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Estimating sex-related bias in job evaluation.

The comparable worth thesis states that jobs, which differ in their content but are of similar value on compensatory factors such as skill, effort, responsibility and working conditions should be paid similarly (Arvey, 1986; Arvey, Maxwell & Abraham, 1985). At present, the principle is guaranteed by law in the European Community and in other countries (e.g. Canada) and states (Washington, Minnesota), thereby heightening the need for an unbiased measurement of job worth (Elizur, 1987b; Elizur & Thierry, 1987). Although job evaluation techniques(1) have been used extensively for the past few decades to assess the relative value of jobs, there is considerable recognition that these procedures may result in systematically biased estimates of the true job worth (Bellace, 1988; Remick, 1981; Wallace & Fay, 1988). Especially the problem of sex-related bias, where female-dominated jobs are underrated and, hence, underpaid, is at stake. In a review, Arvey (1986) discusses four possible 'ports of entry' for sex bias to occur in a typical job evaluation exercise. Bias may be present (a) in the job analysis phase; (b) through the particular choice, definition and anchoring of the compensatory factors; (c) during the evaluation of the jobs against the retained factors; and (d) because of the quantification and weighting of the raw factor scores (i.e. the anchor assignments of the job on the compensatory factors).

The present paper focuses on the latter, quantification stage, in particular within the context of the most popular job evaluation technique, namely the point method (Doverspike & Barrett, 1984). More specifically, it is shown that a local modification of the method allows for an efficient procedure to estimate the extent of sex bias related to the valuation and weighted aggregation of the raw factor scores to a global job worth. So the purpose of the paper is twofold. Firstly, an alternative, called the model-based approach, to the scaling and weighting of the compensatory factors is proposed. Secondly, it is discussed how this alternative may be used to assess the extent of sex-related bias in a given set of job worths. The latter goal is the more important one, however, in that the first objective is best conceived as an intermediate but necessary step on the way to achieve the second purpose.

The focus on the quantification/measurement phase of job evaluation is of particular importance. Whereas significant contributions towards the analysis and prevention of bias in the other three stages have been published (e.g. Arvey, Passino & Lounsbury, 1977; Doverspike & Barrett, 1984; McShane, 1990; Madigan, 1985; Mount & Ellis, 1987; Schwab & Grams, 1985), only Elizur (1987a, b) provides a serious discussion of the measurement issue. As he argues convincingly, the rankings of the jobs on the factors are 'in principle ... no different from the rank positions accorded |to~ contestants in a beauty contest' (Elizur, 1987a, p. 91). That is, the data obtained in job evaluation are not at an interval level of measurement. Hence, the operations of multiplication and addition, usually performed in the point method to obtain a total value score are inadmissible. Elizur (1987a) proposes to solve the issue by the introduction of a scalability criterion: only factors that are monotonically interrelated--i.e. tend to produce the same ranking of the jobs--are retained.

The proposal is not very satisfactory, though, as it excludes factors that are frequently used in most evaluation plans. For instance, this is the case with the factor 'working conditions' which fails to correlate with many other evaluation items (Elizur, 1987a). Also, the scalability criterion is at variance with the idea that compensatory factors should make independent contributions to the evaluation in order to avoid double counting (Arthurs, 1988). Finally, the proposal clashes with current practice in that most evaluation plans are not unidimensional (Davis & Sauser, 1991; Thierry & de Jong, 1989). Hence, it seems that a more general solution to the quantification/aggregation problem is called for. One possible candidate, i.e. the model-based approach to job evaluation, is discussed in the next section.

Model-based approach

Point factor method

This section gives a brief overview of the point factor method. The section also introduces some formal notation, related to the design and the application of the method. While the formalism may at first seem unnecessarily complex, it is of vital importance to the developments reported in the subsequent sections.

