measuring racial disparity in child welfare

0009–4021/2008/020823-36 $3.00 Child Welfare League of America 23

Measuring Racial Disparity in Child Welfare

Terry V. Shaw, Emily Putnam-Hornstein, Joseph Magruder,and Barbara Needell

Overrepresentation of certain racial/ethnic groups in thefoster care system is one of the most troubling and chal-lenging issues in child welfare today. In response, manystates have started reporting outcomes by race and ethnic-ity to identify disproportionately high rates of systemcontact. The identification of disproportional representa-tion is the first step in developing targeted strategies toaddress disproportionality—highlighting where resourcesshould be directed and guiding future research. However,present and future efforts to address disproportionalitymust be accompanied by statistically sound and meaning-ful methods of measurement. In this article, we argue forthe adoption of a relative rate measure of representation—a “Disparity Index”—as the primary instrument for assess-ing racial disparity in child welfare.

Terry V. Shaw PhD, MSW, MPH is an Assistant Professor, School of Social Work, Uni-versity of Maryland, Baltimore, Baltimore, Maryland. Emily Putnam-Hornstein MSWand Joseph Magruder MSW are Graduate Student Researchers, Center for Social Serv-ices Research, School of Social Welfare, University of California at Berkeley, Berkeley, Cal-ifornia. Barbara Needell MSW, PhD, is Principal Investigator/Research Specialist, Cen-ter for Social Services Research, School of Social Welfare, University of California atBerkeley, Berkeley, California.

24 CHILD WELFARE • VOL. 87, #2

Although increasing attention is being paid to the dispropor-tional representation of children of color in the child wel-fare system (Derezotes, Poertner, & Testa, 2005; Magruder

& Shaw, 2007; Needell, Shaw, Magruder, & Putnam-Hornstein,2007a), the question of how to best measure over- and underrepre-sentation over time and across localities has not yet been resolved.This paper argues for the adoption of a “Disparity Index” as asound measure of disproportional representation. Although thenomenclature differs, other fields have identified this index as apreferred means of measuring group differences. In Epidemiologyand Public Health it is referred to as a “relative risk ratio” (Jewell,2004). In Juvenile Justice it is a measure of “disproportionate mi-nority contact” (Butts et al., 2003; Hsia, 2007). The Center for SocialServices Research at the University of California, Berkeley has la-beled it a Disparity Index since it serves as a comparative measureof unequal, or disparate, contact in the context of child welfare(Needell et al., 2007b). The Disparity Index can be used to assessdifferences in rates of contact with the foster care system for racialand ethnic groups (where we anticipate it will prove most inform-ative), but can also be applied as a measure of differences be-tween genders, across age groups, over time, between areas, andthroughout the child welfare experience.

Defining the Problem

In California and across the country, black children comprise afar larger proportion of the foster care population than of theoverall child population. Black children in California made up28.2% of the foster care population on July 1, 2006 but just 7.2%of the child population (Needell et al., 2007b). This dramaticoverrepresentation of black children is being noted with in-creasing concern by policy makers and practitioners. For com-

Address reprint requests to the Center for Social Services Research, University of Califor-nia at Berkeley, School of Social Welfare, 120 Haviland Hall, Berkeley, CA 94720-7400.

Shaw et al. 25

parison, on July 1, 2006, non-Hispanic, white children comprised26.1% of the foster care population and 31.0% of the total popula-tion (Needell et al., 2007). Black children are overrepresentedwhile non-Hispanic, white children are underrepresented in thechild welfare system. While the over-representation of black chil-dren is starting to gain attention, less attention has been paid tothe situation at the other extreme, the underrepresentation ofAsian and Pacific Islander children: in California, Asians and Pa-cific Islanders made up only 2.3% of the foster care populationwhile comprising nearly 9.9% of the child population (Needellet al., 2007b).

