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5A COMPARISON OF FACTOR WEIGHTING METHODS IN JOB EVALUATION

5A COMPARISON OF FACTOR WEIGHTING METHODS IN JOB EVALUATION
5A COMPARISON OF FACTOR WEIGHTING METHODS IN JOB EVALUATION

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Industrial and Labor Relations Review, Vol. 54, No. 4 (July 2001). ? by Cornell University.

0019-7939/00/5404 $01.00

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AN EXPERIMENTAL STUDY OF JOB EVALUATION AND COMPARABLE WORTH

E. JANE ARNAULT, LOUIS GORDON,

DOUGLAS H. JOINES, and G. MICHAEL PHILLIPS*

The doctrine of comparable worth rests on an assumption that each job possesses an inherent worth independent of the market forces of supply and demand. Implementation of comparable worth further requires that inherent job worth be measured with reasonable accuracy.This paper reports the results of an experimental study of comparable worth. Three commercial job evaluation firms rated the same set of 27jobs in an actual company. Statistical analysis of the experimental data indicates that the three evaluators differed in which job trait, or constel-lation of traits, they used to evaluate inherent job worth, implying that at least one of them failed to measure inherent job worth accurately.These results suggest that any attempt to implement comparable worth may be quite sensitive to the evaluator chosen to measure job worth.

*E. Jane Arnault is President of JurEcon, Inc.,Louis Gordon is a statistician at Tradar, LLC., Dou-glas H. Joines is Professor of F inance and Business Economics in the Marshall School of Business, Uni-versity of Southern California, and G. Michael Phillips is Professor of Finance, Real Estate, and Insurance at California State University, Northridge. The authors thank Delores Conway, John Rolph, Peter Rupert,and Mark Zupan for helpful comments on earlier drafts.

An appendix containing more detail on the statis-tical properties of the tests reported in this paper is available from Douglas H. Joines, Department of Finance and Business Economics, Marshall School of Business, University of Southern California, Los An-geles, CA 90089–1427.

dvocates of comparable worth contend that rates of compensation established in unregulated labor markets are frequently inequitable. Economists have long recog-nized that free labor markets may result in a highly unequal distribution of income,and inequality of income has been a source of concern to many observers of labor mar-kets. Those seeking to modify the income distribution set by the market fall into two

basic groups. One group recognizes that different individuals may be endowed with greatly different talents. Even if these tal-ents are appropriately priced by the mar-ket, the resulting income distribution may be very unequal. This group generally ad-vocates income redistribution through gov-ernment tax and transfer programs, but does not necessarily call for direct regula-tion of the labor market.

A second group has much less faith in the workings of the market. They believe that labor markets set inappropriate rates

JOB EVALUATION AND COMPARABLE WORTH807

of pay and need to be regulated. One type of regulation justified by such views is mini-mum wage legislation, which is proposed as a method for raising the earnings of low-income workers.

Another frequently proposed form of labor market regulation is the implementa-tion of a comparable worth plan. The inequities that comparable worth addresses need not be due to a low absolute wage for a given worker, however. These inequities result from a wage considered too low rela-tive to that paid another job, even if both of the jobs in question are highly paid relative to the average job. The labor market regu-lation implied by comparable worth is cor-respondingly more complex than impos-ing a simple minimum rate of pay. It in-volves “fine-tuning” an employer’s entire compensation structure from top to bot-tom.

The information required for this fine-tuning is considerable. It is not sufficient simply to rank jobs according to their sup-posed inherent worth. One must also mea-sure the value of each job and calculate degrees of difference between the values of different jobs. These values are presum-ably not determined merely by someone’s subjective notion of the moral worth of an activity. They are alleged to be something concrete, objective, and measurable.

In this paper we study the measurements of job value that are required for the suc-cessful implementation of comparable worth plans. In particular, we ask whether independent assessments of job worth by several different commercial job evalua-tion firms are mutually consistent. Sub-stantial inconsistencies in these job ratings would cast serious doubt either on the use-fulness of comparable worth as a concept or on the possibilities for applying this concept in practice.

