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Placing Children in Special Education: A Strategy for Equity (1982)

Chapter: Patterns in Special Education Placement as Revealed by the OCR Surveys

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Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
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Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
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Page 323
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
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Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
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Page 325
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
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Page 326
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 327
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 328
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 329
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 330
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 331
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 332
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 333
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 334
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 335
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 336
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 337
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 338
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 339
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 340
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 341
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 342
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 343
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 344
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 345
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 346
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 347
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 348
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 349
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 350
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 351
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 352
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 353
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 354
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
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Page 355
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 356
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 357
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 358
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 359
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 360
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 361
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 362
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 363
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 364
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 365
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 366
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 367
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 368
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 369
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 370
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
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Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 372
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 373
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 374
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 375
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
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Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
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Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 378
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
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Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
×
Page 380
Suggested Citation:"Patterns in Special Education Placement as Revealed by the OCR Surveys." National Research Council. 1982. Placing Children in Special Education: A Strategy for Equity. Washington, DC: The National Academies Press. doi: 10.17226/9440.
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Page 381

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Pallet n Special Eclucation Placement as Revealed by the OCR Surveys JEREMY D. FINN Since 1968 the Office for Civil Rights (OCR) has surveyed schools and school districts regarding student enrollment and placements. This paper describes the results of an analysis of the OCR survey data pertaining to the 1978-1979 school year. The original data consist of simple counts of students obtained from school and district offices at one point in time: Oc- tober 1978. The data do not describe the processes whereby one student (or a group of students) is placed in special programs in any particular set- ting and, therefore, cannot explain how differences in placement rates are created. The data do, however, document the extent of disproportion in special programs by race/ethnicity and gender as well as the demographic conditions under which smaller or larger disproportions are found. It is clear that the placement rates in special education programs are very different both for minority and white students and for males and females. Table 1 gives nationwide percentages of students in each of five special programs. Minorities are classified as educably mentally retarded (EMR) at a rate that is substantially higher than that for white students both in absolute and relative terms. By comparison, the male-female ratio in EMR programs is smaller, but 3 times as many males as females are classified as emotionally disturbed, and almost 2.5 times as many males as females have specific learning disabilities. I am grateful to Robert Serfling, Amado Padilla, Reginald Jones, Richard Eyman' Lyle Jones, Ingram Olkin, and Miron Straf for their reactions and suggestions for improvements to an earlier draft of this paper. 322

Patterns in Placement as Revealed by the OCR Surveys 323 The purpose of this analysis is to illuminate the differences in place- ment rates and, to the extent possible from the survey data, to describe the context in which they arise. This paper summarizes the results of the data analysis in a progression from general to more specific findings. Dif- ferences between minority and nonminor~ty students in EMR placements are described, and the examination is specified by separate racial or eth- nic classifications and by special education programs other than EMR programs. THE 1978 OC R S U RVEY In its 1978 Elementary and Secondary School Civil Rights Survey, OCR sampled approximately 6,000 school districts, or about one third of the districts in the United States. Questionnaires were sent to all district of- fices and to every school in the 6,000 districts, requiring counts of the number of students enrolled, the number enrolled in special education programs, and additional global characteristics of the student population. All student counts were classified by racial or ethnic identity, and some were also classified by gender. Both racial/ethnic and gender classifica- tions were required for students in five special programs, which are, according to the general instructions (Form OS/CR 102), as follows: 1. Educable mentally retarded (or handicapped) a condition of mental retarda- tion which includes pupils who are educable in the academic, social, and occupa- tional areas even though moderate supervision may be necessary. 2. Trainable mentally retarded (or handicapped) a condition of mental retar- dation which includes pupils who are capable of only very limited meaningful achievement in the traditional basic academic skills but who are capable of profit- ing from programs of training in self-care and simple job or vocational skills. According to the "general instructions to the fall 1978 school survey" (Form OS/CR 102), the following racial or ethnic categories are recognized: American Indian or Alaskan Native: A person having origins in any of the original peoples of North America and who maintains cultural identification through tribal affiliation or community recognition. Asian or Pacific Islander: A person having origins in any of the original peoples of the Far East, Southeast Asia, the Pacific Islands, or the Indian subcontinent. This area includes, for example, China, India, Japan, Korea, the Philippine Islands, and Samoa. Hispanic: A person of Mexican, Puerto Rican, Cuban, Central or South American, or other Spanish culture or origin-regardless of race. Black, not of Hispanic origin: A person having origins in any of the black racial groups of Africa. White, not of Hispanic origin: A person having origins in any of the original peoples of Europe, North Africa, or the Middle East.

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Patterns in Placement as Revealed by the OCR Surveys 325 3. Seriously emotionally disturbed a condition exhibiting one or more of the following characteristics over a long period of time and to a marked degree, which adversely affects educational performance: an inability to learn which cannot be explained by intellectual, sensory, or health factors; an inability to build or main- tain satisfactory interpersonal relationships with peers and teachers; inappropriate types of behavior or feelings under normal circumstances; a general pervasive mood of unhappiness or depression; or a tendency to develop physical symptoms or fears associated with personal or school problems. The term includes children who are schizophrenic or autistic. The term does not include children who are socially maladjusted, unless it is determined that they are seriously emotionally disturbed. 4. Specific learning disability a disorder in one or more of the basic psycho- logical processes involved in understanding or in using language, spoken or writ- ten, which may manifest itself in an imperfect ability to listen, think, speak, read, write, spell, or to do mathematical calculations. The term includes such conditions as perceptual handicaps, brain injury, minimal brain dysfunction, dyslexia, and developmental aphasia. The term does not include children who have learning problems which are primarily the result of visual, hearing, or motor handicaps, of mental retardation, or of environmental, cultural, or economic disadvantage. 5. Speech-impaired a communication disorder, such as stuttering, impaired articulation, a language impairment, or a voice impairment, which adversely af- fects a child's educational performance. The sample consists of both "forced" districts, which OCR required to be included because of their compliance status or because they had ap- plied for funds under the Emergency School Aid Act, and "drawn" dis- tricts, chosen at random from within a sampling frame organized by 13 demographic characteristics to ensure that all characteristics of impor- tance to OCR were represented.2 Of the total 6,079 districts sampled, 6,040 provided responses; of these, 2,146 districts were "forced." The total number of schools represented in the sample is 54,082. Because the data are not a simple random sample of the districts of a state or region, sampling weights are provided to allow estimates of state totals or aver- ages. Checks on the accuracy of these projections were made from the 1976 school survey (U.S. Department of Health, Education, and Welfare, 1978a), which followed a similar sampling plan and yielded very reason- able results. The number of districts actually responding to the survey is given for each state in Table 2.3 The District of Columbia and Hawaii each have a 2Details of the sampling design for 1978 are given in U.S. Department of Health, Education, and Welfare (1978b). 3The sampling plan caused the District of Columbia and eight states to be surveyed ex- haustively (Alabama, Florida, Georgia, Hawaii, Louisiana, Mississippi, North Carolina. and South Carolina).

