By R. J. Mokken
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Extra resources for A theory and procedure of scale analysis with applications in political research
Although not only the 0-values but also the 81-values and therefore the locations of the intervals are unknown, an ordering of the 11 subjects and the k items must always be possible in the case of a perfect scale. 1. Only perfect patterns occur. The arrangement of table 2. 3, is such that the items are ordered according to the number or subjects that scored I on them. The number of subjects giving that scale response on item i is denoted as In a total sample of n n1• subjects, the fraction p; = n;/n of subjects doing this for item i may be called the sample difficulty, which should be distinguished from item difficulty as defined above.
Apparently with some claim to success. The concept of a wider population of behavioral items relevant to a construct we wish to measure is well in agreement with intuition. > :,tudied items as indicators of other types of behavior, in spite of the carefulness with which one works, one ends up with the feeling that other items might have done just as well. The whole empirically founded idea of the interchangeability of indices presupposes some thin!.! like a population or universe in which they are embedded.
To return t� our example: we first note a striking dissimilarity in the trace lines or items I and 2. Of course that difference is based on the difTerent con1ent of the items. In question I only respondents whose height is around I. 73 m. will be inclined to say "yes" to item I. 73 m. 73 m.. there is a high probability that they will not give the scale answer ""yes". Items that elicit this behavior have been called point iwns (Mosteller, 1949) or differential items (Loevinger, 1948). On the other hand, the trace line of item 2 indicates quite another type of behavior.
A theory and procedure of scale analysis with applications in political research by R. J. Mokken