The point factor method uses a number of compensatory factors to evaluate the worth of a job. The factors are usually chosen and defined by a compensation analyst or a job evaluation committee (Gomez-Mejia, 1989), and subdivisions of ranks, expressing the degrees (levels or anchors) within each factor, are constructed. Then, the degrees are scaled by assigning a point value to each of the anchors, and weights, reflecting the importance of the compensatory factors, are determined.


Table 1 summarizes the aforementioned stages. In addition, the table defines part of the notation that will be needed later on. Henceforth, the symbols f, |l.sub.f~, |X.sub.fl~, and |w.sub.f~ are used to refer to the factors, the levels within a factor, the point value of the levels, and the weights of the factors respectively. The total number of factors within a given point plan is denoted as F, and the symbol |L.sub.f~ indicates the number of levels within factor f. Finally, the symbols w and |X.sub.f~ refer to the column vector of weights and the scaling of factor f respectively.

Once the point plan has been developed, the jobs can be evaluated. For each job and every factor, the degree, which typifies the job with respect to the factor, is indicated, and the job total point value is obtained by summing the corresponding points, multiplied by the factor weights. The more formal notation for this procedure appears in the lower part of Table 1. For purposes of further reference, the set {|P.sub.j~} will be called a scaling of the job worths, and the symbol {|x.sub.jf~} will be used to characterize the set of job ranks of the jobs with respect to the compensatory factors. In some instances, the latter set will be referred to as the raw factor scores of the jobs.


The development of a point method is typically based on two quantification operations. The first quantification relates to the scaling of the factors, while the second corresponds to the weighting of these factors and the consecutive use of the weights in the calculation of the job worths. In accordance with Hazewinkel (1969) and Elizur (1987a), the model-based approach criticizes these quantifications because they have no theoretical or statistical justification: the data on which both operations are based do not reflect the interval level of measurement property which is typically assumed for the scaling and the weighting of the factors. There is simply not enough evidence to defend the proposition that exact (unique) values can be assigned, for example, to the factor degrees. Only non-unique, lower-level quantifications, which convey either categorical or ordinal information, can be accepted, resulting in a multitude of admissible scalings and weighting schemes.

From now on, the symbols ||omega~.sub.s~ and ||omega~.sub.w~ are introduced to indicate the set of acceptable scalings of the factor degrees and the class of admissible weightings respectively. For the present, it is quite immaterial how these sets can be defined more precisely (such a definition is proposed in the next section). What is important, however, is that it is generally accepted that more than one scaling and weighting of the factors is feasible (e.g. Elizur, 1987a; Milkowich & Newman, 1990; Wallace & Fay, 1988), and that the choice between these admissible scalings and weightings is essentially arbitrary.

To deal with this arbitrary element, we propose a modification to the scaling and weighting stages of the classical point method. The modification, called the model-based approach to job evaluation, no longer aims at a unique (or an interval level) scaling and weighting of the compensatory factors. Instead, the anchor points and the weights are conceived as unknowns or parameters, and the approach focuses on a systematic and rational demarcation of the principles (properties, requirements or constraints) which must be met by the quantifications of these parameters in order to be acceptable.

Essentially, two types of quantification principles can be distinguished, depending on whether the principle is general (i.e. self-evident) or specific to the context of application. The requirement that higher degrees of a factor should be assigned more points is an example of a self-evident quantification property; whereas the constraint that the factor weights should reflect a particular rank order constitutes an example of the second type (cf. Wallace & Fay, 1988).

Consistent with earlier observations, the model-based approach states that both types of principles convey only categorical, ordinal or other non-interval level information with respect to the scaling and weighting of the factors. When adequately formulated--i.e. when the list of retained quantification principles is valid--these properties identify the sets ||omega.sub.s~ and ||omega~.sub.w~ exactly. Whether or not this will be the case in a particular application remains a judgemental issue, however. Because of the inherently subjective nature of job evaluation (Ghobadian & White, 1987; McShane, 1990; Madigan, 1985), the completion of the list of applicable (context-specific) properties cannot be a matter of logic only. Quantification decisions are inevitable, but the process is greatly helped in that only low-complexity decisions are asked for. Also, each decision must be stated explicitly, either by the job evaluation expert or the evaluation committee responsible for the design of the point plan. As a consequence, the evaluation becomes more transparent and less prone to otherwise undetectable bias. Hence, even though the model-based approach does not solve the validity issue related to the scaling and weighting of the compensatory factors, the approach at least offers a unique opportunity to track the decisions which are relevant to the issue.