326 TABLE 2 Districts Sampled and Responding to Question on EMR Programs FINN Approximate Number Percentage of DistrictsNumber with EMR Statein State*Sampled Programs Alabama125125 100.0 Alaska5022 100.0 Arizona22381 96.3 Arkansas348237 94.9 California1,022326 66.6 Colorado11758 91.4 Connecticut16274 90.5 Delaware2412 100.0 District of Columbia11 100.0 Florida6767 100.0 Georgia183187 99.5 Hawaii11 100.0 Idaho11142 95.2 Illinois958320 68.8 Indiana280123 91.9 Iowa389138 60.9 Kansas301105 79.0 Kentucky159108 95.4 Louisiana6666 100.0 Maine17272 93.1 Maryland2521 100.0 Massachusetts336126 47.6 Michigan565202 88.1 Minnesota405142 81.0 Mississippi150150 98.7 Missouri419197 95.4 Montana52162 82.3 Nebraska99666 92.4 Nevada179 100.0 New Hampshire14243 93.0 New Jersey556197 75.1 New Mexico8851 94.1 New York716263 62.0 North Carolina144145 100.0 North Dakota28753 62.3 Ohio566245 92.2 Oklahoma596193 92.7 Oregon32764 87.5 Pennsylvania479317 83.3 Rhode Island3927 88.9 South Carolina929.2 100.0 South Dakota17458 63.8

Patterns in Placement as Revealed by the OCR Surveys TABLE 2 (continued ~ 327 Approximate Number Percentage of Districts Number with EMR Statein State* Sampled Programs Tennessee140 110 99.1 Texas1,077 573 90.8 Utah39 19 100.0 Vermont232 58 56.9 Virginia132 101 99.0 Washington301 91 87.9 West Virginia49 28 100.0 Wisconsin406 143 85.3 Wyoming48 29 89.7 *From 1976 OCR survey, which surveyed districts exhaustively. single administrative school district. Elsewhere the number of districts in a state varies immensely, as do the ways in which districts are defined. A number of states that are predominantly rural have many small districts- e.g., Nebraska, which has a large number of one-school districts a situa- tion that creates unique problems both for the organization of special education programs and for studying enrollment patterns. These districts, which often have small proportions of minorities, cannot be readily com- pared with those with much larger enrollments. To date, OCR has not conducted any checks on the accuracy of the school or district reports. The 1976 survey requested data from all school districts in the country, and the response rate was at least 95 percent in every state. School districts are obligated under Title VI of the Civil Rights Act of 1964 to respond to the survey in a timely and accurate fashion and are reminded of this in the survey instruments. Thus, while the data have not been and should be verified, the conditions under which they are ob- tained suggest that respondents would take reasonable care with their reports. TECHNICAL ISSUES MEASURING GROUP DIFFERENCES IN PLACEMENTS The results by sex in Table 1 show that disproportions may appear larger or smaller depending on whether they are based on the differences of per- centages or on ratios. Because the percentage scale is bounded by zero at

328 FINN one end and 100 at the other, absolute differences between values close to either end are generally limited to being relatively small. In other words, a program for the seriously emotionally disturbed (SED), which has a small proportion of pupils enrolled in total, does not have a large absolute disproportion by gender, even though the process of classifying students as emotionally disturbed results in a male-female ratio of about 3:1. At the same time, there is a greater percentage of females who are not in spe- cial education. In comparison to the nonclassified group, the 3:1 dispro- portion is still more extreme. In the analysis presented in this paper, these problems were addressed by using an index of disproportion derived from recent statistical develop- ments termed log-linear analysis (Bishop et al., 19751. The basic element in the index is the "odds" of being assigned to a particular special educa- tion category. For example, a measurement of the odds of a minority stu- dent's being assigned to an EMR class is the percentage of minority stu- dents who are classified as EMR divided by the percentage of minorities who are not in special programs. From Table 1, this is 2.54/92.60 = 0.027. The odds of a white student's being designated EMR is 1.06/94.12 = 0.011. The disproportion index is the ratio of these two odds, scaled by being transformed to a natural logarithm;4 that is, loge(O.027/0.011) = 0.89. The log-odds index is positive because the EMR odds for minorities is larger than those for whites; it would be zero if the odds for minorities and whites were equal and negative if the odds for minorities were lower than those for whites. The index is not simple to interpret since the measure is unbounded, i.e., it can vary from-oo to +oo depending on the magni- tude of the disproportion. As a rough interpretive device, however, the log-odds index can be transformed to a measure of association, Yule's Q-statistic, which, like a correlation, is limited to values between-1 and + 1.s Thus the association of race or ethnicity (minority versus nonminor- ity) with placement (EMR versus none) is +.42. To see the degree of change in either the log-odds index or Q with a change in disproportion, suppose that the minority-white EMR ratio was 5:1 instead of the actual ratio of approximately 2.5:1.0. That is, suppose that 5.30 percent of racial/ethnic minorities were enrolled in EMR programs 4This is also equivalent to the difference of the logarithms of the two odds, i.e., In (0.027)- In (0.011) = 0.89. sThe relationship is given by ~ = (a-l )/(a + 1), where a = ex and x is the log-odds index. This transformation is the inverse of Fisher's z for correlations and maps x onto the zero-one interval. Q is normally distributed in large samples and attains a value of unity whenever either odds is zero.

Patterns in Placement as Revealed by the OCR Surveys 329 about double the Table 1 value and that 89.84 percent of minorities were not enrolled in any special program instead of the actual value of 92.6 percent. These hypothetical values would increase the log-odds index to 1.66 and the measure of association to Q = .68. DISAGGREGATION OF DATA A second technical issue is the extent to which data on disproportion should be disaggregated. For example, Table 3 presents the percentage of students in each special program for specific racial/ethnic populations. It is clear that the relatively large minority-white differences in EMR place- ments are even more extreme for black students alone (3.46 percent of black students are classified EMR), who also comprise the largest minor- ity population in this country. The disproportions in programs for the trainable mentally retarded and for emotionally disturbed children are also due in large part to the disproportionate representation of blacks in these classifications. At the same time, for Hispanic students the second largest minority group placement rates in EMR, TMR, and SED pro- grams are very close to those for non-Hispanic whites on a nationwide basis. Asian and Pacific Island students have the lowest placement rates of all groups in the same three programs. Table 3 also provides information on the apparent lack of difference be- tween minority and white placements in specific learning disabilities pro- grams. A slightly larger percentage of whites is classified as having spe- cific learning disabilities than blacks, unlike the difference in other special programs, while a still larger percentage of Hispanic students is classified as having specific learning disabilities. Disaggregation by race or ethnicity provides information that is not ap- parent in Table 1.6 To simplify the data presentation, this paper first presents results for all minorities combined; the results are then subdivided for separate racial/ethnic groups. It is an important characteristic of the log-odds index of disproportion that it can be validly computed for each minority group separately, by replacing the odds of placement for all mi- norities with the odds for a particular subpopulation (e.g., blacks or His- panics). Other approaches e.g., the comparison of the proportion of 6 Some further disaggregation by grade is possible with the OCR data, by locating schools within each district that serve only grades kindergarten-6, 7-8, and 9-12, respectively. About three fourths of the schools in the sample can be classified in this manner. While some age-related analysis is possible, the various levels are not comparable because of different dropout rates; dropout information was not gathered in the OCR's 1978 survey.

