New York Police Diversity Management

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Measuring Diversity in Police Agencies

SALOMON ALCOCER GUAJARDO Department of Public Management, The City University of New York, New York,

New York, USA

Despite numerous studies on minority and female integration into police agencies, the use of diversity indices to benchmark and assess changes in the ethnic and racial composition of police workforces has been limited. This study applies the Simpson, McIntosh, and measure of variation indices to data on the New York City Police Department’s police and civilian workforces to obtain workforce di- versity measurements. Pearson and Spearman correlation analyses show that the 3 indices produce diversity measurements that are consistent with one another. Although the indices produce similar scores, the Simpson index is more efficient at measuring diversity and less sensitive to the number of ethnic or racial categories used by the New York City Police Department in comparison to the McIn- tosh and measure of variation indices.

KEYTERMS Minority integration, measure of variation (MV) index, McIntosh index, Simpson index, workforce diversity

Numerous studies have assessed the integration of minority men and women into police agencies (e.g., Harrington & Lonsway, 2004; Hochstedler, Regoli, & Poole, 1984; Martin, 2004; McCluskey & McCluskey, 2004; Schulz, 2004; Stokes & Scott, 1996; Walker, 1983, 1989; Winters, 1991). These studies show that police agencies have increased the number of minority officers within their structures over time. These studies, however, have not assessed the overall level of ethnic or racial diversity that existed in the police agencies prior to the integration of minority officers. The studies have also not as- sessed whether the level of diversity within police agencies has increased significantly from prior years as a result of hiring minority officers. As a

Submitted March 2013; resubmitted May 2013; accepted July 2013. Address correspondence to Salomon Alcocer Guajardo, Department of Public Manage-

ment, John Jay College of Criminal Justice, The City University of New York, 445 West 59th Street, Room 3536, New York, NY 10019. E-mail: [email protected]

2 S. A. Guajardo

consequence, it is difficult to assess how successful police agencies have been at increasing their overall level of diversity over time as the number of minority officers has increased.

This study applies the Simpson, McIntosh, and measure of variation (MV) indices to police employment data to illustrate how to calculate a score of ethnic or racial homogeneity for a police agency. Mathematically speaking, the use of diversity indices helps to benchmark the level of ethnic or racial homogeneity (or heterogeneity) within and between organizations as well as to track whether the level of homogeneity has decreased over time as a result of integrating more minorities. Organizationally speaking, the use of diversity indices helps to assess the effectiveness of an agency with respect to hiring minority men and women. In this regard, it is important to obtain a benchmark of workforce diversity in order to do the following:

• Assess levels of diversity within and between organizations (Lieberson, 1969)

• Evaluate whether an organization’s diversity program and initiatives are accomplishing their goals

• Monitor minority integration and diversity trends for an organization and its departments monthly, quarterly, or annually

• Pinpoint areas within an organization where diversity is decreasing or increasing and understand why the trend is occurring

• Revise or strengthen existing human resources recruitment policies based on quantitative data that inform human resources administrators and ex- ecutives regarding negative or positive workforce diversity practices and outcomes

Without the use of a diversity index that quantifies the level of homogeneity of an organization and its workforce, it is difficult to determine whether the ethnic or racial composition of the workforce is changing significantly over time.

REVIEW OF PREVIOUS STUDIES

Research on minority integration into police agencies has focused primarily on assessing whether members of particular minority groups have been hired by municipal law enforcement organizations. For example, with respect to hiring Black officers, Hochstedler et al. (1984, p. 13) found that Black officers were “grossly underrepresented in police departments” although they had increased in number from 1967 to 1981. Similarly, Walker (1989) found that police departments in the 50 largest cities had made uneven progress in hir- ing Blacks as well as Hispanics from 1983 to 1988. Hochstedler et al., Martin, Walker (1989), and other studies have concluded that police departments

Measuring Diversity in Police Agencies 3

have made attempts to significantly increase the number of Black officers but have been marginally successful in doing so.

Research also shows that police departments have hired more Hispanic officers (Hochstedler et al., 1984; McCluskey & McCluskey, 2004; Stokes & Scott, 1996; Walker, 1989; Winters, 1991). In 1991, Winters found that the Chicago Police Department had hired more Hispanics than Blacks from 1985 to 1987. Similarly, Walker and Turner (1992) found that Hispanics were successful at being hired by police departments where Hispanics composed a significant proportion of the population compared to Blacks. More recently, McCluskey and McCluskey (2004, p. 73) found that the number of Latinos (i.e., Hispanics) employed by police agencies in the 50 cities with the largest municipal agencies “nearly doubled from 1990 to 2000, jumping from 9 percent of the total sworn to 14 percent.”

