situations such an independent procedure does not exist, and hence the prob-
lem of establishing validity in the true sense of the word cannot be solved. In
such situations the case for validity is made to rest on the logic and experi-
mental rigor of the measurement process together with cross checks of the
measurement results with independently acquired facts. For example, Michel-
son's ⁵ procedure for measuring the velocity of light yielded quite highly
reproducible results from trial to trial, but the validity of his estimate of
the velocity of light is allowed to rest on the fact that the use of his estimate
in describing physical phenomena involving the velocity of light does not lead
to significant contradictions or inconsistencies. To take an example from the
social sciences, we may ask whether the current Bureau of the Census pro-
cedure for measuring (estimating) the number of employed and unemployed
persons in the United States from 35,000 households each month is valid, that
is whether the values obtained are "reasonably close" to the true values of
the number of unemployed in these months. The problem of validity here is
extremely difficult. The case for validity is made partly on the logic of the
design of the sampling system and the control exercised in the execution of
the design and analysis of the results, and partly on the precision with which
various statistical quantities known from previous censuses and surveys can
be estimated from the sample results.

It should be pointed out that there are situations in which the purpose of a
measurement process is to provide a sort of index for which the concept of
validity has meaning only in some general and usually unmeasurable sense.
But in such a situation the importance of the requirement of reliability is in
no way diminished. An examination in a given subject taken by a group of
individuals is an example of such a process. The purpose of the examination
is to provide scores or indices on the individuals indicative in some general
sense of how much they know about the subject. The notion of a "true" score
for an individual is useful for conceptual purposes, but it is unmeasurable.
Even so, the examination can and should possess as much reliability as pos-
sible, that is, if a second similar examination in the subject is given to the
group of individuals the ranking of their scores on the second examination
should be in "reasonable agreement" with the ranking of their scores on the
first examination. For a thorough discussion of reliability of an examination,
the reader is referred to Gulliksen ⁶ who also discusses the problem of evalu-
ating the validity of an examination. Procedures for determining values of
cost of living indices, economic indicators, and measures of the effectiveness
of competing weapon systems are further examples of such a measurement
process.

There is a class of highly practical measurement processes in which validity
is crucial and verifiable, which we may call calibration processes. In a cali-
bration process a scale of values of an auxiliary but easy-to-measure variable y
is constructed so that the values of y corresponding to various specified values
of the basic but difficult-to-measure variable x are determined experimentally.

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