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Patterns in Placement as Revealed by the OCR Surveys 331 EMR students who are black with the proportion of the total school popu- lation that is black do not give an accurate portrayal of disproportion in settings with multiple minority groups. This is because the denominators of the EMR proportion and of the total proportion are inflated differen- tially by the number of minority students included who are not black. Further disaggregation by geographic or administrative unit can reveal trends that would not be apparent if the number of children enrolled in each school or district was disregarded. For example, consider a hypo- thetical geographic unit (a state or nation) that has only two school dis- tricts. District 1 has a total enrollment of 3,000 students, consisting of 1,000 white and 2,000 minority students. Of these, 20 white (2 percent) and 20 minority students (1 percent) are classified as EMR. While the rate for minorities in District 1 is slightly lower than that for whites, the situa- tion is the opposite in District 2. The total enrollment is 600, consisting of 400 white and 200 minority students. Four of the white students (1 per- cent) and 18 minority students (9 percent) are enrolled in EMR classes, reflecting a relatively large disproportion. If the geographic unit's total alone is examined, there are 1,400 white students of whom 24 are assigned to EMR classes, yielding a 1.7 percent placement. There are 2,000 minority students, of whom 38 (also 1.7 per- cent) are in EMR classes. While the two percentages are the same at the state level, they disguise several more detailed outcomes the large dis- proportion in the small district and the variability between district prac- tices. This stems from the tendency of large districts to obscure data for small districts in aggregations. Districts that have no students classified in a special program inflate the state's total enrollment proportionate to the percentage of minority stu- dents in the district, distorting aggregate measures of disproportion fur- ther. For example, according to the 1978 OCR survey, in only 12 states did all districts report having EMR students. In 19 of the remaining states, more than 10 percent of the school districts reported having no EMR students at all, and in 8 states more than 25 percent of the districts reported having no EMR students. The average enrollment of 887 districts having no EMR students was 1,336, well below the average of 5,911 stu- dents in districts having EMR programs. While many smaller (often ru- ral) districts maintain other special programs, including those for trainable mentally retarded, emotionally disturbed, or specific learning-disabled students, about one third of the districts having no EMR programs do not operate any of these other programs. Thus, there are essentially two popu- lations of school districts represented in the survey data those with and those without EMR programs. Statistical information regarding racial or

332 FINN sex differences in EMR placement rates can be obtained only from the for- mer set. 7 Placement in special education programs is a district-by-district process, and a wide range of placement rates and racial disproportions may be found among districts operating under the same state guidelines. It is essential that an analysis of special education trends reflects this variability. SCORING DISPROPORTION FOR DISTRICTS AND STATES The 1978 OCR survey provides data from which placement rates and the disproportion index may be calculated for each school district. Of the 5,153 districts in the 1978 sample that have students enrolled in EMR pro grams, 236 districts do not have both whites and minorities in their stu- dent populations. The distribution of the log-odds index for EMR place- ments in the remaining 4,917 districts is given in Table 4 for all minorities combined. A log-odds index of 1.6 (Q = .66) separates 20 percent of the districts with the highest degree of disproportion from those with less dis- proportion; an index value of 2.1 (O = .78) separates 10 percent of the districts with the most extreme disproportions from the rest. The index values in every column of Table 4 have a nearly normal distribution and may be used in normal-theory statistical analysis (e.g., l-tests or F-tests). Small districts present a special problem to the investigation of special education placements, which is reflected in any measure of proportional- ity. A typical rural district or one in a small New England community, for example, may have 500 students of whom all but 20 are white. One stu- dent of the 20 classified as EMR results in a EMR rate of 5 percent for mi- norities. If two are classified as EMR, the minority rate is 10 percent, which is unusually high, and so on. In other words, in districts with a veer low number of minorities enrolled (or with a very low number of whites), small differences in the number of placements create large disproportions that may not reflect a serious problem of overrepresentation or underrep- resentation. Furthermore, if none of the minority students (or none of the whites) is in an EMR class, the odds for that group are zero, and the logarithm is not defined. Recent advances in the analysis of contingency tables provide methods for "smoothing" proportions so that they allow finer differences than the 5-10-15 percent values of the example above. The method of "iterative The proportion of the nation's school districts having no EMR programs may be larger than the OCR's 1978 survey indicates. In 1976, OCR surveyed all districts in the country, and ap- proximately 45 percent reported no EMR enrollment. The 1978 sampling plan may have tended to overrepresent those districts having EMR classes.

Patterns in Placement as Revealed by the OCR Surveys TABLE 4 Relative Frequency Distribution of Log-Odds Measure for All Minorities in EMR 333 District Enrollment (in thousands) Less More Interval All Than 1 1 to 3 3 to 10 10 to 30 Than 30 -5.0 and below 0.3 0.5 0.2 0.1 - - -4.9 to-4.5 0.1 0.2 0.1 0.2 - - -4.4 to-4.0 0.4 0.4 0.6 0.1 - - -3.9 to-3.5 0.6 1.2 0.5 0.2 0.2 - -3.4 to-3.0 0.6 0.5 1.1 0.3 - - -2.9 to-2.5 1.2 2.0 1.1 1.0 0.4 - -2.4 to-2.0 3.2 3.9 3.8 2.3 - - -1.9 to-1.5 4.6 5.6 5.3 3.7 0.7 0.7 -1.4 to-1.0 6.7 6.0 9.4 5.3 0.8 - -0.9 to-0.5 8.2 9.8 10.4 4.4 3.9 - -0.4 to 0 10.9 15.0 10.9 7.7 10.4 3.7 0.1 to 0.5 13.4 13.1 11.6 13.9 23.1 18.4 0.6 to 1.0 15.6 10.2 13.0 22.0 23.8 30.1 1.1 to 1.5 13.5 7.2 13.5 18.0 19.2 25.8 1.6 to 2.0 10.6 7.8 9.7 13.7. 12.7 14.7 2.1 to 2.5 5.1 6.7 4.2 4.9 4.4 5.1 2.6 to 3.0 2.2 3.8 2.2 1.5 0.2 0.5 3.1 to 3.5 1.0 1.7 1.0 0.4 0.2 - 3.6 to 4.0 0.5 1.3 0.3 0.1 - - 4.1 to 4.5 0.3 0.7 0.3 0.1 - - 4.6 to 5.0 0.2 0.4 0.0 - - - 5.1 to 5.5 0.2 0.8 0.1 - - - 5.6 to 6.0 0.1 0.3 0.2 - - - 6.1 to 6.5 0.2 0.4 0.2 - - - 6.6 to 7.0 0.2 0.2 0.2 0.1 - - 7.1 and above 0.1 0.3 0.1 Number of districts in sample 4,917 1,074 1,785 1,507 418 133 Mean 0.42 0.37 0.25 0.59 0.77 1.02 Standard deviation 1.55 1.88 1.57 1.25 0.83 0.67 NOTE: Projections are weighted to nationwide percentages; weights are the inverse of sam- pling probabilities.

334 FINN proportional fitting" (Bishop et al., 1975) is most commonly used when there are many cells in a complex contingency table with few observations (or zeros) but may also be used for smaller tables. In this application it is assumed that any district with few whites or few minority students does not permit accurate estimation of the odds for that group, because of the scale restriction described.8 If all such districts within the state are summed, however, sufficient whites and minorities will be included to obtain fairly accurate estimates of EMR proportions. The state table becomes a "target," and the coarse figures for each small district in the state are adjusted slightly toward those target values. The adjustments are small in all cases but are relatively greater in the smallest districts, where the initial scale in- tervals may be very large. The adjusted proportions are used in the log- odds measure in place of the unadjusted rates. Experience with this pro- cedure has shown that the difference in odds for minorities and whites is changed very little through smoothing, while the estimates of proportions obtained from small samples are refined, and district indexes may be cal- culated when one entry is zero. (Several examples of the procedure are given in the appendix to this paper.) Summary statistics for a state are obtained by averaging the log-odds measure across all districts or subsets of districts (e.g., all districts of similar size). Dispersion measures (e.g., the range or standard deviation) provide an indicator of variability within the state. In every case the descriptive statistics presented in this paper are weighted by the inverse of the sampling probabilities provided from the survey, so that the mean or standard deviation for the entire state is more accurately approximated. Degrees of freedom for tests of significance, however, are based on the ac- tual number of districts in the sample or subsample. GEOGRAPHIC VARIATION IN DISPROPORTION Table 5 presents a summary of disproportion in EMR classes by state and region, as calculated from the 1978 OCR survey. The percentages of mi- nority and white students and males and females who are classified as EMR are calculated for each district having EMR programs, as is the log- odds scoring of the difference. The weighted average and the standard deviation are calculated to estimate the summary statistics for all districts having EMR programs in the state. The average percentage of minority students in EMR classes exceeds Tithe criterion used to identify small districts for this analysis was any district having fewer than 100 minority students enrolled or fewer than 100 whites enrolled.

