THE LOGNORMAL FREQUENCY MODEL AND ADJECTIVE TRAIT NAMES

Summary.-A lognormal model, suggested by Carroll, provides a satisfactory description of the frequency-of-occurrence distribution for trait adjectives which are scaled for likeableness. There are strong similarities between the best-fitting functions for traic adjectives and for nouns from a familiarity scale. The similarities suggest that there may be a family of lognormal functions which are common to words which are selected for grammatical class. Carroll (1967, 1969) has presented evidence that a lognormal distribution provides a satisfactory model for the results of the frequency-of-occurrence count for words from the Lorge magazine portion of the Thorndike-Lorge (T-L) source (Thorndike & Lorge, 1944). The writer has shown that the lognormal model also satisfactorily describes the frequency distribution for 420 nouns in a normative familiariry scale (Bowen, 1969, 1971). The present report is one of a series of methodological studies which develop the generality of the lognormal model for normative words. The report examines the goodness of fit of the model to a disuibution for adjectives from a widely-used likableness (L) scale (Anderson, 1968) and comments upon similarities among distributions which are described by the lognormal model. Method.-The words are 460 of 555 personalicy trait adjectives which have L-scale values and for which T-L frequencies are available. Following Carroll (1967), the method was to determine the goodness of fit of a normal distribution to the distribution of the common logs (@) of the T-L frequencies of occurrence of the words. The T-L frequencies of occurrence of the words were converted to common logs as the first step in the generation of the distribution for @. Adjectives in the A category of the T-L source, with relative frequencies between 50 and 99 words per million (w.p.m.), were assigned a @ value, -4.153, which represents the midpoint of their dass interval. Words in the AA category of T-L, with relative frequencies of 100+ w.p.m., were assigned the same @ value, -4.000, assigned to 100 w.p.m. Second, unit-normal deviates were determined for cum~lative proportions of words in the @ categories. A normal deviate of 3.70 was assigned to the cumulative proportion of 1.00. A plot was made displaying the relationship between @ and unit-normal deviates for cumulative proportions of words. A lognormal function describes the original frequency distribution if the relationship is linear. Resu1~s.-Fig. 1 presents the function relating @ to the unit-normal deviates for cumulative proportions of words. Statistically descriptive characteristics of the original frequency disuibution of the adjectives, and the relationship between frequency and L have been noted elsewhere (IBowen, 1971). Inspection of the figure suggests that a linear equation would provide a satisfactory fit. The Pearson product-moment correlation between the deviates and @ is .946 and the @ variable accounts for approximately 'The writer gratefully acknowledges the support of a research grant and faculty research fellowship from the Research Foundation of the Scate University of New York. The writer extends thanks to Dr. J. B. Carroll, who graciously gave permission to refer to his research bulletin, and to J. W. Strauch, who provided assistance in data analysis and preparation of the figure.