"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 samesource as the quantity objection." by Joel Michell
(1) Why "there was no evidence to support the hypothesis that psychophysical methods measured anything" because "the additivity of psychological attributes had not been displayed"?
(2) Item Response Theory (IRT) has no Additivity, Can IRT correctly measure educational testing performance?
Dear Nan Kong,
The statement of true or false measurement is very rigid and is not even valid for the physical sciences. But it can measure with a certain degree of accuracy. The differentiation of the measurement theories is how to increase the degree of accuracy. It is not right to ignore the evolution of psychological measurement, all existing theories. Additivity is an important concept in all theories of psychological measurement, and each theory has its own way of collecting specific evidence for additivity.
Best
1) Additivity assumptions for validating early psych-phys measurements stems from validation of "individual-differences", where "individuals = 1".
2) Yes, IRT is a more valid measurement system, because it is more precise.
Hope this helps,
Matthew
Hi, Matthew,
Thank you for your interest in this topic.
Please read this paper
(IRT SCORING AND THE PRINCIPLE OF CONSISTENT ORDER):
https://arxiv.org/pdf/1805.00874.pdf
Everyone knows that the area of rectangle is measured by the product of its width and length, but we must not measure the area of rectangle by the summation of its width and length. This is because the product of the width and length has its additive structure in terms of the area while the summation of the width and length has not. Although the summation of the width and length is positively correlated to the area of the rectangle (or, the summation of the width and length measures the area of rectangle with a certain degree of accuracy ), the summation of the width and length is still an incorrect way to measure the area of the rectangle because it can not keep the fundamental structure of the area which is additivity.
Measure is an (isomorphic) mapping from the object which is measured to the real number domain (usually greater than or equal to zero). This object could be area, volume, angle, randomness, uncertainty, (linear) correlation, information or ability etc. Here, isomorphic mapping is the mapping which keeps the additive structure from the object which is measured to the real number domain.