This paper reports the results of an ex-periment in which three commercial job evaluation firms rated the same 27 jobs in a single company. All three firms generate a substantial amount of annual revenue from job evaluation, and each has major corpo-rate clients. The paper presents a statistical test of the hypothesis that all three job evaluation methods measure a single, com-mon trait that might be interpreted as job worth. As noted below, many economists might question whether one can meaning-fully speak of the inherent value of a job independent of market conditions. F or purposes of this study, we do not take a position on this issue. Rather, in imple-menting our test we implicitly assume the existence of a unique trait that might or might not correspond to inherent job worth. We then ask whether the three job evalua-tors have all measured this trait.

The Comparable Worth Movement Comparable worth is one of several poli-cies proposed to reduce the gap between men’s and women’s earnings. The exist-ence of this gap has been widely docu-mented (see, for example, Aaron and Lougy 1986; Johnson and Solon 1986; Blau 1998). There are several ways of accounting for (as opposed to explaining) this pay gap. One way is to identify where the differences in pay arise. They may be accounted for by (i) systematic differences in the pay of men and women performing the same job for the same employer, (ii) a tendency, within a given organization, for women to be con-centrated in lower-paying jobs, and (iii) a tendency for women to work for lower-paying employers. Empirically, item (i) contributes little to the overall gap between men’s and women’s earnings.1 Items (ii) and (iii) are much more important. Aaron and Lougy (1986) reported extensive gen-der segregation of the work force by occu-pation and industry. They and other re-searchers have documented a negative re-lation between industry or occupational earnings and the proportion of workers in the industry or occupation who are female (Bielby and Baron 1986; Johnson and So-lon 1986; Sorensen 1986).2

1See, for example, Ferber and Spaeth (1984), who cited evidence reported by Whitman (1973).

2Blau (1998) documented a reduction of occupa-tional sex segregation. Part of the narrowing of the male-female earnings gap that she found is due to “occupational upgrading” by women.

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The notion that there are “women’s jobs”and “men’s jobs” (for example, nurses and construction workers) and that women’s jobs pay systematically less than men’s pro-vides the rationale for the comparable worth movement. Comparable worth would man-date equal pay within an organization for jobs deemed to be of comparable value. There is some dispute about how much of the difference in earnings between men and women is accounted for by gender segregation within organizations (item ii above) and how much is due to segregation across employers (item iii). This distinc-tion is crucial in judging how far compa-rable worth would go in closing the pay gap between men and women.

Johnson and Solon (1986) estimated that comparable worth would reduce the earn-ings gap only from the current 33.7% of male earnings to between 31.5% and 32.8%. Using data from comparable worth studies of four state governments, Sorensen (1986) concluded that comparable worth would eliminate almost half of the pay gap not already explained by job attributes. Using data for the entire economy, Sorensen (1990) found that within-firm differences in the gender composition of jobs explain 20–23% of the national sex-based earnings gap, as compared with the 14% implied by the analysis of Johnson and Solon. This is the portion of the earnings difference that could be reduced or eliminated if compa-rable worth were implemented throughout the economy.

Data on employment and earnings are sufficient to identify gender segregation of the work force as the primary mechanism generating the earnings gap between men and women. The data are much less clear on the reasons for this gender segregation or for the pay gap more generally. Part may arise because of discrimination in hiring or compensation practices by employers.3 Part may be due to characteristics of individual workers, such as education or experience, that affect their productivity in and qualifi-cation for a given job. Any systematic dif-ferences between men and women in these relevant characteristics would be reflected in a difference between average male and female earnings and in some degree of gender segregation in employment. F i-nally, gender differences in occupational choice may reflect not only employer dis-crimination and gender-related differences in productivity in particular jobs, but also any systematic differences between men and women in their preferences for differ-ent types of work.4

Macpherson and Hirsch (1995) analyzed why female-dominated jobs pay less than male-dominated jobs. They used longitu-dinal data so as to control for unobserved differences in productivity, tastes, and job characteristics better than earlier studies were able to do. They found a negative simple correlation across occupations be-tween wages and the percentage of job incumbents who were female. Use of longi-tudinal data lowered the effect of the pro-portion female by about one-half, “indicat-ing that [unobserved] person-specific la-bor quality or preferences account for much of the previously observed relationship.”They found that adding variables to control for occupational and industry characteris-tics further weakened the effect, and that the “remaining effects of gender composi-tion on female or male wages appear rather small.”5

3Such discrimination must be based on the prefer-ences of employers rather than on an attempt to

minimize labor cost. An employer with monopsony power in the labor market would pay lower salaries to

workers with smaller labor supply elasticities. Labor market studies generally show that women have higher labor supply elasticities than men. Madden (1973) has argued that women may nevertheless have lower labor supply elasticities than men to certain occupa-tions, leading a monopsonistic employer to pay women less than men in those occupations. Aaron and Lougy (1986:6) concluded that at least half of the earnings gap “can be explained by factors unrelated to any possible discrimination by individual employers.”