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338 FINN the average percentage for whites in every state except New Hampshire, Vermont, West Virginia, and Iowa states with a very small number of minority students. Of those states with more than 10 percent minority en- rollments, the average EMR rates for minorities range from 0.85 percent to 9.09 percent with a median of 3.35 percent; for whites the average EMR rates range from 0.59 percent to 2.46 percent with a median of 1.17 per- cent. While the magnitude of the difference varies from state to state, as does the degree of consistency among districts within states, EMR dispro- portion by race or ethnicity is a nationwide phenomenon. There is also systematic regional variation in the extent to which EMR placements for minorities and whites differ. The median state log-odds in- dex for nine northeastern states is 0.06 (O = .03), while state averages range from-1.35 in Vermont to 1.26 in Rhode Island. None of the north- eastern states has an average log-odds index over 1.6, indicating no serious disproportion on a state level. The Midwest is even more homoge- neous, with all average disproportion indexes near zero. In the West, 11 of 13 states have low or nonexistent disproportions by race, while New Mex- ico's average log-odds index is 1.30 (Q = .57) and that for Alaska is 2.28 (Q = .811. Each of these states has more than one large minority group. The border states are a more diverse group, with average log-odds in- dexes ranging from -1.64 in West Virginia, where the percentage of whites in EMR classes is almost 1.5 times that of minorities, to 1.51 in Delaware (Q = .64~. The average disproportion for Maryland is almost as high as that of Delaware. The average disproportion in the southern states is consistently high, ranging from a log-odds index of 0.93 in Arkansas (Q = .43) to 1.86 in Florida (Q = .73), with a median state value of 1.50 (Q = .63~. Except for Alaska, only southern states have average disproportion indexes that approach or exceed the 1.6 value that separates the 20 percent most ex- treme individual districts in the country. The extent to which the same racial difference occurs throughout a state is revealed partially by the standard deviation of the log-odds index. In particular, seven states have relatively small standard deviations (less than .60), indicating relatively homogeneous racial differences throughout: Delaware, Florida, Louisiana, Maryland, North Carolina, South Caro- lina, and Utah. With the exception of Utah, all of these states have more than 25 percent minority enrollment and are located in or near the South. While the high minority enrollment implies that relatively large numbers of minority students attend school in most parts of a state, it does not im- ply that the EMR disproportion is necessarily as high everywhere. For example, Alabama, Mississippi, and Texas also have at least 25 percent

Patterns in Placement as Revealed by the OCR Surveys 339 minority enrollments and are more heterogeneous in placements from one district to another. The average percentage of males in EMR classes is higher than that of females in every state, although the difference on a nationwide basis (Table 1) is not as large as the minority-white disproportion. The state averages for sex disproportion range from 0.13 (Q = .07) in Montana to 0.77 (Q = .37) in Nevada. The standard deviation of the sex differ- ence within each state is relatively small; thus, the extent to which males outnumber females in EMR classes is more consistent across districts throughout the nation than differences by racial or ethnic identity. Within this limited range, there are still some regional trends. The log- odds or association (Q) values are relatively homogeneous in the South and are among the largest average values found anywhere in the nation. The border states of Kentucky, Maryland, and West Virginia also have larger disproportions by sex. To some extent this pattern is similar to that for disproportion by race/ethnicity. It is possible that in these states large percentages of minority males in particular are assigned to EMR pro- grams, creating a sex and a race disproportion simultaneously. Unfor- tunately, the data do not include sex-by-race tabulations, so this possibil ity cannot be explored. The simultaneous occurrence of disproportion by race or ethnicity and by gender can be explored across states and districts, however. At the state level, the log-odds index for race was ranked for the 31 states having more than 10 percent minority enrollment. The rank-order correlation between these and the rankings by sex disproportion is +.42;9 there is a moderate trend for states that have the largest disproportionate assign- ment of minorities to EMR classes also to have the largest relative propor- tion of males in them. At the district level the disproportion index for race was correlated with the index for sex separately within each of the five geographic regions, for each of three district size categories (fewer than 1,000 students; 1,000-9,999 students; and 10,000 or more students). The 15 correlations range from-.20 to +.19, with a median value of-.01; none exceeds the .01 value for a two-sided test of significance. When geographic regions are combined, the correlation for districts with fewer than 1,000 students is .03; for districts with 1,000-9,999 students it is .01; for larger districts it is .13. There is no evidence of a relationship between disproportionate place- ment in EMR classes by sex and disproportion by race/ethnicity on a district 9Statistically significant at p < .05, using a two-sided test.

340 FINN by-district basis. There is an association at the state level, however. To the extent that males and minorities are represented in EMR classes in greater proportions than females and whites, respectively, the phenomenon re- flects practices that vary from one state or region to another more than from one district to another. THE AVAILABILITY PHENOMENON States and regions vary in the proportion of minority and white students actually assigned to EMR classes. The percentages from Table 5 are sum- marized by regions in Table 6 for 31 states with more than 10 percent mi- nority enrollment.~° The five geographic regions are relatively homogene- ous in the minimum and maximum average placement rates for whites, although the low EMR rate for whites in the West does stand out from the other regions. By comparison, there are dramatic differences in both min- imum and maximum values for minorities. The South, with the most con- sistent disproportions in EMR placement, has the highest minimum and maximum average placement rates of any of the geographic regions, up to an average of 9.09 percent of minorities in EMR classes in Alabama. The Northeast and the Midwest, with generally small disproportions, have smaller average placements in EMR classes for minorities. At the low ex- treme, the minimum and maximum average placements for minorities in the West are similar to those for whites in other parts of the country. TABLE 6 Minimum and Maximum Average EMR Percentages by Region Minority White Number Region of States Minimum Maximum Minimum Maximum Northeast 4 1.83 3.35 0.71 1.60 Border 4 2.54 5.20 0.70 2.41 South 11 3.60 9.09 0.84 2.23 Midwest 5 1.57 5.42 1.07 2.46 West 7 0.85 2.51 0.59 1.17 NOTE: For 31 states with more than 10 percent minority enrollment. Minima and maxima were obtained from weighted projections to statewide average values; weights are the inverse of the sampling probabilities. ~°Hawaii and the District of Columbia, each representing only one administrative school district, were not included.

Patterns in Placement as Revealed by the OCR Surveys TABLE 7 Correlations of Disproportion in EMR Placements With Overall Placement Rates 341 Correlations With Correlations With Proportion of All Proportion of All Students District SizeN EMR Students in Special Education Fewer than 1,000 students1,074 0.07 0.07 1,000 to 2,999 students1,785 0.12* 0.12* 3,000 to 9,999 students1,507 0.17* 0.17* 10,000 to 29,999 students418 0.30* 0.22* 30,000 or more students133 0.06 0.34* All districts4,917 0.09* 0.09* NOTE: Correlations are the weighted projections to nationwide values; weights are the in- verse of sampling probabilities. *Significant at p < .01 (two-sided test). On a regional basis the evidence suggests that larger differences be- tween minority and white EMR placements occur in areas where the per- centage of children both minority and white who are placed in EMR classes is high. To explore this relationship further the same 31 states were ranked on EMR placement rates for all students in a state, and each state was classified as being above or below the median. States were also classified as having an average log-odds index for minorities compared with whites above or below the median value for all 4,917 districts (ap- proximately 0.5~. Of the 16 states with "low" EMR rates, 11 have "low" disproportion values, while 5 states with "low" rates have higher dispro- portions by race. Among states with "high" placement rates, 13 of the IS states have disproportions above the median. The regional trend is thus supported at the state level as well. Disproportion is also associated with the overall percentage of students in EMR programs and, for all special education programs, at the district level. The correlations of placement rates with racial disproportion are given in Table 7 for districts in each size category. All correlations are positive, and most are statistically significant when p ~ .01.~ The rela- tionship is strongest among districts with 10,000-29,999 students and is positive but nonsignificant among very small districts. Many of the latter lathe correlations of the size of the EMR program with disproportion by sex (M-F) are positive, ranging from .04 for the smallest districts to .36 for districts with 10,000-29,999 pupils. The correlations of the size of the entire special education program with sex dispro- portion are all small and nonsignificant.