Studies assessing the employment of Asians in police departments show that these individuals continue to be underrepresented and that their em- ployment lags far behind that of Blacks and Hispanics (Stokes & Scott, 1996; Walker, 1983; Winters, 1991). According to Winters (1991), the Chicago Po- lice Department increased the number of sworn Asian officers from 21 to 26 between 1985 and 1987. By 1990, the Chicago Police Department had increased the number of Asian officers to 62 (Stokes & Scott, 1996). In ad- dition, Stokes and Scott (1996) found that Asian officers composed about 9% of the Oakland, California, police force, though Asians accounted for 15% of the city’s general population. Stokes and Scott also found that a number of police departments had not hired one Asian officer by 1990 despite the presence of Asians in the general population. In many police departments, “the employment of Asian American officers does not reflect the Asian American proportion of the population” (Stokes & Scott, 1996, p. 35).

Although these studies are essential for determining whether police agencies have been effective in recruiting and hiring minorities, the research has not addressed the magnitude to which the minority hiring has changed the level of diversity at an organizational and hierarchical level. At an orga- nizational level, there is little research with respect to the level of workforce diversity that existed in police agencies prior to the increased employment of minorities. There is also little research with regard to how much the level of diversity in police agencies has changed as a consequence of hiring more minorities. At a hierarchical level, prior research has not adequately assessed how the diversity within and between police ranks has changed over time as more minority police officers have been promoted. In part, this has re- sulted from the lack of police employment data that are readily available to researchers to facilitate the use of indices to measure changes in workforce diversity. The lack of measurement of the level of diversity within and be- tween police agencies has also resulted from research focusing specifically on the integration of particular minority groups rather than examining the

4 S. A. Guajardo

TABLE 1 Guidelines for Interpreting Simpson Diversity Index Scores

Simpson Score Interpretation

0.00 Absence of diversity (homogeneity) 0.01–0.40 A low degree of diversity/heterogeneity 0.41–0.60 A moderate degree of diversity/heterogeneity 0.61–0.80 A moderately high degree of diversity/heterogeneity 0.81–0.99 A high degree of diversity/heterogeneity 1.00 Absolute (perfect) diversity/heterogeneity

integration of minorities collectively to assess changes in the level of ethnic and racial homogeneity.

REVIEW OF DIVERSITY INDICES

A number of indices have been developed to assess minority integration and diversity within organizations and organized communities. They include the

1. Simpson (1949) diversity index 2. McIntosh (1967) evenness index 3. Nachmias–Rosenbloom (1973) MV index

Because these indices have been used to assess diversity within and between public organizations, they are discussed and applied here. To make the use of the indices relevant to police studies, I apply each index to police and civilian employment data from the New York City Police Department (NYPD) to demonstrate how each produces a measure of ethnic or racial variation or diversity (i.e., homogeneity or heterogeneity).

The Simpson (1949) diversity index (D = 1 – �p2) has been used to measure the degree of homogeneity within communities and organiza- tions (Guajardo, 1999; Pitts, 2005; Starks, 2009). As stated by Simpson (1949, p. 688), the index obtains “the probability that two individuals chosen at ran- dom and independently from the population will be found to belong to the same group.” Mathematically speaking, the index provides a measurement of the level of homogeneity (or diversity) that exists within a workgroup or organization. As developed by Simpson, the index ranges from 0 to 1, where 0 indicates the absence of diversity (i.e., maximum homogeneity) and 1 in- dicates maximum heterogeneity (i.e., diversity; Blau, 1977; Guajardo, 1999; Lieberson, 1969; Pitts, 2005; Simpson, 1949; Starks, 2009).

Because the Simpson index yields a score with a range from 0 to 1, it may be interpreted as in Table 1. Although Table 1 provides a general

Measuring Diversity in Police Agencies 5

FIGURE 1 Application of the Simpson Index.

guideline for interpreting a Simpson diversity score, there are no established cutoff points for each set of measurements.

To obtain a coefficient of diversity for the NYPD police force or a specific workgroup within the NYPD, the Simpson index is applied as in Figure 1 This Simpson score indicates that the NYPD police force has a moderately high level of heterogeneity, with a .63 probability that two police officers selected randomly will have the same ethnic or racial background.

