Occupational Structure of Community General Hospitals: The Harmonic Series Model

Zipf's (1949) generalized harmonic series model of occupational differentiation is tested in 91 community general hospitals. It was not possible to reject this model in the majority of cases and problems of measurement error make it difficult to claim a firm rejection in the remainder. Relationships among the generalized harmonic series parameters are essentially the same as those reported by Mayhew et al. (1972) for military organizations. Accordingly, from this model of occupational differentiation, we can deduce one of Blau's (1970) major theoretical propositions on the division of labor. The findings of this study broaden the base of empirical support for Zipf's model and Blau's proposition. In a recent report, Mayhew et al. (1972) applied Zipf's (1949) harmonic series model of the division of labor to the occupational structure of military organizations. They were unable to reject the (generalized) harmonic series model for any of the units studied. The object of the present inquiry is to extend their analysis to community general hospitals. A replication of this kind is intended to broaden the empirical base of support for Zipf's model. The finding that both hospitals (as we shall show) and military organizations can be described by the same model for the division of labor should be of special interest, since they are frequently considered to represent rather different forms of bureaucratic structure. Military organizations are often assumed to fit a Weberian "rational-legal" model of bureaucratic organization (Childers et al., 1971), while hospitals are often assumed to fit a more "collegial" or "professional" form of bureaucratic organization (Coe, 1970; Litwak, 1961). In examining military organizations, Mayhew et al. (1972) tested the harmonic series model and considered its implications for the relationship between organizational size and the division of labor. They indicate that the presence of the generalized harmonic series and particular relationships among the harmonic series parameters will yield the form of the relationship between size and the division of labor specified by Blau (1970) and Blau and Schoenherr (1971). We shall follow a similar procedure, but will reserve discussion of the relationships among the harmonic series parameters until after we have tested the basic model. The "generalized harmonic series" is an elementary mathematical equation indicating the sum of a series of ordered proportions (see below). It is applied to rank-frequency distributions called Pareto distributions. A Pareto distribution is an ordered set of categories in which order is determined by ranking categories according to their decreasing size (frequency of elements in the category). Thus, for example, a Pareto distribution for city size will show a series of cities (categories) ranked according to decreasing size (population), with the largest city having the first rank, the next largest city having the second rank, etc. In the present inquiry, the categories will be occupational roles and the frequencies in them are the numbers of persons who occupy those roles in hospitals. Accordingly, creating a Pareto distribution for occupational roles in hospitals involves ranking the occupations according to the number (frequency) of personnel in them, the largest receiving the first rank, the next largest receiving the second rank, etc. When we compare a concrete distribution of R The research reported here received support under grant number HS 00028 from the National Center for Health Services Research and Development.