4See Killingsworth (1987) for a detailed analysis of the effects of comparable worth in a general equilib-rium model in which men and women have different tastes for various jobs.

5In addition to research aimed at accounting for the male-female earnings gap, a body of work has appeared that analyzes the effects of comparable

JOB EVALUATION AND COMPARABLE WORTH809

Unlike the studies that have attempted to account for the male-female earnings gap or to determine the effects of compa-rable worth on particular classes of work-ers, this paper deals with the job evaluation process itself. Because the use of job evalu-ation extends beyond comparable worth systems, this evidence is potentially of in-terest outside the comparable worth con-text.

Job Evaluation

The notion of comparable worth is based on the belief that each job possesses some inherent and quantifiable worth indepen-dent of the value placed on it by the market. Implementation of comparable worth re-quires some way of measuring job value. Job evaluation, which has become wide-spread in the United States since World War II, is proposed as a way of doing this. There are now national and regional firms that provide job evaluation services to em-ployers. While there is no single, standard-ized procedure for job evaluation, some general principles do exist.

One such principle is that job worth depends on the characteristics of the job, not those of the workers who hold the job (see Schwab 1980, quoting Dunn and Rachel 1971, and Bellak 1984). As Schwab (1980) pointed out, this notion of worth is an internal one. The value of a job can be determined only within the context of a particular organization, and a given job can presumably have different values to different organizations.6

Despite differences in detail, various job evaluation procedures involve some com-mon steps. First, job descriptions are writ-ten for the jobs in question. Then a set of relevant job characteristics, called compens-able f actors, is identified and a weight is assigned to each factor. These factors fre-quently include the degree of skill, educa-tion, and mental effort required to per-form the job, the pleasantness of the work-ing conditions, and the responsibility in-volved. F inally, the job descriptions are evaluated to determine how much of each compensable factor each job entails. Schwab (1980) identified several prob-lems with the idealized view that job evalu-ation measures the value of all jobs in an organization. He argued that there is no evidence of the construct validity of job evalu-ation, that is, no evidence that the resulting job scores are related to the construct (job worth) they are supposed to measure. He pointed out that construct validation re-quires that the construct be clearly defined, and (p. 59) that “job worth has not been adequately defined nor has a consensus emerged as to its meaning.”7 Schwab also argued that the idealized view does not correspond to job evaluation in practice. He asserted that firms use job evaluation to set rates of pay for jobs for which the exter-nal market is too thin to provide readily observable indicators of value. In effect, the practical application of job evaluation involves fitting a hedonic price equation to those jobs within an organization for which there are readily identifiable market val-ues. The hedonic price model is then used to set the compensation of jobs for which market values are difficult to observe. This view is similar to that of Aaron and Lougy (1986:27), who stated that job evaluation has been used to remove anomalies from wage structures otherwise found to be ac-ceptable, not to change the wage structures in fundamental ways. The objective has been to align wages for particular jobs with

worth on different classes of workers (see, for ex-ample, Smith 1988; Orazem and Mattila 1990; Orazem, Mattila, and Weikum 1992; and Ames 1995).

6This notion itself raises an interesting issue of equity. Application of a single job evaluation proce-dure to two different companies might lead the com-panies to compensate the same job differently. Cur-rent law requires equal pay for equal work within a single company, and a competitive labor market also tends to result in equal pay for equal work across employers. However, an attempt to enforce equal pay for “comparable” work within each company might

lead different companies to different rates of pay for the same job, resulting in unequal pay for equal work across employers.

7This contrasts with the economist’s notion of marginal productivity, which, quite apart from ques-tions of measurement, has a very precise meaning.

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wages paid for other jobs with similar char-acteristics.