In 1967, McIntosh proposed an index for assessing diversity that takes into account the number of different types of members that exist within a community. The McIntosh evenness index (DE) has the following structure:

DE = N−

√ ( ∑

n2i )

N − (N/ √

According to McIntosh, N is the total number of individuals in a community or organization, n is the number of individuals within a particular group, and S represents the number of distinct groups within a community or orga- nization. Similar to the Simpson index discussed previously, DE has a range from 0 to 1 and may be interpreted in a similar fashion as the Simpson index.

6 S. A. Guajardo

FIGURE 2 Application of the McIntosh Index.

Similar to the Simpson index, the diversity score for the McIntosh DE index can be obtained using frequencies or percentages. The same score is obtained regardless of the method used. The mathematical operations necessary to obtain a McIntosh DE score for the NYPD police force are illustrated in Figure 2.

As illustrated in Figure 2, a diversity score of .71 is obtained when the products are entered into the McIntosh formula. Based on the McIntosh DE index score, the NYPD has a moderately high level of diversity, with a .71 probability that two officers selected randomly will share the same ethnic or racial background.

The final index to be illustrated is the Nachmias and Rosenbloom MV. Nachmias and Rosenbloom (1973) introduced their index to assess racial (or minority) integration in U.S. federal agencies. It has the following structure:

MV = ∑

fi fj n(n−1)

2 × ( f /n)2

= T otal Obs er ved Di f f er ences M aximum P os s ibl e Di f f er ences

Although frequencies are usually used to obtain an MV score, percentages may be used as well, as illustrated in Figure 3.

In developing the MV index, Nachmias and Rosenbloom (1973) stated that n is the number of social characteristics (i.e., groups) and f is the total

Measuring Diversity in Police Agencies 7

FIGURE 3 Application of the MV Index.

frequency. The MV index has a range from 0 to 1. According to Nachmias and Rosenbloom, a value of 0 indicates the complete absence of integration and a value of 1 reflects maximum integration.

The assumption underlying the MV index is that it can assess observed and maximum possible differences based on the ethnic or racial compo- sition of an agency’s workforce. According to Nachmias and Rosenbloom (1973, p. 592), “the differences between each social characteristic and every other social characteristic are counted and summed” to find the total num- ber of differences in a group. These observed differences are measured by the numerator of the MV index (i.e., �fifj). With respect to measuring the maximum possible differences, Nachmias and Rosenbloom (p. 592) stated that the “maximum number of differences occurs when all the frequencies of individual attributes in the group are equal.” To obtain the number of max- imum possible differences, Nachmias and Rosenbloom (p. 592) stated that “the expected maximum [possible differences] can be computed by equaliz- ing the frequencies and then finding the number of differences that would be observed if all frequencies were equal.” The denominator of the MV index produces the maximum possible differences (i.e., [n(n – 1)/2] × [f/n]2).

8 S. A. Guajardo

The multiplication matrixes summarize the calculations that are neces- sary to obtain the numerator for the MV index (i.e., �fifj) when it is applied to the employment data for the NYPD. As shown in Figure 3, the denomi- nator is obtained as follows: 10 × 47,389,456 = 473,894,560. When the total observed differences is divided by the maximum possible differences, an MV score of .79 is obtained (MV = .79 = 373,664,713 ÷ 473,894,560). It too indicates that the NYPD has a moderately high level of diversity.

ASSESSING WITHIN- AND BETWEEN-WORKFORCE DIVERSITY

As stated previously, diversity indices help to assess within- and between- workgroup or -workforce homogeneity (or heterogeneity). The Simpson, McIntosh, and MV indices are applied to NYPD police and civilian employ- ment data for 2012 to measure the level of workforce diversity within each police rank and job classification. Table 2 summarizes the ethnic and racial distribution of NYPD employees within and between each police rank and civilian job classification as well as the diversity scores for the police and civilian workforces.

Based on the Simpson index, the NYPD has an overall organizational diversity score of .63. However, the level of diversity decreases generally as police ranks increase. The average Simpson score for the police force is .44. By contrast, the Simpson scores are relatively stable for the civilian workforce. The overall diversity score for the entire civilian workforce is .61, with an average score of ≈.61. In addition, the score for the officials workgroup of .65 shows that this level of diversity exceeds the overall level of .61, indicating that the upper echelon of the civilian workforce is well integrated ethnically and racially.

