This is the third section of Items Decomposition: How to structure the Scores and Items. This section describes, using the graphical representation, how the score associated with all items in a given test (overall score) is related to the subscale scores associated with those items from the subscales through their additive structure that is also the fundamental theoretical structure for General Total Score. Next, the limitation of the items’ graphical representation is discussed and, at the end of this section, some “unusual” item response patterns identified with the graphical representation.
For full essay, please click:Research Items Decomposition: How to structure the Scores and Items (III)
"When in 1940, a committee established by the British Association for the Advancement of Science to consider and report upon the possibility of quantitative estimates of sensory events published its final report (Ferguson eta/., 1940) in which its non-psychologist members agreed that psychophysical methods did not constitute scientific measurement, many quantitative psychologists realized that the problem could not be ignored any longer. Once again, the fundamental criticism was that the additivity of psychological attributes had not been displayed and, so, there was no evidence to support the hypothesis that psychophysical methods measured anything. While the argument sustaining this critique was largely framed within N. R. Campbell's (1920, 1928) theory of measurement, it stemmed from essentially the same source as the quantity objection." by Joel Michell
The conclusion in above comment implies that the Overall Score must be related to its Subscale Score based on their additive structure.
"... it (total score) is the sum of all the sub-scores" ( Ette Etuk) The "sum" here is the additive structure between total score and its sub-scores, but the additive structure of "summation" is only true as a special case, for example, if two sub-scales have some shared items, then total score is not sum of the sub-scores. How to calculate the total sore for general case, please see
Research Total Score and General Total Score
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