This interpretation, if correct, might explain why firms devote resources to job evaluation rather than merely rely on the market to signal job value. For highly spe-cialized jobs, frequent testing of the market might entail substantial search costs on the part of the employer and the employee, and routine use of job evaluation might reduce the frequency with which these search costs are incurred.

Schwab (1980, 1985) also discussed the convergence of different job evaluation pro-cedures, that is, the strength of the relation between the resulting measures of job worth. Clearly, if different procedures do not measure the same trait (for example, job worth), they cannot all be valid mea-sures of that trait. Schwab noted the “pau-city of research on job evaluation” (1985:41) and concluded (1980:62) that “convergence evidence to date suggests that alternative systems do not yield highly similar results, indicating that at least some systems are not construct valid.”8

This paper examines the convergence of the job evaluations performed by three commercial job evaluation firms. A few previous papers have studied convergence.9 However, none seems to have examined the ratings actually produced by different commercial job evaluation firms, each us-ing its own procedures and staff to perform the evaluations.10

The Experiment

F or this study, three commercial job evaluation firms independently rated the same 27 jobs in a single company. The firms used different factor comparison or point methods developed independently of one another. These methods are similar to the procedure used in the well-known State of Washington comparable worth case. Unlike the Washington case, however, the evaluations in our experiment were based solely on job descriptions prepared by the employer. The evaluators judged these job descriptions to be sufficiently clear and detailed to permit reliable evaluation.

The jobs were chosen in part by stratified random sampling based on the salary and gender of job incumbents. In addition to 24 randomly selected jobs, the three jobs with the largest numbers of employees were included in the sample. Each of these had 50% more incumbents than the next larg-est position in the firm. Together, these three jobs accounted for 22% of the total employment and 19% of the total payroll of the firm. We ranked the 27 jobs in descend-ing order by current salary.

Each evaluator assigned each job a point total referred to as the “size” of the job. The three evaluation procedures used dif-ferent job attributes in computing job sizes. Because the ratings supplied by the evalua-tors are not in dollar units, they provide no direct information about appropriate com-pensation. Because they are not even in the same units, the ratings cannot be compared directly one to another. To facilitate com-parison, we used a linear transformation to

8Another potential difficulty arises in the context of comparable worth because the initial ratings mea-sured by the job evaluation firm are subject to subse-quent modification by other parties to the compa-rable worth process. Orazem and Mattila (1990)

provided a detailed case study of the implementation of a comparable worth plan by the state of Iowa. They found (p. 135) that “initial gains to women were ultimately reduced and redirected toward constitu-encies that stood to lose or gain little as a result of the initial plan: union members, professionals, supervi-sors, and those with the highest market wages.”

9See Madigan (1985) and the studies cited in Schwab (1980, 1985), some of which date back to the 1940s.

10A related issue is the “reliability”—that is, repro-ducibility—of the ratings produced by different evalu-ators using the same evaluation procedure. Although managers at the job evaluation firms participating in this study expressed the belief that experienced staff members would all produce nearly identical ratings, it is possible that some of the differences we note below are attributable to the individual raters rather than to the evaluation procedures. Regardless of whether they result from invalid procedures or unre-liable raters, errors in measuring job worth can have serious consequences. Arvey, Maxwell, and Abraham (1985) showed how measurement errors can lead to apparent gender-related pay differences when no such differences actually exist.

JOB EVALUATION AND COMPARABLE WORTH811 rescale each evaluator’s raw scores so that

they each had a mean of 1,000 and a stan-

dard deviation 250. This normalization was

motivated by the fact that the standard

deviation of the 27 salaries was approxi-

mately 25% of the mean salary.

The Experimental Data

Table 1 shows the transformed scores

assigned to each of the 27 jobs by each of

the three evaluators, as well as the average

salary of all incumbents at the time of the

evaluation, also normalized to have a mean

of 1,000 and a standard deviation of 250.

The left-hand panel of Table 2 is a correla-

tion matrix of the job scores and salary.

The correlation between any two evalua-

tors is high (in the neighborhood of 0.8).

These pairwise correlations are similar to

those reported in the studies surveyed by

Schwab (1980, 1985). It is striking to note

that the third evaluator’s scores have a near-

perfect correlation with salary, whereas the

correlations for the first and second evalu-

ators are noticeably smaller.

