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texts), and take a sample from that universe; and (c) establish rules for deciding
whether the answers to the sampled questions are correct or not, resulting in a
vector of judgments of responses. This then is the transduction, from RCA to a
vector of scored responses to the items.
• In the tradition of classical test theory, as described above, the items are viewed
as being “interchangeable” in the sense of being randomly sampled from the
item universe, and hence the information in the vector can be summarized as the
score s, and, equivalently, as the relative frequency s/K that the reader will (on
average) get an item correct.
• Alternatively, the indication could be seen as the vector of responses, thus preserving the information about individual items (such as their difficulty), and thus
modeling the probability of the reader getting each of the items correct, and this
is the direction followed below.
In addition, objectivity must be considered: the measurement of RCA should not be
affected by which readers are the objects of measurement, nor by which items are
used to measure RCA. This was recognized by Louis Thurstone (1928), a historically important figure in psychological and educational measurement, who
addressed the first of these requirements (1928: p. 547):
A measuring instrument must not be seriously affected in its measuring function by the
object of measurement. To the extent that its measuring function is so affected, the validity
of the instrument is impaired or limited. If a yardstick measured differently because of the
fact that it was a rug, a picture, or a piece of paper that was being measured, then to that
extent the trustworthiness of that yardstick as a measuring device would be impaired.
Within the range of objects for which the measuring instrument is intended, its function
must be independent of the object of measurement.
This observation was generalized by Rasch (1961: pp. 331-332), who added a similar requirement for the items:
The comparison between two stimuli [items] should be independent of which particular
individuals [readers] were instrumental for the comparison ...Symmetrically, a comparison
between two individuals should be independent of which particular stimuli within the class
considered were instrumental for the comparison.
He referred to these as requirements for specific objectivity and made that the prime
principle of his approach to measurement. To contextualize this, suppose that the
RCA of readers is to be assessed using a set of items designed for reading comprehension which can be scored, as above, only as correct or incorrect.
Furthermore, assume that the test is composed of a set I of items. Now, two readers m and n can be observed to differ only when they answer an item differently. For
any such pair of readers, m and n, there will be a set of items for which they are both
correct, call it I c , and a set for which they are both incorrect, I i . Then the set of items
on which they differ will be I d , which is I with I c and I i removed—and suppose that
the number of items in I d is D. Suppose further that the number of items that reader
m gets correct in the reduced set I d is s m , and define s n similarly. Then, s m + s n = D,
and s m /D is the relative frequency of m answering an item correctly and n simultaneously answering it incorrectly. Thus the RCAs of m and n (in terms of the success
6 Values, scales, and the existence of properties
texts), and take a sample from that universe; and (c) establish rules for deciding
whether the answers to the sampled questions are correct or not, resulting in a
vector of judgments of responses. This then is the transduction, from RCA to a
vector of scored responses to the items.
• In the tradition of classical test theory, as described above, the items are viewed
as being “interchangeable” in the sense of being randomly sampled from the
item universe, and hence the information in the vector can be summarized as the
score s, and, equivalently, as the relative frequency s/K that the reader will (on
average) get an item correct.
• Alternatively, the indication could be seen as the vector of responses, thus preserving the information about individual items (such as their difficulty), and thus
modeling the probability of the reader getting each of the items correct, and this
is the direction followed below.
In addition, objectivity must be considered: the measurement of RCA should not be
affected by which readers are the objects of measurement, nor by which items are
used to measure RCA. This was recognized by Louis Thurstone (1928), a historically important figure in psychological and educational measurement, who
addressed the first of these requirements (1928: p. 547):
A measuring instrument must not be seriously affected in its measuring function by the
object of measurement. To the extent that its measuring function is so affected, the validity
of the instrument is impaired or limited. If a yardstick measured differently because of the
fact that it was a rug, a picture, or a piece of paper that was being measured, then to that
extent the trustworthiness of that yardstick as a measuring device would be impaired.
Within the range of objects for which the measuring instrument is intended, its function
must be independent of the object of measurement.
This observation was generalized by Rasch (1961: pp. 331-332), who added a similar requirement for the items:
The comparison between two stimuli [items] should be independent of which particular
individuals [readers] were instrumental for the comparison ...Symmetrically, a comparison
between two individuals should be independent of which particular stimuli within the class
considered were instrumental for the comparison.
He referred to these as requirements for specific objectivity and made that the prime
principle of his approach to measurement. To contextualize this, suppose that the
RCA of readers is to be assessed using a set of items designed for reading comprehension which can be scored, as above, only as correct or incorrect.
Furthermore, assume that the test is composed of a set I of items. Now, two readers m and n can be observed to differ only when they answer an item differently. For
any such pair of readers, m and n, there will be a set of items for which they are both
correct, call it I c , and a set for which they are both incorrect, I i . Then the set of items
on which they differ will be I d , which is I with I c and I i removed—and suppose that
the number of items in I d is D. Suppose further that the number of items that reader
m gets correct in the reduced set I d is s m , and define s n similarly. Then, s m + s n = D,
and s m /D is the relative frequency of m answering an item correctly and n simultaneously answering it incorrectly. Thus the RCAs of m and n (in terms of the success
6 Values, scales, and the existence of properties