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Data Transformation Print E-mail
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This module is helpful when dealing with skewed (asymmetrically distributed) data, for which a departure from normality was detected, using the Basic data analysis module. The Transformation module uses two strategies to find the best transformation. Mean, confidence interval for the mean and the table of selected quantiles are produced for the transformed data. Computed characteristics are backtransformed to the original scale. The Exponential transformation is based on skewness minimization, while the Box-Cox transformation is based on the maximum likelihood method. The transformation approach takes into account asymmetry of the data distribution and often yields better mean and quantile estimates. It is intended for systematically skewed data, but not for situations where skewness is caused by several outliers. The transformation technique is used also for asymmetric Control chart limits construction and Capability analysis.

PDF Data Transformation - Pdf manual

Example
Task: Evaluate the risk of exceeding a given limit concentration
Data:
Sample A1 Sample A2 Sample A3
1.03 0.98 1.26
0.81 1.21 0.98
0.95 0.94 1.01
0.95 1.11 1.26
0.8 0.99 0.89
0.66 1.21 0.61
1.12 1.73 0.98
... ... ...
Data Transformation
Protocol Text Output:
Box-Cox transformation :      
       
Task name : Imission    
Selected columns :      
K      
       
Optimal parameter : -8.747184372    
Lower conf. Bound : -13.74718437    
Upper conf. Bound : -3.747184428    
Likelihood without transformation : 94.95683683    
Likelihood with transformation : 99.54248489    
Transformation justified : Yes    
Probability : 99.75%    
Chosen parameter : -8.747184372    
Likelihood : 99.54248489    
Corrected mean : 3.333624202    
LCL : 2.946127603    
UCL : 1.5.3835    
LWL : 3.171194769    
UWL : 3.564367854    
       
Some corrected quantiles p lower upper
  50% 3.333624202 3.333624202
  25% 3.218930376 3.47847871
  20% 3.193892681 3.520966002
  15% 3.166106454 3.57483299
  12.50% 3.150502026 3.608832567
  10% 3.133077393 3.650627264
  7.50% 3.112826781 3.705263081
  6.25% 3.101061994 3.740573934
  5% 3.087613848 3.784765577
  3% 3.060055758 3.891398731
  2.50% 3.051123374 3.931828225
  2% 3.040735583 3.983440441
  1.50% 3.028129927 4.054083763
  1% 3.011665314 4.163517074
  0.50% 2.986414218 4.389581015
  0.25% 2.9640652 4.702883748
Exponential transformation :      
       
Task name : Imission    
Selected columns :      
K      
       
Optimal parameter : 0.552036285    
Chosen parameter : 0.552036285    
Transformation justified : Yes    
Corrected mean : 3.324100632    
Confidence interval :      
Lower : 3.278180549    
Upper : 3.376104884    
LCL : 2.975672034    
UCL : 4.705425313    
LWL : 3.061397425    
UWL : 3.988986984    
       
Some corrected quantiles p lower upper
  50% 3.324100632 3.324100632
  25% 3.214754639 3.474957108
  20% 3.19178706 3.52151522
  15% 3.166606987 3.581315398
  12.50% 3.152597472 3.619286162
  10% 3.137057619 3.665988344
  7.50% 3.119126628 3.72675602
  6.25% 3.108769527 3.765678873
  5% 3.096981669 3.813822533
  3% 3.072985833 3.926441033
  2.50% 3.065251458 3.96753373
  2% 3.056282053 4.018521303
  1.50% 3.045432546 4.085437311
  1% 3.031316526 4.182131091
  0.50% 3.009779832 4.354311328
  0.25% 2.990822609 4.535780887
  0.13% 2.973878377 4.727160015
  0.10% 2.968783079 4.790972897
  0.03% 2.943760512 5.154762031
Data Transformation
 
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