The Relationship Between Organization Size and Supervision Ratio

The Relationship Between Organization Size and Supervision RatioAuthor(s): Bernard P. IndikSource: Administrative Science Quarterly, Vol. 9, No. 3 (Dec., 1964), pp. 301-312Published by: Sage Publications, Inc. on behalf of the Johnson Graduate School of Management,Cornell UniversityStable URL: http://www.jstor.org/stable/2391443 .

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Bernard P. Indik

The Relationship between

Organization Size and

Supervision Ratio

The structure of organizations has long been of interest to students of administration. Parkinson's observation' of the disproportionate increase of "chiefs" to "Indians," as organizations increase in size, is not supported by the data presented in this paper.2 We have found in the five sets of organizations studied here that the relationship between organization unit size and supervision ratio is logarithmic in form and negative in slope. Several reasons for this finding are suggested and explored; no rationale, however, has yet been experimental- ly proven.

Bernard P. Indik is an assistant professor, Department of Psychology, Rutgers University.

ORGANIZATIONAL unit size and ratio of supervision are variables which are relatively easy to measure. Though there has

IC. N. Parkinson, Parkinson's Law and Other Studies in Administration (Boston, 1957).

2The data to be reported were collected with the cooperation of the Survey Research Center, University of Michigan; the Research Program of the Institute of Management and Labor Relations, Rutgers; The State University, and the Psychology Department, Rutgers; The State University, New Brunswick, N. J., with the support of Navy Contract Nonr-404(10), Group Psychology Branch, Office of Naval Research.



302 ADMINISTRATIVE SCIENCE QUARTERLY

been considerable literature (both classical3 and recent4) built up in both sociology and administration on the relationship between these variables, few conclusions have been systematically derived from examination of the empirical data available.5 In this paper we intend to explore empirical data and theoretical explanations to find out which possible interpretations agree with the data. Since very different kinds of organizations are to be discussed here, several definitions are necessary before we can continue.

An organizational unit is defined as a system containing two or more members who share the over-all purpose or purposes of the system and who are related to each other in a prescribed manner within the boundary of the system. For the specific requirements of this set of studies only organizational units whose sites were geographically separated from each other were considered. To avoid the confounding effect of other structural variables, only organizational units consisting of three-level authority hierarchies were considered.

Supervision ratio is defined as the ratio of the number of supervisors to the total number of members; applying this definition to the different organizational units, however, raised a rather difficult problem: What is a supervisor? For our purposes this category included those individuals whose functional role involved mainly direct interpersonal supervision or key organizational administrative decision making. This definition excluded those non-rank- and-file personnel higher in the organization who were serving mainly clerical functions.

"I. Hamilton, The Soul and Body of an Army (London, 1921), p. 229; L. Urwick, "Organization as a Technical Problem," in L. Gulick and L. Urwick, eds., Papers on the Science of Administration (Institute of Public Administration, New York, 1937).

"F. W. Terrien, The Effect of Changing Size upon Organizations (First Annual Report of the Institute for Social Science Research, San Francisco, 1963); M. Haire, "Biological Models and Empirical Histories of the Growth of Organizations," in Mason Haire, ed., Modern Organization Theory (New York, 1959); S. Melman, The Rise of Administrative Overhead in the Manufacturing Industries of the United States, 1899-1947, Oxford Economic Papers, 3 (1951), 64-66, 89.

SE. Dale, Planning and Developing the Company Organization Structure (Ameri- can Management Association Research Report No. 20; New York, 1952), pp. 57-59; Doris R. Entwisle and J. Walton, Observations on the Span of Control, Administra- tive Science Quarterly, 5 (1961), 522-533; P. Blau and W. R. Scott, Formal Organiza- tions (San Francisco, 1962), pp. 225-227; R. Bendix, Work and Authority in Industry (New York, 1956), pp. 221-222.



SIZE AND SUPERVISION 303

Two alternative hypotheses suggest themselves. The first is that as the size of the organizational unit increases, the ratio of supervision will tend to increase. This expectation is based on Parkinson's Law and on the mathematical specifications of Kep- hart,6 which show that there is some pressure and necessity to increase supervision at a faster rate than that by which the organization increases. The alternative hypothesis of this set of studies is that as the size of the organizational unit increases, the ratio of supervision will tend to decrease. A qualification should be added that we expect this to be true so long as the role of the lower-level individuals in the local units remains the same, that is, if the complexity of task of lower-level individuals in the system increases as size increases, then the supervision ratio may increase with size.