The positive association among scores is

not surprising. For example, all evaluators

assigned more points to the job description

entitled “Executive Secretary II” than to

those for “Collator Operator,”“Receiving

Clerk,” and “Office Clerk.” If job evalua-tion is to be useful in implementing compa-rable worth, however, it must measure how much one job is worth relative to another. Here the three evaluators were not in close agreement. F or example, one evaluator assigned 75% more points to the executive secretary than to the collator operator, while another assigned only 30% more points. Similarity among total job scores could occur if each of the evaluators measured and assigned weight to some of the same factors. Similarity between the job scores and salary could occur if some of these factors were also compensated by the mar-ket. The bottom row of Table 2 suggests that this is in fact the case, since all three sets of scores are positively related to salary. This similarity says little about whether the scores are useful in providing measures of inherent job worth that are more “appro-priate” than the market wage. The notion of comparable worth is based on the premise that the market wage does not appropri-ately measure the value of a job. Measures of inherent worth thus constitute suggested corrections to the market wage. If compa-rable worth is to be meaningful in practice, there should be some similarity across evalu-ators not merely in gross measures of job worth, which may simply reflect factors al-ready compensated by the market, but also in the implied adjustments to the market wage.

The right-hand panel of Table 2 shows partial correlations between point scores after the influence of salary is removed. These partial correlations, which might be interpreted as correlations among the sug-gested modifications to existing salary, are considerably lower than the simple correla-Table 1. Normalized Salary and Job Scores.

Evaluator

Job Salary123 11,5401,3751,6901,638 21,4281,2659181,290 31,4181,2891,3481,382 41,3189621,1371,262 51,2401,1658991,182 61,2001,2891,2731,346 71,1441,6831,4191,206 81,1278361,0131,046 91,1169838991,050 101,0891,1471,107986 111,0431,2891,3481,170 121,0329629941,022 131,0239721,1181,022 141,023********* 15895836820890 168881,0531,167890 17888769899874 188801,039820954 19877836820870 208451,1331,013842 21834895918838 22793830899862 23731704820778 24711734850752 25687699696670 26662728696656 27569677598530

812INDUSTRIAL AND LABOR RELATIONS REVIEW

tions reported in the left-hand panel. The fact that they are all positive indicates that the salary adjustments implicitly suggested by the three evaluators are not totally unre-lated to each other. However, the exist-ence of detectable partial correlations among the gross scores does not mean that the implied salary adjustments are strongly enough related to each other to provide unambiguous instructions for modifying the existing pay scale.

Simple and partial correlations provide some evidence on the convergence of the three sets of job evaluations, and these statistics have been reported in some of the earlier literature on the convergence of job evaluations. These correlations do not pro-vide an explicit answer to the question of whether the three sets of ratings measure the same trait, nor have previous studies of convergence. If they do not measure the same trait, then at least some of the ratings must be measuring something other than inherent job worth. An explicit statistical model is required to resolve this issue. We now provide such a model and report the resulting test.

A Statistical Model of Job Evaluation Suppose the score assigned to job j by evaluator e is given by (1)

Y ej = αe + βe W j + εej j = 1, …, N

e = 1, …, M

where αe and βe are parameters, W j is inher-ent job worth, and εej is a random variable with zero mean and variance equal to σ2e

. In addition, assume that cov(W j , εej ) = 0 for all

evaluators and that cov(εej , εfj ) = 0 for any two evaluators e and f .

If inherent job worth were observable,(1) would be a regression equation. The R 2from this regression could be viewed as an indicator of the reliability of evaluator e in measuring job worth. Since job worth is unobservable, (1) is a latent-variable model with a single unobserved factor W j . Latent-variable models have been used extensively in the literature on the measurement of unobservable traits. For example, a model similar to (1) could describe the situation where a test score Y ej is used to measure some underlying ability W j .

If job worth is viewed as a random vari-able, one can without loss of generality assume that it is scaled to have a zero mean and unit variance. In that case, the ana-logue to the regression R 2 is β2e /(β2e + σ2e ),which we will denote by ρ. This is the notion of reliability used in the educational testing literature (see, for example, J ?reskog 1971).11 Note that

Table 2. Correlations between Evaluator Scores and Salary.