342 FINN enroll only white or only black students, so that disproportion is largely a function of the size of one student group or the other; these tend to cancel each other across many districts. The positive relationship between the size of EMR programs and the disproportionate placement of minorities in those programs occurs at dis- trict, state, and regional levels. The association may be interpreted in one of several ways. First, it is possible that the high proportion of minorities is creating an overall EMR program that is large. This may be an artifact since a relatively large number of EMR students of any group will tend to inflate the overall size of the program. Second, the size of the program may encourage greater disproportion in placements. That is, a large EMR program may open the door to mechanisms that allow minorities to be placed in these classes in relatively larger proportions. Third, both the size of the program and the disproportion may be simultaneous results of other exogenous factors, e.g., relatively large groups of educationally handicapped children, state or district guidelines for the classification of EMR students, and inferior instruction for minority (and white) students. It is clear that when the size of an EMR program is curtailed i.e., its availability reduced-fewer students are involved, whether or not the rela- tive degree of disproportion is changed. The data do indicate that, in gen- eral, smaller degrees of disproportion occur in relatively smaller EMR programs. DEMOGRAPHIC CHARACTERISTICS AND DISPROPORTION ExRo~tMENT The correlation between racial disproportion and total district enrollment is .05 for all districts. (Table 4 provides more detail.) Except for the smallest districts the average disproportion increases with district size. The standard deviation decreases as district size becomes larger, reflect- ing the absence of extreme disproportions in either direction. The mean disproportion among districts with 30,000 or more students is the highest, not because of many high disproportions but because very few districts have small or negative minority-white differences. On one hand, the size of larger districts in general appears to play a limiting role in the magni- tude of racial disproportion in EMR classes. Districts with very small enrollments, on the other hand, sometimes have extreme disproportions in both directions. While few students are affected within any one district, the disproportions may involve a sizable number of students when totaled to the state or regional level.

Patterns in Placement as Revealed by the OCR Surveys PERCENTAGE OF MINORITY ENROLLMENT 343 To examine the relationship of racial composition to EMR disproportion, districts were classified as having 0-10, 10-30, 30-50, 50-70, 70-90, or 90-100 percent minority enrollment. A two-way fixed-effects analysis-of- variance model was fit to the average log-odds index with percentage of minority enrollment and geographic region as factors of classification. Or- thogonal polynomial contrasts for unequal intervals were tested for the minority enrollment factor to determine the degree of complexity of the re- lationship of racial composition to disproportion. Individual districts in a particular size interval were considered as replicated observations; five separate analyses were conducted, one for each size interval. The mean disproportion index for each size of district and each minority enrollment division is given in Table 8 and Figure 1. Tests of significance indicate a distinct relationship of minority enroll- ment to EMR disproportion for each district size category. Specifically, a cubic trend is significant at the .01 level for both the smallest districts (fewer than 1,000 pupils) and for districts with 1,000-2,999 students. This appears in Figure 1 as an increase in disproportion from close to zero, when minority enrollment is 10 percent or less, to values between 1.1 and 1.5 that remain relatively constant for districts with up to 70 percent minority enrollment. Additional minority enrollment causes the curves to turn upward again and peak with very high disproportion as the minority enrollment approaches 90-100 percent. The interaction of region and percent minority is also statistically TABLE 8 Mean Log-Odds Index for Districts by Percentage of Minority Enrollment Percentage of Minority Enrollment District Size 0 to 10 10 to 30 30 to 50 50 to 70 70 to 90 90 to 100 Fewer than 1,000 students-0.07 1.21 1.48 1.12 1.52 4.17 1,000 to 2,999 students-0.09 1.24 1.37 1.35 0.98 2.03 3,000 to 9,999 students0.32 1.15 1.41 1.29 0.82 0.01 10,000 to 29,999 students0.58 1.15 1.11 0.99 0.59 0.06 30,000 or more students1.13 1.34 1.00 0.97 0.66 - 0.02 NOTE: Percentages are the weighted projections to nationwide values; weights are the inverse of sampling probabilities.

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Patterns in Placement as Revealed by the OCR Surveys 345 significant for small districts. Border states with few minorities (0-10 per- cent) have minority-white differences that are larger than the slightly negative values given in Table 8, while northeastern states tend to have still more negative differences (i.e., greater proportions of whites in EMR classes than minorities). Also, small districts in the southern states with 90 percent or more minority do not attain the extremely large racial dif- ferences exemplified by the average values. A substantial portion of the nation's small all-minority school districts are in the South (15 of 41 in the sample). While EMR disproportion is relatively large, it is not as extreme as, for example, small all-minority districts in the West. Placement practices in small school districts in particular are worthy of further investigation. The analyses for districts with 3,000-9,999 students and 10,000-29,999 students each produced a significant quadratic pattern of disproportion. This is apparent in Figure 1 as the parabolic curves for the two sets of dis- tricts. Each has a low, positive disproportion when the percentage of mi- nority enrollment is small. The mean disproportion increases and peaks for districts with 10-70 percent minority enrollment, much like the smaller districts. The average disproportion becomes lower again, however, when the minority enrollment is 70-90 percent and approaches zero for districts that are essentially all minority. For both medium-sized intervals, the interaction of region with percent- age of minority enrollment is also significant, indicating that not all re- gions follow the pattern exemplified by the average curve. The most note- worthy exception occurs for districts with 10,000-29,999 students. As with the smaller districts, northeastern states with less than 10 percent minor- ity enrollment are substantially below the nationwide average of 0.58; the Northeast mean disproportion is 0.33. Neither value is large, however. The disproportion curve for the largest districts yields a significant linear effect, indicating that it is statistically indistinguishable from a monotonically decreasing pattern of means. The average disproportion for large districts is more than 1.1 when the proportion of minority students is 10 percent or less, increases slightly for districts with 10-30 percent mi- nority enrollment, and decreases and approaches zero as the minority en- rollment increases to 90-100 percent. The interaction of this trend with re- gion is nonsignificant, so that the same pattern is characteristic of all five geographic areas. 'fit should be noted that not all regions have very large districts with the entire range of minority proportions. The Northeast, in particular, contributes only eight districts to this analysis, none of which has less than 30 percent minority enrollment. Since the northeastern average disproportion is generally low, this may partially account for the higher dispropor- tions among large districts with small minority enrollments (see Table 8).