We speculate further that the relationship of size to supervision ratio will be curvilinear (logarithmic), since less interpersonal supervision per member is necessary as members are added, and since alternative forms of control (bureaucratic control and role prescriptions) may tend to appear as organization size increases. The placement of the curve indicates to an essential degree a characteristic related to the amount of interpersonal control potentially exercised by supervision in the set of organizations.

As an ancillary part of several studies of organizations, data were accumulated on organizational unit size and on the ratio of supervisors to organizational members.

Five sets of data are available. The five sets of organizations were selected in order to obtain a range (though not systematic in a sampling sense) of data including two sets of business organizations and three sets of voluntary organizations. Each set of organzations studied will be described in detail below.

ORGANIZATIONS STUDIED

A. Package Delivery Stations (N = 32) The organizations included in this part of our study consisted

of 32 package delivery organizations located in metropolitan areas. The typical organizational form is shown in Figure 1. The

"C. N. Parkinson, op. cit.; W. M. Kephart, A Quantitative Analysis of Intragroup Relationships, American Journal of Sociology, 55 (1950), 544-549.




STATION MANAGER

r~~~~~~~~~~~~~~~~~~~~~~~~~~~

DAY SUPERVISOR NIGHT SUPERVISOR

DELIVERY DRIVERS PACKAGE SORTERS AND LOADERS

Figure 1. Structure of a typical delivery organization.

organization structure had three levels, and the major structural variation was the number of members in each of the organizations. The size of the 32 units varied from 15 to 61 members. Each unit was subject to and functioned within the policies of the parent firm. The common objective was the delivery of packages to cus- tomers at the lowest possible cost per package to the delivery organization. The lower-level members were markedly controlled in their behavior by sets of time-study standards against which each person's performance was compared. This was an all-male organization.

B. Automobile Sales Dealerships (N = 36) The organizations included in this part of the study consisted of

36 automobile dealership organizations located in or adjacent to metropolitan areas. The typical organizational form is shown in Figure 2. The basic hierarchical structure showed three levels, and the major structural source of variation was the number of members in each of the organizations. The various dealerships differed in respect to having combined or separated departments for new and used automobile sales, but this appeared to be irrelevant for our purposes since the number of supervisors per salesman did not covary with this characteristic for dealerships of the same size. The total size of the 36 units varied from 25 to 132 members. Each unit, though independently owned, functioned within certain common policies of the supplying firm toward the basic objective of profitable sales and servicing of automobiles and automobile parts.

The behavior of lower-level employees in this situation was




OWNER OR

GEN. MGR.

OFFICE SALES SERVICE PARTS OR MGR. MGR. MGR.

BUSINESS USED 5 NEW MGR. CAR CAR

OFFICE SALESMEN SERVICE PARTS STAFF DEPT. DEPT.

Figure 2. Structure of a typical automobile sales dealership organization.

partially controlled by quotas which they were assigned both in sales and other measurable performances. However, the amount of time controlled by these quotas was not nearly as stringent as in the case of the package delivery stations. The men controlled a good portion of their own time, especially that period of time when they were off the sales floor (about four hours a day). The amount of necessary supervisory control was moderate.

C. Volunteer Fire Companies (N = 12) Twelve volunteer fire companies belonging to the same state

volunteer fire company association were studied. They were located in smaller communities adjacent to a large metropolitan area. The local units of this parent organization had a dual organizational structure. The fire-fighting structure included a chief, his officers, and the rank and file. This organization overlapped with the companies' other functional organization that handled social events. The "social events" organization included the president, his officers, and the rank and file. There is some overlap in the officers in both structures. This too was an all-male organization.

D. Industrial Labor Union Locals (N = 8) Eight labor union locals located in an eastern metropolitan

state allowed us to obtain data. These locals were members of the same district of a large international union. The local unions were basically structured into three-level hierarchies. These included



3o6 ADMINISTRATIVE SCIENCE QUARTERLY

the decision makers (the president, business agents, or executive boards), the other officers (stewards), and the rank and file. The need for supervisory control was intermittent in these locals. Members of these organizational units were both males and females.

E. Nonpartisan Political Organization Chapters (N = 28) The organizations included in this part of the study were 28

local associations affiliated with the same national organization. Each of the units was located in a metropolitan area. The typical voluntary association unit had the organizational structure shown in Figure 3. The basic hierarchical structure showed three levels,

PRESIDENT

| s s ~COMMITTEE CHAIRMEN | \ ~~~~AND TASK-GROUP

|BOARD LEADERS

| RANK-AND-FILE MEMBERS l

Figure 3. Typical structure of voluntary associations.

and the major structural source of variation was the number of members in each of the organizational units. The president and board members were locally elected for limited tenure. The size of the units varied from 101 to 2,983 members. Each unit functioned within the policies of the parent national organization toward the objective of increasing citizen participation in political activities. The organization operated basically through the skills and supervisory activities of its leaders, who attempted relatively little control over member behavior. Its members were all females.