Since the literature suggests it would be ill-advised to assumethe incidence of child abuse or neglect in the black community isgreater than in the general population, or that it is lower in theAsian and Pacific Islander community (Sedlak & Broadhurst, 1996;Sedlak & Shultz, 2005), the disproportional representation shouldbe defined as any significant deviation from the null. Thus, no nor-mative judgment of directionality should be imposed on the meas-ure of representation—it is of interest and concern if a group isoverrepresented relative to its presence in the population and ofinterest and concern if a group is underrepresented. While it iscommon to assume that less contact with the child welfare systemis an inherently good thing, both over- and underrepresentationshould raise questions of possible bias and group-specific barriersto service.

Measuring the Problem

While defining disproportional representation is a necessary firststep, the more difficult task is identifying a meaningful measureof representation. First and foremost, the measure needs to be astatistically sound assessment of the degree to which a group istruly represented (whether in the child welfare system, the juve-nile justice system, the health care system, or any other systembeing examined). As we will outline in detail, a common measure


used for examining racial/ethnic representation—looking at theproportion of a given group experiencing an event relative totheir proportion in the population—is limited by its mathemati-cal construct and is therefore an inadequate measure of disparity.Second, the measure needs to be easily interpretable. Reportingrates per 1,000 offers a standardized measure of representation,but these rates can be cumbersome to discuss and can be easilyconfused with rates per 100 (or percents). While computingodds ratios is an alternative method of comparison, discussingrepresentation in terms of “odds” complicates its interpretation.Third, the measure should be based on data that is easily com-piled. The Disparity Index presented here offers a statisticallysound, easily interpretable method of utilizing existing data toexamine disproportionality.

Measures of Racial Representation

Racial Breakouts by Percentages and Rates Per 1,000

Perhaps the simplest method of examining the representation of agroup is by computing either rates per 100 (percentages) or ratesper 1,000. This method is very straightforward to calculate, con-sisting of the number of children of a particular group experienc-ing some event divided by the number of children in the broaderpopulation of that same group. The result can be multiplied by100 to produce a percent or by 1,000 to produce a rate per 1,000.In the example population shown in Table 1, the total percent ofchildren in care is 0.11% or 1.1 per 1,000 children in the popula-tion. For black children the percent of children in care is 0.3% or 3 per 1,000 black children in the population and for non-blackchildren the percent of children in care is 0.1% or 1 per 1,000 non-black children in the population. Within the same location andtime period this method offers a good way to look at relative dis-proportionality. Rates and percents provide a basic starting pointfor examining disparity. They allow the comparison of one group,time period, or geographic area with another.

Shaw et al. 27

The Disproportionality Metric

Disproportional representation is calculated by comparing the pro-portion of a given group experiencing some event, to that group’sproportion in the overall population. (In the disparity spreadsheetreferenced later in this paper, this measure is referred to as the “Dis-proportionality Metric”.) Computing the Disproportionality Met-ric is methodologically simple and easily understood. From Table 2,examine County “A” as an example of computing the Dispropor-tionality Metric. County “A” has a black child population of 25,000and a total child population of 500,000. It also has a foster carecaseload of 550 children of whom 75 are black. To compute the Dis-proportionality Metric for black children in foster care, the numberof black children in care (75) would be divided by the total num-ber of children in care (550), and then this proportion would be divided by the total number of black children in the population(25,000) as a proportion of the total child population (500,000). Asnow shown, a Disproportionality Metric of 2.728 is computed, in -dicating that black children are overrepresented in the foster caresystem in County “A” compared to their representation in the

TABLE 1Calculation of Percentage Representation and Rates per 1,000

COUNTY A

IN CARE POPULATION PERCENT IN RATE PER

(%) (%) CARE 1,000

Black 75 (13.6%) 25,000 (5%)

Non-Black 475 (86.4%) 475,000 (95%)

Total 550 (100%) 500,000 (100%)550

500 0001 000 1 1

,, .

⎛⎝⎜

⎞⎠⎟

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475

475 0001 000 1 0

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75

25 0001 000 3 0

,, .

⎛⎝⎜

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550

500 000100 0 11

,. %

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� �

475

475 000100 0 1

,. %

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75

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population as a whole: the proportion of black children in care is2.8 times greater than what is to be expected based on their pres-ence in the child population.