346 FINN In general, the size of larger districts may impose constraints on pro- grams for mentally retarded students that both limit the degree of dispro- portion and mediate the effects of greater minority enrollments. Among medium-sized and large districts, increased minority enrollments are not associated with increased racial disproportion in EMR classes. In fact, the opposite is true. Detailed analysis (not shown) indicates that as the per- centage of minority enrollment increases, the minority EMR placement rate diminishes to close to that for whites, and the difference between white and minority rates approaches zero. Whether this is due to different assessment and placement procedures in districts with large numbers of minorities, different definitions of retardation, or different dropout ratesi3 or whether it is a function of the availability of other facilities and re- sources (e.g., Title I programs) is not addressed by the survey data. At the same time, small districts with more than 50 percent minority enrollment exhibit increasing disproportions that are worthy of further study. SOCIOECONOMIC STANDING The 1978 OCR survey provides limited data on the socioeconomic stand- ings of families whose children attend school in a given district. The school questionnaire requires a count of the number of students who pay full price for a daily lunch, the number of lunches that are served free under government subsidy, and the number of reduced-price lunches. It is not clear that all parents whose children qualify for reduced-price or free meals were informed of the program and made formal application or that the application reached the appropriate school officials. Further, the in- come cutoffs by which eligibility is determined depend on the number of children in a family, so that eligibility does not directly imply a given in- come level. Also, schools in middle- or high-income areas having entirely full-price lunch programs cannot be differentiated by socioeconomic sta- tus (SES) from the survey data. Under these conditions, only a gross index of SES is possible. The measure used was simply the proportion of lunches served in the district for which full price was paid. The correlations of SES with EMR disproportions by race/ethnicity are given in Table 9. The association is significantly negative for all districts combined (r = - .20) and similar for districts with up to 9,999 students. However, correlations for separate geographic regions (not shown) indi- cate exceptions in the northeastern and border states, where the correla ~3According to the OCR's 1978 survey, the proportion of students suspended is inversely related to minority enrollment, so suspensions are probably not a contributing factor.

Patterns in Placement as Revealed by the OCR Surveys TABLE 9 Correlations of Socioeconomic Status With Disproportions in EMR Placement Correlation With Disproportion District SizeaNb (Minority-White)C Fewer than 1,000 students1,037 - 0.224 1, 000 to 2, 999 students1, 754 - 0.23 ~ 3,000 to 9,999 students1,493 - 0.154 10,000 to 29,999 students412 - 0.07 30,000 or more students131 +0.35 All districts4,827 - 0.20~ a The correlation of district size with socioeconomic status for the entire sample is-.08. bNinety districts were eliminated that did not provide lunch program information. c Correlations are the weighted projections to nationwide values; weights are the inverse of sampling probabilities. Significant at p < .01 (two-sided test). 347 tions are low positive. For medium-sized districts (up to 29,999 students) the correlation is negative but nonsignificant. This is supported by very small positive and negative values for separate geographic regions. For districts with 30,000 or more students the correlation is significant and positive. Among the largest districts, relatively more minority stu- dents are enrolled in EMR classes when the population served has higher income levels. These figures may disguise a plethora of more complex fac- tors, however.~4 For example, the correlation of district size with SES is itself negative, so that the positive .35 value is specific to a set of districts with relatively low income levels. The lower SES districts within this group are the same districts that have 60 percent or more minority enrollment as well as EMR rates for minorities that are close to those for whites. The higher SES districts in this group tend to have more part-time EMR place- ments (see the section below on time spent in EMR classes). There is a general tendency for greater EMR disproportions to occur in lower SES districts. This is attributable in part to the percentage of students in EMR programs in a district. The relative size of EMR pro ~4The correlation may also be biased by regional differences. The largest districts are pri- marily "forced" into the sample, such that 79 of 131 districts were in the border or southern states. These regions have much higher disproportion levels and somewhat higher mean SES levels.

348 FINN grams has a strong and consistent association with SES (r= - .31 for all districts in the sample). EMR classes may be small or nonexistent in upper-class communities and are accompanied by little racial dispropor- tion. In lower SES communities, both the program size and racial dif- ference are larger. The association of SES with EMR disproportion, however, is mediated by a number of additional factors and even contradicted in some subsets of school districts.~5 Minority enrollment a significant concomitant of SES has a strong but complex relationship to disproportion as well. Un- fortunately, the OCR survey does not provide cross-tabulations of race by participation in the subsidized lunch program, so the two characteristics cannot be disentangled. DESEGREGATION AND RACIAL BALANCE It has been hypothesized that court-ordered desegregation can become an antecedent of high EMR disproportions if classes for mentally retarded students are perceived as an alternate route toward class or school "reseg- regation.'? The OCR questionnaire data cannot reveal whether this is the case since the survey provides no time frame to interpret the question. A positive response to the OCR survey may indicate a program implemented in the recent past, in the more distant past, or perhaps still in preparation. Nevertheless, it is possible to compare the districts under court order with others in the same state that are not. Also, the racial balance among schools in each district may be examined, apart from the official desegre gation status. In general, districts subject to desegregation orders are larger than those that are not (average enrollment of 14,722, compared with 3,707) and have higher percentages of minorities enrolled (average percentage of 39.9, compared with 13.7~. These differences may reflect the tendency of courts or federal agencies to focus their attention on large cities where minority populations are extensive. Table 10 provides several ways of examining the differences between the two groups of districts on a state- by-state basis. The average log-odds index of disproportion was calculated separately for districts under court order to desegregate and those not under court order. They reveal few if any differences. The means for 38 states were The correlation of SES with disproportion by sex (M - F) is consistently negative and significant for all but the smallest districts. That is, in general, more males are assigned to EMR programs in lower SES districts.

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352 FINN compared by use of a t-statistic, and no test of significance exceeded the .05 critical value (or .01~. Furthermore, the same procedure was employed for districts in each of five size intervals in each state. Seven of the test sta- tistics exceeded their respective .05 critical values in size-different states, four in one direction and three in the other. The results, viewed in this manner, strongly support the conclusion that there is no difference in dis- proportion between districts under court order to desegregate and those not under such orders. The percentage of districts in each category that exceed the state's aver- age disproportion level also is shown in Table 10. In 25 of the 38 states the percentage of districts exceeding the state average is higher among court- ordered districts than the other districts; in the remaining 13 states the percentage is lower. The split is significantly different from half and half using a one-sided test, but only when p < .05. Viewed in this manner, there is some tendency for court-ordered districts to have higher dispro- portions. The final column of Table 10 lists the proportion of districts in each category that exceed an extreme disproportion level of one standard deviation above the state's average. In 10 of the 38 states, a greater per- centage of court-ordered districts fall in this extreme range than the other districts; 7 of these are in the South or the border states. There appears to be a slight trend for districts under court order to de- segregate to have higher EMR disproportions than other districts, espe- cially among the southern states. The difference is small in most cases. It is not possible to interpret these differences as arising from the desegrega- tion order in any case since the EMR disproportion may have preceded the order in time and may even have prompted the court's intervention. Other measures may be derived from the OCR survey data to reflect the minority-white imbalance in individual schools. Two indexes of racial im- balance were calculated for each district, Taeuber's "index of dissimilar- ity" (D) and a more refined index derived from an information theoretic basis (H). ~6 Each attains a value of zero if the proportion of minorities in every school is equal to the proportion in the district as a whole, i.e., an "even" distribution of minorities, indicating the least amount of racial isolation. Values of D and H approach 1 as the distribution of minorities becomes increasingly uneven. Both D and H are equal to 1 if some schools in a district are comprised only of minority students and the rest only of whites, i.e., total segregation. The correlations of these measures with the index of disproportion are these indexes are described and compared by Zoloth (1976).