Correlations Partial Correlations Controlling for Salary

Evaluator

Evaluator

1

23

12Evaluator 2.82.61Evaluator 3.79.83.48.71Salary .73

.73

.96

11

Although our usage follows J ?reskog, the term “reliability ” is also used to denote lack of idiosyncratic errors by individual raters using a given evaluation method. Our concern, however, is with the degree to which the different evaluation methods measure the concept of interest —job worth. This latter character-istic is also referred to as validity. Because none of the job evaluation firms regarded lack of inter-rater reli-ability as a serious issue in applying their job evalua-tion methods, we interpret our results as evidence on the validity of the evaluation methods themselves. In addition, although we frequently refer to “evaluator e,” for example, this expression should be regarded as shorthand for “an evaluator using job evaluation method e.”

JOB EVALUATION AND COMPARABLE WORTH

813

(2)

var(Y ej ) = β2e + σ2e

.If a second evaluator f is available, produc-ing a second set of scores Y fj , then (3)

cov(Y ej , Y fj ) = βe βf .

If the number of evaluators M is three, then

the parameters of the system of equations (1) are exactly identified (Barnett 1969;Theobald and Mallinson 1978). If there are three evaluators (called A, B, and C),then the reliability of evaluator A is given by (4)

ρa

= cov(Y aj ,Y bj )cov(Y aj ,Y cj ) cov(Y bj ,Y cj )var(Y aj )

= β2

a

β2a + σ2a

As noted above, this expression is analo-gous to a regression R 2. Also note that ratings from at least two other evaluators, B and C, are required to measure the reliabil-ity of evaluator A. Similar expressions mea-sure the reliabilities of evaluators B and C.These reliabilities can be estimated using the sample analogues to the population variances and covariances in equation (4).Applying this formula to our three sets of job evaluation scores results in estimated reliabilities of 0.78, 0.86, and 0.80 for evalu-ators 1, 2, and 3, respectively.

These estimated reliabilities are appro-priate only if model (1) is correct. In particular, they are appropriate only if all three evaluators measure the same under-lying trait and their scores differ solely because of idiosyncratic measurement er-ror. With only three evaluators, this hy-pothesis cannot be tested.

Regarding salary as a fourth instrument permits such a test, because system (1) is over-identified when M = 4. Salary may be an imperfect measure of inherent job worth W j . If all three evaluators are measuring the single trait inherent job worth, how-ever, they should agree on the reliability of salary (or any other indicator) as a measure of job worth. This implication constitutes the intuitive basis for our test. With three

evaluators, there are three different ways of

expressing the reliability of salary as a mea-sure of inherent job worth. We test the null hypothesis that all three evaluators are measuring the same trait by testing whether these three expressions for the reliability of salary are significantly different from each other.12

In particular, let Y 0j denote salary. Let ρab denote the reliability of salary measured using the scores of evaluators A and B, that is,(5)

ρab

= cov(Y 0j ,Y aj )cov(Y 0j ,Y bj )

cov(Y aj ,Y bj )var(Y 0j )

Let ρac and ρbc be defined in a similar man-ner. Now consider the difference between any two of these expressions for the reli-ability of salary (for example, ρab and ρac ). If model (1) is correct and all three of the evaluators measure the same trait, then the population variances and covariances of their scores are given by (2) and (3) above,and the difference between the two expres-sions for the reliability of salary is given by

(6)

In other words, if model (1) is correct and

all evaluators measure the same trait, all measures of the reliability of salary are equal in population. This forms our null hypoth-esis.13 Under the alternative that the evalu-

.

.

ρab – ρac =

cov(Y 0j ,Y aj )cov(Y 0j ,Y bj )var(Y 0j )

cov(Y 0j ,Y cj )cov(Y aj ,Y bj ) –cov(Y aj ,Y cj )

=

β0βa

β20 + σ20

β0

βa = 0.

