On the Sigmoidal Law Relating Association Value (A) and Scaled Meaningfulness (M′)

Abstract

This study was conducted to test an inductive hypothesis, based on judgments of the relative number of associations ( a′) evoked by 2100 CVC trigrams in 200 Montana college Ss, that association value ( a) is a sigmoidal function of scaled meaningfulness ( m′). Whereas the earlier investigation used a representative sample of only 21 CVCs to compute m′, we selected 500 stimuli from the full range of values and had them rated by 200 Georgia college Ss. Measures of reliability for the a′ scale ( r = .993) and of internal consistency for the m′ scale (average error = 2.8%) are again very high. The cross-cultural regressions for the a and m′ scales are both linear, with r ≥ .97 for mean scores grouped in 25 categories of 20 CVCs each. Confirming and extending Noble's 1957 and 1961 findings, the present function relating a and m′ is clearly S-shaped and may be regarded as an empirical law. The analysis-of-variance ( η2) test of curvilinearity, applied to 12 equidistant groupings using all 500 CVCs, is significant ( P < .001). Among the major implications are: (1) the contemporary m′ scale is superior to the classical a scale and its cognates, (2) the practice of treating these two variables as identical or even linearly related is erroneous, (3) continued equivocation about a and m′ in research on verbal behavior can lead to serious errors of prediction and faulty explanatory inferences.