Patterns in Placement as Revealed by the OCR Surveys 353 given in Table 11. In general, the correlations are low. To the extent that EMR disproportion and racial imbalance are related, the association is negative. That is, districts with larger EMR disproportions are those in which the racial composition of the schools is more nearly balanced; those with racial imbalances tend to have more similar EMR rates for whites and minorities. Table 11 displays a set of correlations that is largely negative across region and district size intervals, although not all are statistically signifi- cant. Those that are, with a single exception, are for districts in the in- termediate size ranges (1,000-9,999 students). Otherwise, the correlations of racial imbalance with disproportionate EMR assignment are small and may represent a negligible association for small and large districts in the country as a whole. Community and school perceptions of racial balance may differ depending on the proportion of minority students in the local districts. However, the same pattern of relationships no association among small districts, significant negative association among medium- s~zed districts was found when the percentage of minority enrollments was statistically controlled. In general, there is some tendency for dif- ferences in minority and white EMR rates to occur in districts in which schools are more "racially balanced." The effect is not strong among larger districts i.e., among those in which desegregation orders are the most common and thus does not add support to the "resegregation" hypothesis. TABLE 11 Correlations of Log-Odds Index With Measures of Racial Imbalance Fewer Than 1,000 to 10,000 or More 1,000 Students 9,999 Students Students All RegionDH D HDH DH Northeast-0.05- 0.08 - 0.18* - 0.09- 0.11- 0.01 - 0.09*- 0.03 Border-0.09- 0.06 - 0.26* - 0.21*- 0.41*- 0.20 - 0.17*- 0.12* South-0.010.04 - 0.17* - 0.08*- 0.12- 0.09 - 0.10*- 0.04 Midwest-0.05- 0.04 - 0.16* - 0.10*0.040.12 - 0.11*- 0.05 West0.000.10 0.04 0.110.060.05 0.010.09 All-0.09*- 0.05 - 0.20* - 0.07*0.040.10 - 0.13*- 0.02 NOTE: All correlations are the weighted projections to regional values; weights are the in- verse of sampling probabilities. *Statistically significant at p ~ .01 (two-sided test).

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Patterns in Placement as Revealed by the OCR Surveys STUDENT SUSPENSIONS AND EMR DISPROPORTION 355 The OCR questionnaire requires districts to report the number of students who were suspended for "at least one school day during the 1977-78 year." Both the percentage of all students suspended and the percentage of minority students who were suspended during the year were recorded for this analysis. Average suspension rates are given in Table 12 by district size and minority enrollment. On a nationwide basis, 3.3 percent of all students and 4.1 percent of minority students were suspended at least once in 1977-1978. Suspension rates increase monotonically with district size and peak at 5.4 percent of all students and 7.3 percent of minorities in the largest districts. The proportion of suspensions are lowest in all-white and in all-minority districts and highest in the 30-70 percent minority range. Large districts in this range suspend more than 9 percent of all minority students more than twice the nationwide rate for minorities and almost three times that for all students. The correlations of suspensions with EMR disproportion are given in Table 13. Among small school districts and the very largest, there is no association of suspensions with disproportion in EMR placements. Among districts with 1,000-29,999 students enrolled, however, there is a positive association of racial disproportion with suspension rates.~7 Furthermore, the association is stronger with minority suspension than with overall stu- dent suspensions. Thus, middle-sized districts tend to suspend greater TABLE 13 Correlations of Suspension Rates With Racial Disproportion in EMR Placement Correlation With Correlation With District Size All Suspensions Minority Suspensions Fewer than 1,000 students 1,000 to 2,999 students 3,000 to 9,999 students 10,000 to 29,999 students 30,000 or more students All districts 0.08* 0.03 0.11* 0.23* 0.34* 0.13 0.12* NOTE: All correlations are the weighted projections to nationwide values; weights are the inverse of sampling probabilities. *Statistically significant at p < .01 (two-sided test). Tithe correlations of EMR disproportion by sex (M-F) with suspensions are generally very low and nonsignificant.

356 FINN numbers of minority students and to assign them to EMR classes in greater numbers concomitantly. ~8 Whether either of these practices is an antece- dent of the other or whether both are functions of a plethora of other pos- sible determinants is not revealed by the survey data. TIME SPENT IN EMR CLASSES The OCR questionnaire solicits information on the amount of time stu- dents spend in special education classes, categorized as "less than 10 hours per week, 10 hours or more per week but less than full-time, or full- time." There is some ambiguity in the item for EMR programs since it is not clear whether the intent is to count (1) hours outside the regular class, (2) all time during which the child is receiving some special attention, whether in the regular class or not, or (3) the total amount of time the child is considered retarded (which would usually be full-time). While dif- ferent respondents may have interpreted the item differently, it is likely that the most common interpretation is the first i.e., a report of the pro- portion of time EMR students spend outside the regular classroom so that the response "less than 10 hours" describes children who are largely mainstreamed. The average proportion of EMR students assigned for the three time in- tervals is summarized in Table 14.EMR programs usually involve more than 10 hours per week of class time; that is, they are not generally attended for one or two class periods but for most of the school day. In fact, 49.4 percent of all districts having EMR programs report no students enrolled in EMR for less than 10 hours per week, while 16.8 percent of districts place all EMR students in full-time special programs. The profiles of Table 14 indicate that typical districts spl* EMR students about equally between full-time and somewhat less than full-time programs; the latter may be, for example, all academic courses or all classes but one. Larger districts tend to have more full-time EMR placements. The correlations between the proportion of full-time EMR students and differential placements for minorities and whites (Table 14) are negative in every size interval and attain their largest values for schools with 10,000-29,999 students. In general, there is a tendency for the highest racial disproportions to occur in districts with many part-time EMR place- ments. Among large districts, those with the greatest disproportions tend have less than 50 percent minority enrollment (see Table 81. In these set ~8The same pattern is obtained for each geographic region except the West, where EMR disproportion is not related to either suspension index.

Patterns in Placement as Revealed by the OCR Surveys TABLE 14 Distribution of Amount of Time Spent in EMR Classes 357 Average Percentage of EMR Students Correlation of Percentage Full-Time Less Than More Than With Racial District Size 10 Hours 10 Hours Full-Time Disproportion Fewer than 1,000 students 26.1 44.7 29.2 - 0.08* 1,000 to 2,999 students 15.7 44.7 39.6 - 0.07* 3,000 to 9,999 students 12.2 41.0 46.8 - 0.10* 10,000 to 29,999 students 11.0 35.9 53.2 - 0.24* 30,000 or more students 11.3 40.1 48.5 - 0.21 NOTE: All percentages and correlations are the weighted projections to nationwide values; weights are the inverse of sampling probabilities. *Statistically significant at p < .01 (two-sided test). tings, for whatever combination of administrative factors and characteris- tics of the student population, less than full-time EMR placement for minorities may be deemed sufficient. The survey data do not permit comparisons on a student-by-student basis. Nevertheless, to the extent that these variables are related on a districtwise basis, it is not the case that the placement of minorities in EMR classes is associated with greater amounts of time spent in those programs. DISPROPORTION IN OTHER SPECIAL EDUCATION PROGRAMS The average proportions of minority and white children assigned to four special programs other than EMR are listed by state in Table 15. Of the 5,486 districts in the sample with one or more special programs and with both minority and white students enrolled, 4,917 (90 percent) have children classified as EMR, 93 percent have children classified as having specific learning disabilities (SLD), and 85 percent have children classified as speech-impaired (SI). In contrast, only 2,651 districts (about 48 percent) have students who are trainable mentally retarded (TMR), and 2,628 have students classified as seriously emotionally disturbed (SED). The latter programs are less common than the others, although districts may con- tract with outside agencies for these infrequently needed services. The figures in Table 15 are the average placement rates for just that subset of districts in a state that report having one or more students enrolled in the specific program category.