Since a variety of scalings and weightings of the compensatory factors is admissible, it follows that the scaling of the job worth is also not unique. Henceforth, the set of all such feasible scalings of the job worths is indicated by the symbol ||omega~.sub.p~. If, as is the case in the model-based approach, the set {|x.sub.jf~} is accepted as a given, then the heterogeneity of ||omega~.sub.p~ reduces to the variety in both ||omega~.sub.s~ and ||omega~.sub.w~. How the latter two sets are operationalized is discussed next.

Admissible scalings and weightings

The definition of the set ||omega~.sub.s~ (||omega~.sub.w~) amounts to the systematic enumeration of the quantification principles which separate the admissible scalings (weightings) from the inadmissible ones. Since some of these principles are specific to the application context, a generally valid specification of ||omega~.sub.s~ and ||omega~.sub.w~ is neither necessary nor possible. Hence, the definition of both sets first concentrates on the minimal (general or self-evident) requirements any acceptable scaling or weighting should fulfil.

With regard to the scaling of the factors, three such general properties can be distinguished: a scaling is admissible if and only if (a) the lowest factor anchor receives a non-negative point value; (b) higher factor degrees receive more points; and (c) the highest factor level, whatever the factor, is assigned an arbitrarily chosen, but constant point value Q. Although the latter constraint may seem to be unduly restrictive, it is not if the factors can be weighted differently.

As to the weighting of the factors, only one constraint is retained: all weights should lie between a pre-specified minimum and maximum value. While the constraint allows for a differential treatment of the factors in terms of their importance, the requirement also excludes the eventuality that the job values are predominantly determined by only one of the retained factors.

In any particular application, the minimal specification of ||omega~.sub.s~ and ||omega~.sub.w~ must be augmented with the appropriate set of situation specific requirements. These express organizational policy decisions, priority statements or any other information (e.g. the scaling properties which can be derived from the careful examination of the verbal description of the factor degrees) which is relevant to the scaling and weighting of the variables.

Summarizing, the model-based approach abandons the idea that the factor degrees and the weights are measurable properties. Instead, they are conceived as parameters which must comply with a set of minimal and a number of application specific requirements. The first objective of the approach is to identify these quantification principles, and this results in the definition of the set ||omega~.sub.s~ of admissible factor scalings and the set ||omega~.sub.w~ of acceptable factor weightings. Because the quantification principles do not convey interval level information, both sets have an infinity of elements. Any pair of elements, one from ||omega~.sub.s~ and the other from ||omega~.sub.w~, leads, when combined with the raw factor scores of the jobs, to an admissible quantification of the job worths; and the totality of all these acceptable job evaluations constitutes the set ||omega~.sub.p~. The heterogeneity of the latter set is the price paid for honouring the limited capabilities of human judgement. In terms of validity, the price is justified, though, for it seems plausible that biased or erroneous evaluations are easier to come by when highly specific (i.e. interval level quantification decisions) but otherwise unattainable judgements are called for.

