the importance of normality - asq orange...

The Importance of NormalityOrange Empire – February 8, 2016

Larry Bartkus

What is Normality?

– The normal (or Gaussian) distribution is a very commonly

occurring continuous probability distribution

– Normal distributions are extremely important in statistics and are

often used in the natural and social sciences

– The Gaussian distribution is sometimes informally called the bell

– Physical quantities that are expected to be the sum of many

independent processes (such as measurement errors) often

have a distribution very close to the normal

Normal Data vs Non-normal Data

Commonly found in nature

Easy to identify

No major mathematical

manipulations are necessary

Easy to explain and justify

Solid predictions can readily be

Often difficult to recognize and

sometimes hidden

Can be confused with outliers

Statistical manipulations are

sometimes needed to utilize

distribution

Difficult to explain or justify

Normal Data Non-normal Data

Normal Distribution

Non-normal Distribution

Time (t)0 200.00

Lognormal

λ = 0

Weibull

λ = 0

Exponential

λ = 0

Probability Density Function

Why Graph Data

12108642

Median

8.07.57.06.56.0

1st Q uartile 5.0000

Median 7.0000

3rd Q uartile 9.0000

Maximum 12.0000

6.1712 7.8288

6.0000 8.0000

1.9867 3.1952

A -Squared 0.27

P-V alue 0.660

Mean 7.0000

StDev 2.4495

V ariance 6.0000

Skewness -0.000000

Kurtosis -0.544920

Minimum 2.0000

A nderson-Darling Normality Test

95% C onfidence Interv al for Mean

95% C onfidence Interv al for Median

95% C onfidence Interv al for StDev

95% Confidence Intervals

Summary for A

Why Graph Data

108642

Median

8.07.57.06.56.0

Median 7.5000

Maximum 11.0000

6.1791 7.8209

5.7354 8.0000

1.9677 3.1646

A -Squared 0.61

P-V alue 0.101

Mean 7.0000

StDev 2.4260

V ariance 5.8857

Skewness -0.216101

Kurtosis -0.923506

Minimum 2.0000

95% C onfidence Interv al for StDev

95% Confidence Intervals

Summary for B

Assessing for Normality – Distribution Analyzer

Assessing for Normality – Anderson Darling

1612840

Median

Median 2.5724

Maximum 16.4155

2.4541 5.5224

1.8680 3.7050

3.2721 5.5232

A -Squared 2.77

P-V alue < 0.005

Mean 3.9883

StDev 4.1086

V ariance 16.8803

Skewness 1.90297

Kurtosis 3.02385

Minimum 0.3286

95% C onfidence Interv al for StDev95% Confidence Intervals

Summary for C2

Project: NORMALITY EXAMPLES 2011-06-22.MPJ

Assessing for Normality – Anderson Darling

Assessing for Normality – Ryan Joiner

151050-5

Mean 3.988

StDev 4.109

RJ 0.863

P-Value <0.010

Probability Plot of C2

Normal

Assessing for Normality – Ryan Joiner

0.2600.2590.2580.2570.256

706050403020

EW Data 4

Mean 0.2581

StDev 0.0006815

RJ 1.000

P-Value >0.100

Probability Plot of EW Data 4

Normal

Sensitive to Normality

Non-Sensitive

Confidence intervals on means

T-tests

ANOVA, including DOE and

Regression

X-bar Charts

Sensitive

Confidence Intervals on standard

deviations

Tolerance Intervals, Reliability

Intervals

Variance tests

Cpk, Cp, Ppk, Pp

I-Charts

1) Measurement Resolution

Equipment lacks granularity

2) Data Shift

During collection of from a process a

shift has occurred

3) Multiple Sources of Data

Multiple operators machines,

Lots of Material, etc.

4) Truncated Data

There’s a stop somewhere

or there’s a sorting process

7 Common Reasons for Failing Normality

0.2600.2590.2580.2570.256

706050403020

EW Data 4

Mean 0.2581

StDev 0.0006815

RJ 1.000

P-Value >0.100

Probability Plot of EW Data 4

Normal

12.011.210.49.68.88.07.2

Median

10.410.310.210.110.09.9

1st Q uartile 9.610

Median 10.083

Maximum 12.618

10.121 10.370

9.934 10.264

0.747 0.923

A -Squared 2.11

P-V alue < 0.005

Mean 10.245

StDev 0.826

V ariance 0.682

Skewness 0.656745

Kurtosis -0.222344

Minimum 9.002

Summary for N(10,1) Truncate at 9

5) Presence of Outliers

Data has one or more points

that are anomalies. These differ

greatly from the rest of the population.

6) Too Much Data

When there are too many

data points involved in

the assessment. >100

7) Underlying Distribution is Not Normal

Some processes are not intended to be

normal such as time, microbio, pull force

7 Common Reasons for Failing Normality

12011010090

Median

116114112110108

Median 112.90

Maximum 122.40

107.48 113.94

107.73 116.08

6.27 11.03

A -Squared 0.70

P-V alue 0.060

Mean 110.71

StDev 7.99

V ariance 63.87

Skewness -1.17564

Kurtosis 1.99926

Minimum 86.20

Summary for EW Data 2

8765432

Median

5.105.055.004.954.90

Median 5.0000

Maximum 8.2000

4.9042 5.0306

4.9000 5.1000

0.9762 1.0658

A -Squared 0.54

P-V alue 0.167

Mean 4.9674

StDev 1.0190

V ariance 1.0384

Skewness -0.0380120

Kurtosis 0.0171328

N 1000

Minimum 1.5000

Summary for N(5,1) Rounded to 0.1

Non-normal Data

Let’s First Treat the Data as Normal

Non-normal Data

Group Discussion

– What are the consequences of failing a capability

that should be acceptable due to an error in the

normality distribution assumption?

– What are the consequences of accepting a

capability study as satisfactory when it should fail

due to an error in the normality distribution

assumption?

Any Questions?

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