With respect to the diversity scores produced by the McIntosh DE index, Table 2 shows that the index produces slightly higher scores in comparison to the Simpson index. For the NYPD police force, the McIntosh index produces a score of .71; for the civilian workforce, a score of ≈.68 is obtained. The average scores produced by the McIntosh index are also higher than those produced by the Simpson index. Specifically, the average McIntosh score for the police force is ≈.47, whereas the average score for the civilian workforce is ≈.68. For the NYPD data, the McIntosh index generates higher diversity scores generally in comparison to the Simpson index.

Of the three indices, the MV index produces the highest scores. The MV score for the NYPD police force is ≈.79, with an average of .55. The MV score for the civilian workforce is ≈.77, with an average of ≈.76. These results suggest that the NYPD has a very high degree of ethnic and racial integration, meaning that both the police and civilian workforces are ethnically and racially heterogeneous. A similar inference can be made for the ethnic and racial integration of a number of police ranks and civilian job classifications.

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10 S. A. Guajardo

TABLE 3 Descriptive Statistics for the Simpson, McIntosh, and Measure of Variation Indices

Descriptive Statistic Simpson McIntosh Measure of Variation

NYPD-widea

Mean 0.495 0.535 0.619 Median 0.509 0.541 0.636 Standard deviation 0.137 0.173 0.171 Minimum 0.242 0.234 0.302 Maximum 0.675 0.778 0.844 N 25 25 25

Police force Mean 0.443 0.468 0.554 Standard error of the mean 0.032 0.039 0.040 Median 0.451 0.469 0.564 Standard deviation 0.131 0.161 0.163 Minimum 0.242 0.234 0.302 Maximum 0.658 0.751 0.823 N 17 17 17

Civilian workforce Mean 0.606 0.677 0.758 Standard error of the mean 0.024 0.034 0.031 Median 0.639 0.722 0.799 Standard deviation 0.069 0.097 0.086 Minimum 0.491 0.519 0.614 Maximum 0.675 0.778 0.844 N 8 8 8

Note. NYPD = New York City Police Department. aCombines the scores for each police rank and civilian job classification.

The formula used by the MV index produces higher scores in comparison to the Simpson and McIntosh indices.

COMPARISON OF INDICES

As Table 2 shows, the Simpson index produces the lowest diversity scores for the NYPD police and civilian employment data, whereas the MV in- dex produces the highest scores. Table 3 provides descriptive statistics for each index. When the diversity scores for the police and civilian workforces are analyzed jointly, the results show that the Simpson index produces the smallest average and median diversity scores in comparison to the McIntosh and MV indices. The Simpson index also has the smallest standard deviation from the mean in comparison to the McIntosh and MV indices. Of the three indices, the distribution of the McIntosh index has the most variation. The descriptive statistics also show that each index produces a negatively skewed distribution for the NYPD data.

Measuring Diversity in Police Agencies 11

Table 3 also shows that the Simpson index produces the smallest di- versity scores for the police force in comparison to the McIntosh and MV indices. For the police force, the Simpson index produces a mean score of .44 and a median of .45, whereas the MV index produces a mean score of .55 and a median of .56. The results also show that the Simpson index has a smaller standard deviation and range in comparison to the McIntosh and MV distributions. Whereas the Simpson and MV indices produce slightly negatively skewed distributions, the McIntosh index produces a positively skewed distribution.

When the diversity scores are analyzed for the civilian workforce, the Simpson index produces the smallest mean and median compared to the McIntosh and MV indices. The Simpson index also produces the smallest coefficient for the standard error of the mean in comparison to the McIntosh and MV indices. Compared to the McIntosh and MV indices, the Simpson index also has the smallest range. Similar to the McIntosh and MV indices, the Simpson index is negatively skewed.

CONSISTENCY OF INDEX SCORES

To assess the extent to which the indices produce consistent diversity scores relative to one another, I sorted the Simpson scores in ascending order to determine whether the McIntosh and MV indices produced similar scores for each police rank and civilian job classification. In addition, Pearson and Spearman correlation coefficients were calculated for the three sets of diversity scores to estimate the level of similarity among the measure- ments. Because the formula of each index treats the data elements differ- ently to produce a measure of diversity, it was important to evaluate the indices with regard to the extent to which their scores varied from one another.

Table 2 shows that the McIntosh index produces lower scores than the Simpson index for the police ranks of deputy chief, deputy inspector, inspector, lieutenant detective squad, and captain. For the other police ranks, the McIntosh index produces higher scores in comparison to the Simpson index. With respect to the MV scores relative to the Simpson scores, Table 2 shows that the MV scores are consistently higher. Because the McIntosh index produces scores slightly lower than the Simpson index on several police ranks, whereas the MV index produces higher scores for the same ranks, the McIntosh index may not have sufficient discriminatory power to assess adequately the level of diversity within some police ranks. It may also be the case that both the Simpson and MV indices are overestimating the degree of diversity for some police ranks.