Estimating sex-related bias

Criterion for sex-related bias

Because the specification of ||omega~.sub.p~ exhausts everything that can be said on the job worths, no further choice is possible between its elements: they are all equally acceptable and equally defensible. The scalings are not equivalent with regard to the presence or absence of sex bias, however. To show this, a set of J jobs, which are either male- or female-dominated (i.e. jobs for which 70 per cent or more of the job holders are male or female |Bellace, 1987~), is considered. Defining d as the proportion of points assigned to the male-dominated jobs (i.e. d = ||Sigma~.sub.j~|I.sub.j~|P.sub.j~/||Sigma~.sub.j~|P.sub.j~ with |I.sub.j~ equal to one when j is a male-dominated job and zero otherwise), it is obvious that d will vary over ||omega~.sub.p~, with |d.sup.+~ (|d.sup.-~) as the maximum (minimum) possible value. In plain words, this means that the acceptable scalings of the job worths are not equally beneficial for the male- (female-) dominated jobs. Whereas the scaling, associated with the proportion |d.sup.-~, is maximally advantageous for the female jobs, the reverse holds for the quantification which is characterized by d equal to |d.sup.+~. To assure that both male- and female-dominated jobs are treated equally, only the scaling, for which d is equal to (|d.sup.+~ + |d.sup.-~)/2, is admissible. All the other elements of ||omega~.sub.p~ are systematically biased in favour of either the male or the female jobs.

It might be argued that the proposed criterion for the absence of sex-related bias is defective in two respects. Firstly, the proposal might be objected to on the ground that it confounds the notion of discrimination with the actual allocation of the jobs to males and females. This objection is unjustified, though, because the criterion focuses on sex-related bias, and not on some unqualified form of discrimination. Moreover, the usage of the distinction 'male- vs. female-dominated jobs' parallels the approach of the procedures used to scan for sex-related discrimination in compensation. These procedures (regression, structural equations modelling, non-parametric analysis of covariance, etc.) also start with classifying the jobs (or the job holders) as either male or female, and their results typically depend on this distinction.

Secondly, the criterion might be judged inadequate because it does not guarantee that the quantification rules and the policy considerations, on which the definition of ||omega~.sub.p~ is based, are themselves free of discrimination. Although justified, the objection does not really undo the advantages of our proposal in that the application of the model-based approach necessitates an explicit statement of these rules and considerations. Also, as hinted at above, it is reasonable to assume that, because of their lower level of complexity, the adopted rules and principles are definitely easier to assess in terms of their discriminatory potential.

Quantification of sex-related bias

The model-based criterion of sex-related discrimination allows for a distinction between biased and non-biased evaluations only. From a practical perspective, it would be preferable, however, to have a measure that quantifies the extent of the bias. Such a quantification is required, for example, to assess whether a given set of job worths is only marginally biased. Fortunately, a discrimination index, DI, is easily conceived of in the framework of the model-based approach. The index, which is formally defined as

|Mathematical Expression Omitted~

indicates how much the ratio of points actually attributed to the male-dominated jobs deviates from the non-discriminating ratio (|d.sup.+~ + |d.sup.-~)/2, and scales this deviation in terms of the difference between |d.sup.+~ and |d.sup.-~. The previous specifications of ||omega~.sub.p~, |d.sup.+~ and |d.sup.-~ imply that the value of the index, over the set ||omega~.sub.p~, is restricted to the closed interval { -1, +1}. A value of -1 (+1) expresses maximum discrimination against males (females), and a value of zero indicates no sex-related bias.

Besides measuring the extent of the bias, the index offers at least two other advantages. Firstly, the quantification allows for between-organization comparisons. Secondly, the index can be used to conceive of a more practical criterion by defining absence of discrimination in terms of an upper limit on the (absolute) value of the DI index.

Calculation of the discrimination index

In actual applications, the calculation of the DI index associated with an existing set of job worths, pertaining to J jobs which are either male- or female-dominated, involves a three-step procedure. The first step compares with the development phase of the classical point method. The only difference is that the model-based approach does not aim at a unique quantification of both the anchor worths and the factor importances, but instead focuses on an explicit definition of the scaling and weighting properties. As discussed in the previous section, the step results in the demarcation of the set ||omega~.sub.p~, and in practical settings the process reduces to an adequate inventory of the quantification principles that are situation specific. To facilitate the task for the evaluation committee, a structured decision process, such as the delphi method or a nominal group technique, may be used (Milkovich & Newman, 1990). For a more thorough discussion of the issue, the reader is referred to the final section of the paper.

