Data Transformation
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.

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 ... ... ...

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