Although the Disproportionality Metric is easy to calculate andinterpret, it also employs a mathematical design that imposes asignificant constraint to its utility for purposes of comparison (i.e.,over time, across areas, or between groups). The Disproportional-ity Metric has a theoretical upper bound that is uniquely set foreach group under examination based on that group’s size relativeto the total population—it must always be less than or equal to1 (population proportion). This causes the measure to suffer fromtwo related drawbacks. First, since the theoretical ceiling is a func-tion of the population proportion for a given group, it is difficultto meaningfully compare the level of disproportionality for onegroup (for instance, black children in County “A”) with the dispro-portionality for another group (black children in County “B”).Even attempting to use this measure to assess the degree to whichthe overrepresentation of black children in County “A” has changedover time can be problematic since the size of the black populationas a proportion of the total population may have increased or de-creased (i.e., the theoretical maximum for the measure from one

TABLE 2Calculation of the Disproportionality Metric (DM)

COUNTY A

METRIC (DM)

IN CARE (%) POPULATION (%) RATE PER 1,000 DISPROPORTIONALITY

Black 75 (13.6%) 25,000 (5%) 3.0

Non-Black 475 (86.4%) 475,000 (95%) 1.0

Total 550 (100%) 500,000 (100%)

475550

475 000500 000

86 4

950 909

,,

. %

%.� �

75550

25 000500 000

13 6

52 728

,,

. %

%.� �

Shaw et al. 29

year to the next may also have changed). This is a major flawsince a key criterion of a good measure is its ability to measurechange over time.

Secondly, the Disproportionality Metric is biased toward show-ing no effect when the identified group of interest comprises a largeproportion of the population. For an area with a large populationof the group being examined, the theoretical ceiling will be farlower than for an area with a smaller group population proportion.While somewhat difficult to conceptualize, the key is to imaginean extreme situation in order to demonstrate how the problem isstill a factor (albeit on a lesser scale) with real world data.

In continuing with our earlier example for County “A,” but tak-ing it to an extreme, imagine that the 75 children in care representnot 13.6% of all children in foster care, but 100%. Although 100%of children in care are black, black children comprise just 5% of thechild population. Now imagine County “B.” Of children in care,100% are black, as was the case in County “A,” but in County “B”black children comprise a much larger proportion of the total pop-ulation (50%). As shown in Table 3, due to the mathematical formof the Disproportionality Metric, the theoretical maxima are dra-matically different for the two counties. Despite the fact that blacksare represented in care at a rate of 3 per 1,000 in both counties, andconstitute 100% of the in care population, the proportion of thepopulation that is black drives the upper bound of the index. For

TABLE 3Example of DM Theoretical Maximum Values

IN CARE POPULATION RATE PER DISPROPORTIONALITY

(%) (%) 1,000 METRIC (DM)

Blacks 75 (100%) 25,000 (5%) 3.0(County A)

Blacks 750 (100%) 250,000 (50%) 3.0(County B)

100

520 0

100

502 0

%

%.

%

%.

�

�

⎫

⎬⎪⎪

⎭⎪⎪

TheoreticalMaxiima


County “A” the ceiling will be set at 1/.05 (20); for County “B” theceiling will be set at 1/.5 (2).

The possible values for the Disproportionality Metric in County“A” are thus allotted a range that spans from zero to 20, while pos-sible values for the Disproportionality Metric in County “B” are restricted to a far more limited range of just zero to 2. Not only dothese differently sized ranges make it very difficult to compare theDisproportionality Metric for blacks in these two counties, but thereis the additional problem that the likelihood of having a very highDisproportionality Metric is far greater in County “A” than it isin County “B.”

The Disparity Index

Fortunately, a comprehensive measure of disparity that meaning-fully compares differences between groups, across areas, and overtime can be computed from the same data. If localities are able tocollect child welfare event level information broken out by ethnic-ity, then they have all of the information needed to use the meas-

FIGURE 1Explanation of Unique Theoretical Maxima

Shaw et al. 31

ure recommended in this paper to examine the over- or underrepresentation of various racial and ethnic groups.

