19
Annex C (informative) Strength of welded joint .30
Annex D (informative) Water consumption in a petroleum enterprise .38
Annex E (informative) The hub total hours used on a task .45
Annex F (informative) ANOVA formulae .51
Bibliography .56
Foreword
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bodies (ISO member bodies). The work of preparing International Standards is normally carried out
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electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
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iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 69, Applications of statistical methods,
Subcommittee SC 7, Applications of statistical and related techniques for the implementation of Six Sigma.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
iv © ISO 2020 – All rights reserved

Introduction
Analysis of variance (ANOVA) is a collection of statistical models used to analyse the differences
among group means and their associated procedures (such as "variation" among and between groups),
developed by statistician and evolutionary biologist Ronald A. Fisher. In the ANOVA setting, the observed
variance in a particular variable is partitioned into components attributable to different sources of
variation. In its simplest form, ANOVA provides a statistical test of whether or not the means of several
groups are equal, and therefore generalizes the t-test to more than two groups. ANOVA models are
useful for comparing (testing) three or more means (groups or variables) for statistical significance. It
is conceptually similar to multiple two-sample t-tests, but is more conservative (it results in less type I
error) and is therefore suited to a wide range of practical problems. In Six Sigma, ANOVA is used to find
out if there are differences in the performances of different groups, and ultimately to find out if these
differences count, or are important enough that a significant change or adjustment should be made. It
serves as a guide on which aspect(s) of a process improvements can, or should, be made.
ANOVA is the synthesis of several ideas and it is used for multiple purposes. As a consequence, it is
difficult to define concisely or precisely. Classical ANOVA for balanced data does the three following
things at once.
1) As exploratory data analysis, an ANOVA is an organization of an additive data decomposition, and
its sums of squares indicate the variance of each component of the decomposition (or, equivalently,
each set of terms of a linear model).
2) Comparisons of mean squares, along with an F-test allow testing of a nested sequence of models.
3) Closely related to the ANOVA is a linear model fit with coefficient estimates and standard errors.
In short, ANOVA is a statistical tool used in several ways to develop and confirm an explanation for the
observed data. Additionally:
1) it is computationally elegant and relatively robust against violations of its assumptions;
2) it provides industrial strength by (multiple sample comparison) statistical analysis;
3) it has been adapted to the analysis of a variety of experimental designs.
As a result, ANOVA has long enjoyed the status of being the most used (some would say abused)
statistical technique in psychological research. "ANOVA "is probably the most useful technique in the
field of statistical inference. ANOVA is difficult to teach, particularly for complex experiments, with
split-plot designs being notorious.
There are three main assumptions:
1) independence of observations — this is an assumption of the model that simplifies the statistical
analysis;
2) normality — the distributions of the residuals are normal;
3) equality (or "homogeneity") of variances, called homoscedasticity — the variance of data in groups
is expected to be the same.
If the populations from which data to be analysed by a one-way analysis of variance (ANOVA) were
sampled violate one or more of the one-way ANOVA test assumptions, the results of the analysis can be
incorrect or misleading. For example, if the assumption of independence is violated, then the one-way
ANOVA is simply not appropriate, although another test (perhaps a blocked one-way ANOVA) can be
appropriate. If the assumption of normality is violated, or outliers are present, then the one-way ANOVA
is not necessarily the most powerful test available. A nonparametric test or employing a transformation
can result in a more powerful test. A potentially more damaging assumption violation occurs when
the population variances are unequal, especially if the sample sizes are not approximately equal
(unbalanced). Often, the effect of an assumption violation on the one-way ANOVA result depends on the
extent of the violation (such as how unequal the population variances are, or how heavy-tailed one or
another population distribution is). Some small violations can have little practical effect on the analysis,
while other violations can render the one-way ANOVA result uselessly incorrect or uninterpretable. In
particular, small or unbalanced sample sizes can increase vulnerability to assumption violation.
vi © ISO 2020 – All rights reserved

TECHNICAL REPORT ISO/TR 22914:2020(E)
Statistical methods for implementation of Six Sigma —
Selected illustration of analysis of variance
1 Scope
This d
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