–β0βa

12

The test we use is described more fully in an appendix available from the authors. As noted there,our test is related to instrumental variables tech-niques in econometrics, and salary might be regarded as an instrument for the unobservable inherent worth Wj in equation (1).13

The prediction that all reliability measures for salary are equal if evaluators measure the same trait is unaffected by any errors the evaluators themselves may make in measuring that trait. These errors,represented by ε in equation (1), do not affect the covariances in equation (4), and the variances of the measurement errors do not appear in that equa-

814INDUSTRIAL AND LABOR RELATIONS REVIEW

tion. A greater measurement error variance results in a larger standard error for the difference between two reliability measures, however, thus making it more difficult to detect a failure of evaluators to measure the same trait. By reducing an evaluator ’s reliability in measuring a given trait, larger measure-ment error may impair the implementation of a com-parable worth plan.14

The derivation of this distribution and its mo-ments is contained in an appendix available from the authors on request.15

Sensitivity analyses show that these results are robust with respect to the deletion of any one obser-vation from the sample and to logarithmic and square-root transformations of the data. Furthermore, small-sample simulations indicate that the asymptotic re-sults reported here are conservative, that is, that the data probably reject the null hypothesis even more

ators do not all measure the same trait, at least one of the differences is non-zero.Three estimates of the reliability of sal-ary can be computed. The estimated reliabilities are

ρ?12 = 0.65, ρ?13 = 0.89, ρ?23 = 0.84.

Perhaps because of sampling variation,

these three point estimates are not identi-cal. Under the null hypothesis that all evaluators measure the same trait, how-ever, the point estimates should not differ by too much. The pairwise difference be-tween any two of these reliability estimates has an asymptotic normal distribution.14The ratios of the three differences to their standard errors are

ρ?12 – ρ?13 se 12,13= –3.27,

ρ?12 – ρ?23 se 12,23= –2.65,

ρ?13 – ρ?23 se 13,23

= –0.61.

The marginal significance level for the null

hypothesis that all of these differences are zero is 0.003, thus providing strong evi-dence that the three evaluators did not measure the same trait.15

Conclusion

This paper reports the results of an ex-perimental study of comparable worth.Three commercial job evaluation firms rated the same set of 27 jobs in an actual company. Statistical analysis of the experi-mental data indicates that the three evalu-ators did not measure the same trait. This finding implies that not all of the evalua-tors accurately identified and measured a unique, objective value of each job corre-sponding to its “inherent worth ”—the kind of measure that is required for implemen-tation of a comparable worth plan. There are at least two possible explanations for this apparent failure. F irst, many econo-mists would argue that no meaningful no-tion of job value exists other than marginal productivity, and that there is no obvious relation between marginal productivity and the job evaluation procedures commonly used. Second, Schwab (1980) has con-tended that no precise definition of job worth has emerged from the literature on job evaluation and that, as currently prac-ticed, job evaluation does not really try to measure job worth, but instead serves a much more limited purpose.

Regardless of the reason for them, the pronounced differences among the three sets of job scores have important implica-tions for comparable worth. They indicate that inherent job worth is not a construct that is easy to define objectively or to mea-sure reliably. Thus, the scores provided by different job evaluators do not provide mutually consistent adjustments to existing pay scales. The outcome of any attempt to implement comparable worth will depend heavily on which evaluator is chosen to perform the implementation.

strongly than the large-sample test suggests. Details of these results are available from the authors on request.

J ?reskog (1971) discussed a likelihood-ratio test based on the assumption that W j and the εej are normally distributed. We have not relied on the normality assumption.

