In the methods of magnitude estimation and magnitude production,
numerical estimations of sensation magnitude are obtained for a series
of stimuli of varied intensity. The objective of the experiment is to establish
precisely the functional relationship between stimulus intensity and sen-
sation intensity. To accomplish this objective, valid measurements must
be made of both stimulus and sensation intensity. It is important that the
validity of both stimulus measurements and psychophysical judgments
of sensation intensity be experimentally demonstrated. This has tradition-
ally taken the form of demonstrations of additivity and transitivity of
measurements.

Techniques of physical measurement, when correctly used, generally pro-
duce valid measurements of the stimulus. It has been the tradition in
physical science that any new method of measurement, in order to become
widely accepted, must withstand vigorous tests of its validity. One test
of validity requires that the measurements produced by a new method
be in agreement with those produced by another method that is known
to be valid. If a method with established validity does not already exist,
other procedures must be used to test the validity of the new method.
One such test is to evaluate the additivity of the measurements produced

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