The Pearson and Spearman correlation coefficients show that the McIn- tosh and MV indices produce scores consistent with the Simpson index (see

12 S. A. Guajardo

TABLE 4 Correlation Analysis of Workforce Diversity Scores for the NYPD Police and Civilian Workforces for 2012

Index 1 2 3

Police ranks (n = 17)a 1. Simpson — .999∗ 1.00∗

2. McIntosh evenness — 1.00∗

3. Measure of variation —

Police ranks (n = 17)b 1. Simpson — 1.00∗ 1.00∗

2. McIntosh evenness — 1.00∗

3. Measure of variation —

Civilian job classification (n = 8)a 1. Simpson — 1.00∗ 1.00∗

2. McIntosh evenness — 1.00∗

3. Measure of variation —

Civilian job classification (n = 8)b 1. Simpson — 1.00∗ 1.00∗

2. McIntosh evenness — 1.00∗

3. Measure of variation —

NYPD-widec (n = 25)a 1. Simpson — .998∗ 1.00∗

2. McIntosh evenness — .998∗

3. Measure of variation —

NYPD-widec (n = 25)b 1. Simpson — 1.00∗ 1.00∗

2. McIntosh evenness — 1.00∗

3. Measure of variation —

Note. NYPD = New York City Police Department. aPearson correlation coefficients. bSpearman correlation coefficients. cCombines the scores for each police rank and civilian job classification. ∗α = .001.

Table 4). When the diversity scores for the police ranks are correlated, the correlation analyses show that the Simpson and McIntosh scores align with the Simpson scores. The analyses also show that the McIntosh scores align with the MV scores. Similar results are obtained for the scores calculated for the civilian job classifications. When the diversity scores for the police ranks and job classifications are grouped together, the Pearson and Spear- man correlations are consistent with those obtained for the police and civilian workforces.

MEASUREMENT EFFICIENCY

Of the three indices presented here, the Simpson index is the most efficient with respect to measuring the level of homogeneity within and between

Measuring Diversity in Police Agencies 13

the NYPD workforces. The mathematical operations that are required by the index are few in comparison to those required by the McIntosh and MV indices. Compared to the Simpson and McIntosh indices, the MV in- dex is the least efficient with regard to measuring the level of variation within and between workforces. To calculate the numerator of the MV in- dex for one police rank with five ethnic/racial categories, about 10 mul- tiplications and five summations are required. To obtain the denominator term, the MV index requires about five mathematical operations. From a measurement efficiency perspective, the Simpson index provides the most straightforward method for obtaining a diversity score for an organization and its workgroups, whereas the MV index is the most cumbersome and least efficient.

SENSITIVITY TO ETHNIC/RACIAL CLASSIFICATIONS

The number of ethnic or racial categories used by an organization influences scores of the McIntosh and MV indices and not those of the Simpson in- dex. The reason why the Simpson index is not influenced by the number of ethnic or racial categories used is that it does not use the number of different ethnicities or races to calculate either a numerator or denominator. By contrast, the McIntosh index uses the number of different ethnic or racial categories in its denominator term, making it sensitive to the number of dif- ferent classifications used by an organization. For example, when five ethnic or racial categories are used,

√ S = 2.23; when seven categories are used,√

S = 2.65, which would lower the diversity score if there is an absence of data in several of the categories. Of the three indices, the MV index is the most sensitive to the number of ethnic or racial categories used because the numerator term utilizes the number of categories on three occasions. For instance, when five ethnic or racial categories are used, [n(n – 1)]/2 = 10 ([5 × 4]/2 = 20/2 = 10) and (f/n)2 = (f/5)2. If the number of categories is expanded to seven from five and there are no employment data for the last two categories, [n(n – 1)]/2 = 21 ([7 × 6]/2 = 42/2 = 21) and (f/n)2 = (f/7)2, which would decrease the index score because there would be no change in the value of the numerator as the value of the denominator increases. Under this scenario, the use of the MV index would lead to an incorrect inference that the level of ethnic or racial variation (i.e., heterogeneity or diversity) has decreased.