RESULTS

The results of the data collections in each case can be seen in Figure 4. In each instance where higher-level clerical personnel were present, they have been eliminated from consideration as supervisors. In each of the sets of organizations there is a significant negative slope to the curves: as size of the local organizational unit increases, the supervision ratio declines. The relation-



SIZE AND SUPERVISION 307 ship is logarithmic, curvilinear, and asymptotic to the axis. The curves are therefore plotted on semilogarithmic scales. There is a striking similarity in the slope of the curves. In all five cases, the data became surprisingly linear when plotted on semilogarithmic scales, and in four of these five cases the slope of the lines is remarkably alike (the exception is the slope for the eight local unions). The similar slopes are sharp and decline at much the same rate (Figure 4 and Table 1). Not only do sizable increases in the number of lower-level members take place before any increase at all takes place in the number of supervisors, but as the size of the organizations increases, the organizations seem to take in more and more lower-level members before adding new supervisors.

Table 1. Organization size and supervision ratio fitting a linear logarithmic curve. *

Pearson r correlation Set of organizations N x = ea+by coefficients

Package delivery stations 32 x = e408-7-48 _.375 (p <.05)

Automobile sales dealerships 36 x = e4 79-6545Y -.514 (p <.01)

Volunteer fire companies 12 x = e4 35-3.83Y -.644 (p <.02)

Industrial labor union locals 8 x = e6.91-21a60Y -.925 (p <.001)

Nonpartisan political organization chapters 28 x = e684-6-251 -.821 (p <.001)

X = organization size; y = supervision ratio.

From Table 1 we can see that the general equation of the fit of the logarithmic curve is of the form x = ea+by where the sign of the b coefficient in all five cases is negative, indicating a negative slope. The proposed curves fit the data quite well as is shown in Table 1 by the correlation coefficients for each set of data.7 The curve for the package delivery stations fits least well, but all of the five correlation coefficients are statistically significantly different from zero at less than the p .05 level of significance.

For the purpose of this analysis we have considered x to be 7I would like to thank S. A. Foote for advice on curve fitting.




+ O

*. . xu

0~~~~~~~~~

tO ~ ~ xEO GJ . N-- U x

LU~X

0~~~~~~~~~ > 0

0~~~~~~~~~~ 0) , _ _ _

U .

. - , o

. _ __ 0 o

U) C' O c' 2 0 )

co cr '

(nCV CV) C~l

--------- X- - -

~~~~~~~~~~~~ X.

N

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0

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'40

* ~~~~~~~~~~~+- 0

*,~~~~~~~4 ~ 1

CO CV) C0 OUL

.lJ'9WuW 70401 0; (Msp'Oa) SM?T!AJodS io 017>d

Figure 4. Covariation of organizational unit size and supervision ratio for five sets of organizations.




the natural logarithm of organization size and y to be the supervision ratio. This was done rather than having y = ea+bx where y would equal the natural logarithm of the supervision ratio and x would equal organization size, because the former curve gave a better fit to the five sets of data. It should also be noted that the fit of the present curves is not adequate for each set of data for extremely large organizations and that at extremely small sizes the other hypothetical curves would not adequately fit the data.

We may assume that the initiating point of each set of data is close to the smallest viable form of that organization. If we take a dynamic view, the structure of the local unit is set early, and as size increases there is a decline in supervision ratio. Additions to the supervision component come as size increases occur but not at a sufficient rate to maintain the earlier level of supervision ratio.

DISCUSSION

Clearly the data support the second of the two suggested hypotheses. This second hypothesis, then, needs to be explored in detail. Let us first approach the problem of how widespread are the findings reported here. We do have five sets of data, but we have not sampled all organizations; further, Terrien and Mills have reported, contrary to the present findings, that in school districts as size increases the ratio of administrative personnel to total members increases.8 The discrepancy between these, the present data, and the Terrien and Mills data, may be the latter's inclusion of staff nonsupervisory personnel in their administrative component; recently Terrien has found evidence in agree- ment with the present findings when this factor was considered.9 Secondly, the phenomena we have reported may be limited to local units at the lower levels of multiunit organizations. There are, however, indications that size of company and span of control are positively correlated at the top of organizations as well as at the bottom local unit level.10

Anderson and Warkov suggest that if functional complexity stays the same, size and supervision ratio are negatively cor-

8F. W. Terrien and D. L. Mills, The Effects of Changing Size upon the Internal Structure of Organization, American Sociological Review, 20 (1955), 11-13.

