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 |
|
QC-Expert 
