A Transformation Yielding an Additive Representation of Data in a Two-Way Array.

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Abstract:

It is common practice when seeking an additive representation of data in a two-way array to try out various transformations using Tukeys single degree of freedom for nonadditivity as an index of the extent of the deviation of the reexpressed data from additivity. It is shown that when data fit Tukeys model and an additive representation exists in the sense defined by Luce and Tukey 1964, the transformation required to obtain the additive representation is fylog wavelength gamma 1 - wavelength microns, where wavelength is the weight for the degree of freedom for nonadditivity. The transformation is unique up to a linear transformation. This result is in apparent conflict with power transformations suggested by Anscombe and Tukey 1963. Author

Author(s):
Paulson, James A.
Author Organization(s):
PORTLAND STATE UNIV OR DEPT OF PSYCHOLOGY
Descriptive Note:
Technical rept.,
Pagination:
0027

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
TR-80-1
Contract/Grant Number(s):
N00014-79-C-0214
Task Number(s):
RR0420601
Project Number(s):
RR04206
 Subject Terms
Joint Capability Areas:
JCA_1_Force Support; JCA_1.2_Force Preparation; JCA_1.2.3_Educating; JCA_6.4.1_Secure Information Exchange; JCA_5_Command and Control; JCA_1.2.1_Training; JCA_5.3_Planning; JCA_6.4_Information Assurance; JCA_6_Net Centric; JCA_1.1_Force Management; JCA_1.3_Human Capital Management; JCA_1.3.2_Personnel Management
Communities of Interest:
Biomedical
Descriptor(s):
*Transformations(Mathematics), *Data processing, *Arrays, Data management, Random variables, Degrees of freedom, Fitting functions(Mathematics), Linearity
Field(s)/Group(s):
Numerical Mathematics
Keyword(s):
Knowledge representation, Tukeys single degree of freedom, Nonadditivity, PE61153N, WUNR154429
Report Date:
1980 Aug 15