9F. W. Terrien, op. cit. 10E. Dale, op. cit., and Doris R. Entwisle and T. Walton, op. cit.




related." This is directionally consistent with our findings, since within each of the five sets of organizations each of the local units serves the same function.

Two related questions present themselves. Why does a set show a particular curve? What makes a set of organizational units a set? Let us consider these questions jointly. It is from Figure 4 and Table 1 that we can see that each set of data has its negatively sloped curve of fairly similar form. If one looked at the data irrespective of the set of organizations considered, little of a systematic nature could be concluded except that very large units tend to have relatively small supervision ratios. However, con- sidering the points from each set of organizations as a set, the data are then organized into more interpretable form. Plotting on semi- log grids straightens out the curves. This kind of presentation of the data shows that small units show higher supervision ratios than middle-size units, which in turn show higher supervision ratios than large units when each set of data is considered separately. This conclusion is supported for all five sets of data, but it is least supported for the volunteer fire companies. The reason in the latter case may be that the size range is not sufficient to allow us to explore this proposition adequately.

With the findings in mind what can we say about a set? Within each set of organizations studied there is a group of persons who share the over-all purpose, a common set of policies, and a common three-level hierarchical structure. These essential facts might lead to the results shown, but the reason they would is as yet unclear.

A possibility may be that the top management of each of these organizational sets feels that one of the benefits of large size is that less supervision per member is necessary due to the similarity of tasks of the added members. However, in three of the sets of organizations studied (those where the necessary data were available), increased size was associated with increased task specializa- tion'2 implying the need for more supervision per member-so that this explanation is not especially tenable.

"J. R. Anderson and S. Warkov, Organization Size and Functional Complexity: A Study of Administration in Hospitals, American Sociological Review, 26 (1961), 23-28.

12B. P. Indik, Organization Size and Member Participation: Some Empirical Tests of Alternative Explanations, Human Relations, 17 (1964).




However, it might also be that the placement of each of these curves reflects at its origin (the a coefficient) the initial size of a viable organizational form given the purposes and policies of the set of organizations, and that the placement of the curve reflects the degree of interpersonal control over the members of the respec- tive sets necessary for viable maintenance of the organizational units. The data available here on the relationship of organization size to other forms of control are not clear.

It may be that a combination of the amount of behavior to be controlled per member per day, and the restriction to specific behaviors required by the organization involved, sets the placement of the curve. To be more specific, of all sets of organizations the delivery-service organizations require both the largest amount of behavior control per member (eight hours per day) and the most delimiting controls of member behavior, since each member must conform (within narrow limits) to standard behavior requirements as set by time-studied rates of performance. At the other extreme, the political organization chapters have the least necessity for interpersonal control or, for that matter, control of any kind over their members. Most members may be contacted only once or more a month while relatively few members spend any portion of their time constrained by organizational requirements that control their behavior.

The three sets of organizations whose curves fall between these two extreme curves might be there for a combination of reasons compatible with the present explanation. (It should be remem- bered that this is post hoc conjecture and needs to be explored in detail in future studies.) The automobile dealerships directly constrain the behavior of their salesmen to four hours per day on the sales floor and allow the rest of the sales time of salesmen to be allocated by themselves so long as sales quotas are maintained; specific behavior of the salesmen is not rigidly controlled. The members of the volunteer fire companies are less controlled in terms of time by their supervisors than are the members of the delivery-service organizations and the automobile sales dealerships; however, they are more constrained to specific risky behavior when they are fulfilling their organizational roles. They are certainly more frequently controlled by organizational constraints than are the members of the voluntary political organizations.




The industrial labor union locals also fit this pattern; they function very much like the volunteer fire companies when they are small and somewhat like the voluntary political organizations when they are large. To be more specific, when the local union is small, a core of leaders and cadre are more constrained and controlled when emergencies arise, but the time constraints are not nearly as severe as they are for the members of the delivery organizations, nor are they as minimally controlled as the voluntary political organization members. However, as the size of the local increases, the per-member constraints on behavior and the concomitant interpersonal (supervisory) control necessary for the local's viability decline, and then approach the functional level of the voluntary political organizations.

Further, the levels of the b coefficient for each set of organizations seem to be characteristic of each particular set of data and may reflect the differential need for interpersonal supervisory control for each kind of organzation. Both of these explanations support the structure-function position in that from structural characteristics of a system, the functional properties and processes flow. In this case, from a simply obtained bivariate structural relationship one may infer significant functional characteristics of an organization.



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The Relationship Between Organization Size and Supervision Ratio