Standardizing the Data
main topic               

In all cases, the standardized values (Z) are obtained by:

Z = (X - m) / s

where m is the overall mean for a particular part, and s is the estimate of the process standard deviation for each X. The estimate of s depends on the method chosen.

When you choose the Relative to size (combine all observations, use log) option for estimating s, X is the natural log of the data.

The following table shows how the Z-values vary depending on the method chosen to estimate s:

Run #

Fiber #

Thickness

Mean

Constant Z

Relative to size Z

By Parts Z

By Runs Z

1

134 

1.435

1.5015

-0.9288

-0.9674

-0.9554

-0.6731

1

134 

1.572

1.5015

0.9846

1.0022

1.0129

0.7136

1

134 

1.486

1.5015

-0.2165

-0.2131

-0.2227

-0.1569

2

221 

1.883

1.7847

1.3729

1.1774

1.1973

0.8800

2

221 

1.715

1.7847

-0.9735

-0.8518

-0.8490

-0.6240

2

221 

1.799

1.7847

0.1997

0.1865

0.1742

0.1280

3

134 

1.511

1.5015

0.1327

0.1473

0.1365

0.1477

3

134 

1.457

1.5015

-0.6215

-0.6388

-0.6394

-0.6921

3

134 

1.548

1.5015

0.6494

0.6698

0.6681

0.7232

4

221 

1.768

1.7847

-0.2332

-0.1909

-0.2034

-0.2117

4

221 

1.711

1.7847

-1.0293

-0.9024

-0.8977

-0.9341

4

221 

1.832

1.7847

0.6606

0.5812

0.5761

0.5995

5

077 

1.427

1.3883

0.5405

0.5529

0.6104

0.6104

5

077 

1.344

1.3883

-0.6187

-0.7520

-0.6987

-0.6987

5

077 

1.404

1.3883

0.2193

0.1991

0.2476

0.2476