The Disparity Index (DI) can be thought of as the likelihood ofone group experiencing an event, compared to the likelihood ofanother group experiencing that same event. It can be easily calcu-lated by dividing the Disproportionality Metric for one group bythe Disproportionality Metric for another group, or by taking a ra-tio of their respective rates per 1,000. For example, the DisparityIndex for black children compared to non-black children in fostercare would be calculated by dividing the Disproportionality Metricfor black children by the Disproportionality Metric for non-blackchildren. This is graphically represented in Figure 2.

The Disparity Index provides an unbiased comparison of thelevel of representation for one group (for example, black children)

FIGURE 2Explanation of Disparity Index


versus all others (in this example, all non-black children) by effec-tively removing the unique theoretical maxima. Since the black chil-dren and non-black children exist within the same base population,the population counts are effectively “cancelled out” of the equationas shown in Table 4. With these numbers cancelled out, the compar-ison is simplified to the number of children in care for each groupand the number of children in the population for each group.

The Disparity Spreadsheet

Just outlined are several methods of exploring racial representa-tion—rates per 1000, a measure of disproportionality called theDisproportionality Metric, and the Disparity Index. The first twoare descriptive measures, either of which may be used to computethe Disparity Index. All are easily calculated and presented usinga disparity spreadsheet tool which is available for download freeof charge from the Performance Indicators Project at the Centerfor Social Services Research, School of Social Welfare, University of

TABLE 4Calculation of Disparity Index (Black vs. non-Black) for County “A”

Another way to calculate the disparity index is with the rates:

DIrate for Black

rate for all others

# Blac

� �

kk children in care# Black children in popullation

# Other children in care# Other childdren in population

� �

7525 000

475475 000

0 00,

,

. 33

0 001

33 0

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per 1,000

1 per 1,000

DIDM

DMblack

non-black

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75550

25 000500 000

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550475 000

500 000

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000 000

475 000500 000

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75

,

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4475 000475 25 000

3 00,

* ,.�

�DIDM

DMblack

non-blackk

� �2 7280 909

3 00..

.

Shaw et al. 33

California, Berkeley (http://cssr.berkeley.edu/CWSCMSreports/dynamics/ disprop/). The main page of the Microsoft Excel spread-sheet can be seen in Figure 3.

Two types of count data are needed to compute Disparity us-ing the spreadsheet. The first are counts of child welfare contact,by race/ethnicity, for a specified time period and for a given geo-graphic area. The second are point in time population counts, againby race/ethnicity, for the same geographic area. Both of these countsneed to be broken out by the various groups for which compar-isons are desired. The spreadsheet allows Disparity Indices to becomputed for as many as five different racial/ethnic groups, up tofour decision points, and six age groupings.

Many areas are unlikely to have data that allow for the full useof the spreadsheet: the area may be too small to support this num-ber of stratifications, the data may not available, or it may be thatsuch refinements are not preferred. However, this should in noway preclude its use. A county with data limited to a point-in-timecount of all children in foster care by race/ethnicity, with corre-sponding child population data, is still able to use this tool to ex-amine racial/ethnic disparity. In other words, the functionality ofthis spreadsheet remains in the absence of complete data.

This spreadsheet is designed to compute Disparity Indices bygroups designated by the user (specified in the “Labels” tab).Within the “Data” tab, data may be entered, stratified by age group(e.g., infants, 1- to 2-year-olds, etc.) or point of contact (e.g., allega-tions, substantiated allegations, entries, etc.). After entering thedata in one or all of the tabs, disparity indices will automaticallybe produced (i.e., the formulas are already entered and will be cal-culated using the data supplied in the base tabs).