The second step of the procedure consists of the computation of the quantities |d.sup.+~ and |d.sup.-~. Both computations amount to solving a non-linear fractional programming problem that can be simplified to a standard linear program. This assures that the values obtained correspond to the global maximum (minimum) of d over ||omega~.sub.p~. Finally, the proportion of points actually attributed to the male-dominated jobs is calculated, and DI is computed as in Equation (1).



The example is based on a real application of the model-based approach in a mid-sized firm from the distribution sector. Because of complaints about the wage structure, management decided to investigate the present job worths |p.sub.j~ for the presence of sex-related bias, and an independent expert was appointed to guide the process. Although the expert proposed a total of eight dimensions to evaluate the jobs, only the following three factors are used in the example: degree of instruction (a five level factor), extent of supervision (four levels) and degree of control (also four levels).

With the definition of the factors and the anchor degrees at hand, an evaluation committee, headed by the expert and composed of employer and employee representatives, was asked to perform a scaling and a scoring task. The purpose of the former task was to obtain the application specific definition of ||omega~.sub.p~, and, to meet the objective, a nominal group technique (Milkovich & Newman, 1990) was used. Each member of the committee was asked to rate independently the lower and upper bound value of the factor degrees, TABULAR DATA OMITTED assuming that the highest anchor received a total of 100 points. In addition, the members were instructed to specify their ideas with regard to the ranking of the factors. Next, the individual opinions were gathered on a blackboard, and the committee members were given the opportunity to clarify their proposal. Finally, the evaluation expert led a discussion session focusing on the quantification principles which could be derived from the different proposals. Table 2, which summarizes the obtained consensus, indicates that the agreement concerns (a) the ranges of quantification for the factor anchors (cf. the upper part of Table 2); (b) the difference in scale value of consecutive factor degrees (the middle part of Table 2); and (c) the order of factor weights.


The scoring task of the committee related to the evaluation of 10 benchmark job|s.sup.2~ with regard to the compensatory factors. The results of the task are reported in Table 3: for each job, the anchor assignments as well as the corresponding indicator vectors are listed.

In addition, Table 3 also indicates the current job worth and the sex type of the jobs; male-dominated jobs are coded by 1, while 0 means that the job is female-dominated.

Estimation of systematic bias

As shown previously, the estimation of the DI-index, associated with the set {|p.sub.j~} of current job worths, involves the calculation of |d.sup.+~ and |d.sup.-~. The corresponding fractional programming problems are detailed in Appendix 2. Solving these problems results in a value of 0.7254 for |d.sup.+~, whereas a value of 0.6256 is obtained when d is minimized. As the actual proportion d of points attributed to the male-dominated jobs, calculated on the basis of the job worths {|p.sub.j~}, is equal to

|Mathematical Expression Omitted~

the discrimination index DI, associated with the latter set, is equal to 0.230:

|Mathematical Expression Omitted~

This means that the present job worths |p.sub.j~ discriminate in favour of the

male jobs and that the sex-related bias attains 23 per cent of the maximum possible discrimination (over the set ||omega~.sub.p~).


The discussion of the model-based approach to job evaluation focuses on three topics: significance, limitations and further developments. The contribution is significant because the framework allows an estimation of the extent of systematic bias related to the quantification and weighting stages of the point method of job evaluation. As such, the contribution is quite unique in that it is the first procedure to achieve this purpose in a systematic and generally applicable way. There is an additional aspect to the relevance of the approach, however. This second aspect concerns the implications of the framework with regard to the actual practice of the point method. In the previous sections, it has been emphasized that the scaling and weighting stages of the method should concentrate on the quantification properties, and not on the interval level scaling of the anchor and job worths. This implies that the relatively small set of highly specific quantification decisions should be replaced by an explicit statement of a larger number of simpler evaluations. Not only is the latter approach less prone to errors and biases, but the procedure also creates a more transparent and, hence, a more easily accepted evaluation environment.