CONCLUSION

Although there is no rule of thumb on which index to use to measure diversity within and between organizations, the Simpson index is the most

14 S. A. Guajardo

straightforward to use despite producing lower scores compared to the McIn- tosh and MV indices. In addition, unlike McIntosh and MV scores, Simpson scores are not sensitive to the number of ethnic or racial categories used by the organization because the Simpson index does not use the number of categories to calculate either a numerator or denominator term (Guajardo, 2013). In comparison to the McIntosh and MV indices, the Simpson index is the most efficient with regard to its use of employment data to obtain a diversity score.

The use of diversity indices to assess the ethnic and racial composition of police agencies is needed to determine how well police agencies inte- grate minorities within their structures over time. Diversity indices are also needed to assess differences within and between police ranks and civilian job classifications. In order to measure, benchmark, and assess the level of diversity within and between police agencies, researchers need to select a diversity index that is efficient with regard to its use of the employment data and that has the ability to produce reliable and valid scores repeatedly. Researchers should also be aware of the strengths and weaknesses of the index that they have chosen to measure diversity within and between police agencies.

REFERENCES

Blau, P. M. (1977). Inequality and heterogeneity. New York, NY: Free Press. Guajardo, S. A. (1999). Workforce diversity: Monitoring employment trends in public

organizations. Public Personnel Management, 28(1), 63–85. Guajardo, S. A. (2013). Workforce diversity: An application of diversity and integra-

tion indices to small agencies. Public Personnel Management, 41(1), 27–40. Harrington, P., & Lonsway, K. A. (2004). Current barriers and future promise for

women in policing. In B. R. Price & N. J. Sokoloff (Eds.), The criminal justice system and women (pp. 495–510). New York, NY: McGraw-Hill.

Hochstedler, E., Regoli, R. M., & Poole, E. D. (1984). Changing of the guard in Amer- ican cities: A current empirical assessment of integration in twenty municipal police departments. Criminal Justice Review, 9(1), 8–14.

Lieberson, S. (1969). Measuring population diversity. American Sociological Review, 34, 850–862.

Martin, S. E. (2004). The interactive effects of race and sex on women police officers. In B. R. Price & N. J. Sokoloff (Eds.), The criminal justice system and women (pp. 527–542). New York, NY: McGraw-Hill.

McCluskey, C. P., & McCluskey, J. D. (2004). Diversity in policing: Latino repre- sentation in law enforcement. Journal of Ethnicity and Criminal Justice, 2(3), 67–81.

McIntosh, R. P. (1967). An index of diversity and the relation of certain concepts to diversity. Ecology, 48, 392–404.

Measuring Diversity in Police Agencies 15

Nachmias, D., & Rosenbloom, D. H. (1973). Measuring bureaucratic representation and integration. Public Administration Review, 33, 590–597.

Pitts, D. W. (2005). Diversity, representation, and performance: Evidence about race and ethnicity in public organizations. Journal of Public Administration Research and Theory, 15, 615–631.

Schulz, D. M. (2004). Invisible no more: A social history of women in U.S. policing. In B. R. Price & N. J. Sokoloff (Eds.), The criminal justice system and women (pp. 483–494). New York, NY: McGraw-Hill.

Simpson, E. H. (1949, April 30). Measurement of diversity. Nature, 163, 688. Starks, G. L. (2009). Minority representation in senior positions in U.S. federal agen-

cies: A paradox of underrepresentation. Public Personnel Management, 38(1), 79–90.

Stokes, L. D., & Scott, J. F. (1996). Affirmative action and selected minority groups in law enforcement. Journal of Criminal Justice, 24(1), 29–38.

Walker, S. (1983). Employment of Black and Hispanic police officers. Review of Applied Urban Research, 5, 1–6.

Walker, S. (1989). Employment of Black and Hispanic police officers, 1983–1988: A follow-up study. Omaha: University of Nebraska at Omaha.

Walker, S., & Turner, K. B. (1992). A decade of modest progress: Black and Hispanic police employment in the 50 largest cities, 1983–1992. Omaha: University of Nebraska at Omaha.

Winters, C. A. (1991). Hispanics and policing in Chicago and Cook County, Illinois. The Police Journal, 64(1), 71–76.

CONTRIBUTOR

Salomon Alcocer Guajardo is an Associate Professor of Public Management at John Jay College of Criminal Justice, The City University of New York. He serves as the coordinator for the undergraduate Criminal Justice Manage- ment Program. His research on workforce diversity has appeared in Public Administration Review, Public Personnel Management, and the Review of Public Personnel Administration.

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