Conclusion

The extent to which certain groups of children are systematicallyoverrepresented or underrepresented in the child welfare sys-tem is of concern to policy makers and practitioners alike. The


FIGURE 3Disparity Spreadsheet—Example of California Data by Ethnicity

Shaw et al. 35

ability to make comparisons across areas, within an area overtime, and between various groups should be a key feature ofany measure adopted for use. The Disparity Index provides amethodologically sound measure for all of these comparisons.These indices are constructed such that compositional changesto the population in a given area are reflected in the index. Whilethe Disproportionality Metric may be misleading in situationswhere the group of interest comprises a relatively small or largeproportion of the population, the Disparity Index corrects forthis potential bias by comparing the relative rates of the twogroups. Additionally, because Disparity Indices can also be com-pared across specific decision points (or system levels), it allowsfor a more refined understanding of where disproportionalityexists. This allows policy makers and practitioners to assess thedegree to which contact at each level of the system contributes tooverall disparity.

Any conclusions drawn from the Disparity Index need to bethoughtfully and cautiously constructed. Like any other computedmeasure, the information from the Disparity Index should not beused in isolation to argue that biased decision making or institu-tionalized racism are (or are not) at play. The size of the countsused to compute the disparity indices must be taken into accountas must the nuances of local policies, and specific population char-acteristics unique to the area being assessed. As is always the case,the accuracy of rates (and thus the accuracy of a comparison ofrates) is dependent on the accuracy of both foster care counts andcensus data or intercensus population estimates. Finally, risk ad-justments for rates of poverty and other factors would be ideal andin their absence it is important to keep in mind that these other fac-tors likely contribute to disproportionate child welfare contact. De-spite these limitations, using a relative rate of representation (theDisparity Index) as the standard measure of racial disparity offerspractitioners and policymakers alike a valuable and much neededtool for the identification, tracking, and subsequent discussion ofracial/ethnic disproportionality in child welfare.


This research was funded by the California Department of Social Services and the Stuart Foundation.

References

Butts, J., Bynum, T., Chaiken, J., Feyerherm, W., Laws, M. B., Leiber, M., & Snyder, H. (2003,May 8). Recommended relative rate measures for disproportionate minority contact.Report presented at The Disproportionate Minority Contact (DMC) Peer Review Meeting.

Derezotes, D., Poertner, J., & Testa, M. (2005). Race matters in child welfare: The overrepresenta-tion of African American children in the system. Washington, DC: Child Welfare League ofAmerica Press.

Hsia, H. (2007). A disproportionate minority contact (DMC) chronology: 1988 to date. U.S Depart-ment of Justice, Office of Juvenile Justice and Delinquency Prevention, DisproportionateMinority Contact. Retrieved August 13, 2007, from http://ojjdp.ncjrs.org/ dmc/ about/chronology.html

Jewell, N. (2004). Review of statistics for epidemiology. New York: Chapman & Hall/CRC.

Needell, B., Shaw, T., Magruder, J., & Putnam-Hornstein, E., (2007a, July). Racial dispropor-tionality and disparity in child welfare: The disparity index. Paper presented at the NationalChild Welfare Data and Technology Conference, Washington, DC.

Needell, B., Webster, D., Armijo, M., Lee, S., Cuccaro-Alamin, S., Shaw, T., Dawson, W., Pic-cus, W., Magruder, J., Exel, M., Smith, J., Dunn, A., Frerer, K., Putnam-Hornstein, E., &Ataie, Y. (2007b). Child welfare services reports for California. Retrieved May 3, 2007, fromUniversity of California at Berkeley Center for Social Services Research Web site: http://cssr.berkeley.edu/CWSCMSreports

Sedlak, A. J., & Broadhurst, D. D. (1996, September). Third national incidence study of childabuse and neglect (Contract No. 105-91-1800). Washington, DC: National Center on ChildAbuse and Neglect.

Sedlak, A., & Schultz, D. (2005). Race differences in risk of maltreatment in the general childpopulation. In D. Derezotes, J. Poertner, & M. Testa (Eds.), Race matters in child welfare:The overrepresentation of African American children in the system (pp. 47–62): Washington,DC: Child Welfare League of America Press.

Magruder, J., & Shaw, T. V. (2007, July). Children ever in care: An examination of cumulative dis-proportionality. Paper presented at the 10th National Child Welfare Data Conference(Making IT Work), National Resource Center for Child Welfare Data and Technology(NRCCWDT), Washington, DC.

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