JOB EVALUATION AND COMPARABLE WORTH815

REFERENCES

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利用需要系数法来确定负荷计算

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价值工程 置,是一项十分有意义的工作。另外恶意代码的检测和分析是一个长期的过程,应对其新的特征和发展趋势作进一步研究,建立完善的分析库。 参考文献: [1]CNCERT/CC.https://www.doczj.com/doc/7212174367.html,/publish/main/46/index.html. [2]LO R,LEVITTK,OL SSONN R.MFC:a malicious code filter [J].Computer and Security,1995,14(6):541-566. [3]KA SP ER SKY L.The evolution of technologies used to detect malicious code [M].Moscow:Kaspersky Lap,2007. [4]LC Briand,J Feng,Y Labiche.Experimenting with Genetic Algorithms and Coupling Measures to devise optimal integration test orders.Software Engineering with Computational Intelligence,Kluwer,2003. [5]Steven A.Hofmeyr,Stephanie Forrest,Anil Somayaji.Intrusion Detection using Sequences of System calls.Journal of Computer Security Vol,Jun.1998. [6]李华,刘智,覃征,张小松.基于行为分析和特征码的恶意代码检测技术[J].计算机应用研究,2011,28(3):1127-1129. [7]刘威,刘鑫,杜振华.2010年我国恶意代码新特点的研究.第26次全国计算机安全学术交流会论文集,2011,(09). [8]IDIKA N,MATHUR A P.A Survey of Malware Detection Techniques [R].Tehnical Report,Department of Computer Science,Purdue University,2007. 0引言 现有的压缩算法有很多种,但是都存在一定的局限性,比如:LZw [1]。主要是针对数据量较大的图像之类的进行压缩,不适合对简单报文的压缩。比如说,传输中有长度限制的数据,而实际传输的数据大于限制传输的数据长度,总体数据长度在100字节左右,此时使用一些流行算法反而达不到压缩的目的,甚至增大数据的长度。本文假设该批数据为纯数字数据,实现压缩并解压缩算法。 1数据压缩概念 数据压缩是指在不丢失信息的前提下,缩减数据量以减少存储空间,提高其传输、存储和处理效率的一种技术方法。或按照一定的算法对数据进行重新组织,减少数据的冗余和存储的空间。常用的压缩方式[2,3]有统计编码、预测编码、变换编码和混合编码等。统计编码包含哈夫曼编码、算术编码、游程编码、字典编码等。 2常见几种压缩算法的比较2.1霍夫曼编码压缩[4]:也是一种常用的压缩方法。其基本原理是频繁使用的数据用较短的代码代替,很少使用 的数据用较长的代码代替,每个数据的代码各不相同。这些代码都是二进制码,且码的长度是可变的。 2.2LZW 压缩方法[5,6]:LZW 压缩技术比其它大多数压缩技术都复杂,压缩效率也较高。其基本原理是把每一个第一次出现的字符串用一个数值来编码,在还原程序中再将这个数值还成原来的字符串,如用数值0x100代替字符串ccddeee"这样每当出现该字符串时,都用0x100代替,起到了压缩的作用。 3简单报文数据压缩算法及实现 3.1算法的基本思想数字0-9在内存中占用的位最 大为4bit , 而一个字节有8个bit ,显然一个字节至少可以保存两个数字,而一个字符型的数字在内存中是占用一个字节的,那么就可以实现2:1的压缩,压缩算法有几种,比如,一个自己的高四位保存一个数字,低四位保存另外一个数字,或者,一组数字字符可以转换为一个n 字节的数值。N 为C 语言某种数值类型的所占的字节长度,本文讨论后一种算法的实现。 3.2算法步骤 ①确定一种C 语言的数值类型。 —————————————————————— —作者简介:安建梅(1981-),女,山西忻州人,助理实验室,研究方 向为软件开发与软交换技术;季松华(1978-),男,江苏 南通人,高级软件工程师,研究方向为软件开发。 数据快速压缩算法的研究以及C 语言实现 The Study of Data Compression and Encryption Algorithm and Realization with C Language 安建梅①AN Jian-mei ;季松华②JI Song-hua (①重庆文理学院软件工程学院,永川402160;②中信网络科技股份有限公司,重庆400000)(①The Software Engineering Institute of Chongqing University of Arts and Sciences ,Chongqing 402160,China ; ②CITIC Application Service Provider Co.,Ltd.,Chongqing 400000,China ) 摘要:压缩算法有很多种,但是对需要压缩到一定长度的简单的报文进行处理时,现有的算法不仅达不到目的,并且变得复杂, 本文针对目前一些企业的需要,实现了对简单报文的压缩加密,此算法不仅可以快速对几十上百位的数据进行压缩,而且通过不断 的优化,解决了由于各种情况引发的解密错误,在解密的过程中不会出现任何差错。 Abstract:Although,there are many kinds of compression algorithm,the need for encryption and compression of a length of a simple message processing,the existing algorithm is not only counterproductive,but also complicated.To some enterprises need,this paper realizes the simple message of compression and encryption.This algorithm can not only fast for tens of hundreds of data compression,but also,solve the various conditions triggered by decryption errors through continuous optimization;therefore,the decryption process does not appear in any error. 关键词:压缩;解压缩;数字字符;简单报文Key words:compression ;decompression ;encryption ;message 中图分类号:TP39文献标识码:A 文章编号:1006-4311(2012)35-0192-02 ·192·

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