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Macros for the Design and Analysis of Experiments |

**%adxtrans**(*dsin, dsout, resp, model, intvllo,
intvlhi, numintvl*)

dsin | names the SAS data set that contains the coded design and the original, untransformed values of the response variable. |

dsout | names the output SAS data set to contain the coded
design and the transformed values of the response.
The value for dsout can be the same as
dsin. In this case the original values of
the response variable are replaced by the
transformed values. |

resp | names the response variable for analysis. The
Box-Cox family of transformations requires all
values of resp to be positive. If resp
has zero or negative
values but you still want to estimate an optimal
transformation, add an amount c to each response,
where c is greater than the absolute value of the
most negative value of resp. |

model | lists the independent variables for analysis. |

intvllo | is the bottom end of the range for computing the likelihood. The default value is -2. |

intvlhi | is the top end of the range for computing the likelihood. The default value is 2. |

numintvl | is the number of intervals tested in the range for computing the likelihood. The default value is 21. |

The ADXTRANS macro uses maximum likelihood theory to estimate an
optimal transformation within the class of
*power transformations* of the form

The ADXTRANS macro is useful in situations where the original form of the measurements for the response variable is not the best one to use when analyzing the data. For example, in many situations the original data are not normally distributed, but after applying a log transformation, the transformed data are normally distributed.

Suppose the RESULT data set contains factors T1, T2, and T3 along with values for a response variable BURST. To estimate an optimal Box-Cox power transformation using the defaults for the number of intervals and the ends of the range, use the following statements:

%adxgen %adxtrans(result,tresult,burst,T1 T2 T3)The design with the transformed values for the response is stored in the TRESULT data set.

ADXCONF | a character variable of length 1. The value of ADXCONF is an asterisk (*) if the associated value of is within a 95% confidence interval of the estimated optimum. Otherwise, the value of ADXCONF is a blank. |

ADXLAM | the value of . |

ADXLIKE | the log-likelihood based on the fit of the model to the transformed response. |

_RMSE_ | the root mean squared error based on the fit of the model to the transformed response. |

effect | t-values for estimates of parameters for
effects in the model. The names for effect
depend on the model. If the parameters in the model
are T1 and T2, the ADXREG data set contains new
variables T1 and T2, whose values are the t-values
for the parameter estimates. The variable that
contains t-values for the intercept parameter is
named INTERCEP. |

The ADXTRANS macro lists

- the values of (ADXLAM)
- the root mean squared error (_RMSE_)
- the confidence interval indicator (ADXCONF), which is either an asterisk or blank, as described for the ADXREG data set above
- a plot of
*t*-values against

The data require a transformation if the confidence interval does not contain . A plot of _RMSE_ against should dip fairly steeply with a minimum in the region of the optimum value. Typically, many of the parameter estimates might appear to be significant outside the region of the optimum , but near it only a few will be highly significant and the rest will be insignificant.

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