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By R. J. Mokken

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Example text

I}. and pallern 9. {0. 0. 0. 0, 0, 0}. We have to change more than three "crror"-iterm to convert this pattern into any one of the other po-,sible perfect respon'e pallern.... , therefore the minimum number of "crror"-itcm ... : possible perfect re'>pon<,c patterns. Here the related perfect pallern is not the one predicted by the principle of reproducibility from the ... core, but another perfect pallern leading to fewer errors. 2 that this approach led to the fallaciou<> procedure of allocating a new score on the basis of the pattern which mo�l closely re'>embled it.

And .. > with monotone trace lines. For methods of analyzing point item� we refer the read er to Mo steller (1949) and Torgerson (1958. 31�-7). A !.! 3 usc or monotone item :-.. Properties ofthe perfecT scale In general we shall consider the case of 11 subject�. each an�wcring to the same set of k items, each item being scored dichotomously. According to conventional statistical practice each item will receive a score of I when the scale response is given and 0 when it is not. � ..... k. (I. I) where X; is the score for item i.

Calc. 3 we have given a ver sion of 1 he usual picture for a fou r-item scale adapted to our purposes. ,imultancou view of th e trace lines for four (perfect) G-items. 2. :e. the trace line of item 3. :atcs the probability of a po�itive response (the scale alternative). value� to the left of value Ba. At point B,1• this probability jumps to one. e. greater than) Ba. The breaking point Ba therefore represents the item difllculty of item 3. Items can be represented by their difficulties (B1). 3 we can see that item 2 i' more difficult than item 3 (Be > Ba) and that the convention of item numbering mentioned above has been followed.

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