The implementation of the approach is not without problems, however. In practical settings, it may not always be straightforward to determine the additional constraints such that ||omega~.sub.p~ contains only the admissible scalings of the job worths; even though some structured decision process (such as the delphi or another nominal group technique, Milkovich & Newman, 1990) is used. One alternative approach then consists of proposing a less general formulation of the quantification principles. For the more restrictive these principles are, the less additional requirements have to be formulated for the resulting set ||omega~.sub.p~ to be adequate.

Another way to deal with the problem consists of confronting the evaluators with the solution vectors (i.e. the sets of values for the scaling and the weight parameters associated with d equal to |d.sup.+~ and |d.sup.-~ respectively. When these vectors show no anomalies, in the sense that the scaling of the anchors and the weighting of the factors are not at variance with either the available data or the consensus of the committee members, the present specification of ||omega~.sub.p~ is verified. In case of such anomalies, inspection of the solution vectors will make it easier for the committee to specify the additional constraints which prohibit the undesired features of the scaling.

A final approach to the identification of the application-specific requirements consists of the use of a pre-established checklist of quantification principles. Apart from prompting such questions as 'Should factor f be scaled progressively (degressively)?', the checklist may point, for example, to the possibility of rank ordering the differences in anchor points. However, whatever heuristics are followed, it must be repeated that the enumeration of the quantification properties is not a matter of logic only. Because of the inherent subjective nature of job evaluation, the choice and definition of these principles will always retain a judgemental aspect. This aspect is guided by the modelling framework, though, in that the approach (a) asks for low-complexity decisions only, and (b) provides the opportunity clearly to specify the available decision alternatives. So, assuming that the competence level of the evaluation expert or committee which has to make these decisions is comparable to that required in the design of the classical point method, there is reason to believe that the end result will be less erroneous.

A second limitation of the present approach is that it does not lead to a unique quantification of the job worths. Neither does the approach result in a proposal to correct an existing evaluation for the presence of sex-related bias. Both limitations are not really critical, though, because the framework is not primarily designed to handle those issues: the approach first and foremost aims at estimating the extent of sex-related bias in (a) the quantification of the factor levels, and (b) the weighted aggregation of the resulting scores to global worths. A similar argument applies to the criticism that the method is too sophisticated to be acceptable by the parties involved in the job evaluation process. As a device to scan for discrimination, the ultimate question is not whether the approach is simple, but whether the procedure fulfils its purpose adequately.

Although we argued that the limitations mentioned above are not crucial, it would be preferable to deal with these shortcomings in a more constructive way. Obviously, the latter task relates to the third discussion topic concerning the possibility for further developments. A promising approach to at least two of the limitations--the operations, associated with the introduction of the set ||omega~.sub.p~ and the optimization of the proportion d, are inevitable--consists of broadening the scope from the process of job evaluation to the problem of fair compensation. More specifically, one could conceive a third set of principles which describes the admissible ways in which both the job total worths and external market information can be translated to base wages. With the latter extension, the modelling approach might provide a rational framework for the implementation of the comparable worth principle. Using existing market wages (or the base wages presently paid by the organization) a new wage set could be determined which (a) fits the target pay scheme as closely as possible; and (b) is an admissible function of the, as yet, unknown collection of non-biased job worths. As a byproduct of solving the latter problem, a unique quantification of the worths would be obtained, thereby indicating in what way the present biased evaluation needs correction. Work related to the extension is currently in progress, and an account of the results will be given shortly.


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1 Throughout the paper, job evaluation is discussed from the applied measurement perspective. The perspective 'views job evaluation as a measurement problem of how to compare jobs ... in order to determine their relative value to the organization' (Elizur, 1987a, p. 6).

2 Actually, the committee rated 17 jobs. However, only 10 of these are either male- or female-dominated.


I gratefully acknowledge the assistance of Pol Coetsier in the conceptualization stage of the paper and of John Arnold, Geert De Soete, Bill Whiteley and three anonymous reviewers for comments on an earlier draft.
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Author:De Corte, Wilfried
Publication:Journal of Occupational and Organizational Psychology
Date:Mar 1, 1993
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