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Patterns in Placement as Revealed by the OCR Surveys TRAINABLE MENTALLY RETARDED 361 The nationwide rate for TMR enrollments, according to Table 3, is 0.23 percent of all students in this classification, and 0.19 percent of white students. The proportion of minority students in TMR classes exceeds the proportion for whites in 34 states, but there is not a great deal of consis- tency in either the magnitude or direction of the differences. The few con- sistencies that are supported by the log-odds indexes for TMR placement occur in midwestern states (e.g., Iowa, Nebraska, North Dakota, and Wisconsin), where there are much lower placement rates for minorities than for whites, and in the West, where minority-white differences tend to be small. SERIOUSLY EMOTIONALLY DISTURBED Nationwide rates for children who are seriously emotionally disturbed are also relatively small. The percentage of all children classified as SED is 0.32 percent; for white students it is 0.29 percent; and for blacks the only minority to diverge by much from either figure it is 0.50 percent. The minority placement rate exceeds that for whites in 28 states and in the Dis- trict of Columbia, almost always by small amounts, and the log-odds in- dex shows little or no consistency in direction. In particular, there is no consistent trend for minorities to be assigned disproportionately to SED programs in the South; rather the rates are similar or even higher for white students in this region. SPECIFIC LEARNING DISABILITIES Classes for those labeled SLD have the greatest proportion of students on a national basis of all special education programs. The nationwide rate is 2.31 percent for all students and the same for white students and varies from 1.27 percent of Asian or Pacific Island students to 3.49 percent of American Indian or Alaskan native students. The national rate for blacks is very close to that for whites. The average percentage of minorities in SLD programs exceeds that of whites in 40 states. The high proportion of minorities in Alaska typifies dis- tricts throughout the state regardless of size, while those in Iowa, Kansas, Nebraska, Nevada, Texas, and Utah reflect high SLD rates for minorities in the smallest districts. There is some tendency for districts in these states to have a low proportion of children in EMR classes and to make more ex- tensive use of the SLD classification. For example, Alaska, Nevada, and Utah have statewide EMR proportions for all students that are substan

362 FINN tially below the nationwide rate of 1.4 percent and SLD proportions that are well above the national rate of 2.3 percent. The average disproportion in SLD classes, as given by the log-odds in- dex, is not large, however; except for Alaska, the highest positive value is only +0.85. The large average rates for minorities in some states is in- flated by some unusually high percentages in a few districts, while the average log-odds index is not affected to as great an extent. The standard deviation of the index, especially for small districts, is relatively large, re- flecting high within-state diversity. Tests of significance were conducted on the average disproportion for each of three district size intervals in each of three regions of the country. The results are summarized in Table 16, which gives a general picture of the direction of difference between minorities and whites in SLD place- ments. In the northeastern and midwestern states, there is a significant trend for minorities to be placed in SLD classes to a lesser extent than whites, especially among small and medium-sized districts. In the South and among small districts in the West, significantly more minorities than whites are placed in SLD classes. In the border states and among all dis- tricts with more than 10,000 students enrolled, there is no evidence of average minority-white disproportion in either direction. Thus, differences in minority and white SLD placements are generally small and inconsistent. Disproportion varies from district to district and from region to region and depends on specific demographic characteris TABLE 16 Direction of Minority-White Difference in Test for Disproportions in Specific Learning Disabilities District Size 10,000 or 1 to 999 1,000 to 9,999 More Region Students Students Students Northeast Border South Midwest West Negative Negative Positive Positive Negative Negative Positive NOTE: Only results significant at p < .01 are shown. '9These were l-tests for Ho:,u = 0.

Patterns in Placement as Revealed by the OCR Surveys 363 tics as well. In general, it can only be concluded that SLD dispropor- tion when it reflects greater percentages of minorities than whites- is not as extreme as disproportion in EMR programs.20 SPEE CH- IMPAIRED The proportions of different racial groups in classes for SI students are ho- mogeneous, including Asian or Pacific Island students, who are repre- sented in other special programs to a lesser extent. The average assign- ment rates given in Table 15 are similar from state to state, except where the figures are inflated by a high proportion of minority students in small districts. The average log-odds indexes for 29 states are negative, indicat- ing some (weak) trend for whites to be assigned to special speech classes in greater proportion than minorities. SUMMARY The results for special education classifications other than EMR are more variable than consistent. The data clearly demonstrate that disproportion- ate assignment of students in such programs depends on the region of the country, the particular state, and district characteristics. It is not possi- ble to conclude that there is no disproportion in one special program category, while there is in another. Disproportion occurs everywhere to a lesser or greater degree, in one direction or the other, in each special edu- cation classification in different ways and depends on many situational characteristics. The extensive correlational analyses conducted for placements in EMR programs were not undertaken for other classifications and may reveal ad- ditional trends. It is clear from the state and regional patterns, however, that disproportionate EMR placements for minorities are greater and more consistent than differences in other programs. The data do not ad- dress the question of why this occurs-a question that can only be answered through a more process-oriented investigation. EMR DISPROPORTION IN SEPARATE RACIAL OR ETHNIC GROUPS Table 17 lists the average percentage of students in EMR programs and the average log-odds index for each minority group identified by the OCR 20Tests of the mean difference in specific learning disability and EMR disproportions revealed a significant difference in every region of the country.

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Patterns in Placement as Revealed by the OCR Surveys 367 questionnaire, in every state in which the specific group comprises more than 1 percent of the school population. The averages are calculated for every district in the state that has both nonminorities and any students of the minority group in attendance. The nonminority rate, listed for com- parison, is for all districts in the state (from Table 5~. BLACKS Blacks comprise more than 1 percent of the student enrollment in 41 states and in the District of Columbia. Since they are also the largest mi- nority group in 35 states and in the District of Columbia, the analysis of EMR placement rates for all minorities combined is most like that for blacks alone. However, some noteworthy differences arise when black placements are compared separately with those for whites. In three states, blacks have disproportion indexes that are lower than the all-minority re- sults in important ways. In Alaska and Rhode Island, both having sub- stantial positive all-minority indexes, the average disproportion for blacks alone is close to zero. In Wisconsin, with an all-minority average of 0.02, the log-odds index for blacks alone is-1.26; i.e., blacks are enrolled in EMR programs at a lower rate than are whites. In each of these states a higher disproportion for another large minority group raises the all- minority figure (Hispanics in Rhode Island and Wisconsin, and Alaskan natives in Alaska). In five states the disproportion for blacks alone is well above that for all minorities: Arkansas, Missouri, Nevada, Oklahoma, and Texas. These exceptions, while showing changes from the all-minority results of Table 5, maintain the same pattern of noticeably higher EMR place- ment rates for blacks on a nationwide basis, especially in the South and in particular states in the border and western regions. HISPANIC S Children of Hispanic origin- the second largest minority group- com- prise more than 1 percent of the public school enrollment in 31 states; more than 5 percent of the enrollment in 12 states; and more than 10 per- cent of the enrollment in Arizona, California, Colorado, New Mexico, New York, and Texas. On a nationwide basis the proportion of Hispanic students in EMR classes is slightly below that for nonminorities and well below that of blacks. However, the average percentage of Hispanic stu- dents in EMR classes exceeds that of nonminority students in 26 of the 31 individual states. The six states with the highest proportion of Hispanic students vary in

368 FINN the degree of EMR disproportion. In California and New York the EMR placement rates for Hispanics are close to those for nonminority whites in districts of all mixes. In Arizona, Colorado, and New Mexico, there are small or negative disproportions when the percent of Hispanic-origin stu- dents is low or moderate (up to about 50 percent), that is, the Hispanic EMR percentage is close to or below that of nonminority students. In each state, however, there are a number of districts in which Hispanics com- prise 70 percent or more of the student body; there, EMR disproportion is high. In Texas the disproportion is relatively large in all districts with 10 percent or more Hispanic students and small among districts with smaller Hispanic enrollments. To explore this varied pattern further, a subsample of districts was chosen in which Hispanic students comprised at least 5 percent of the dis- trict's enrollment and the number of Hispanic students was at least 50. This resulted in 854 districts being selected from the larger sample, of which 765 have EMR programs. The characteristics of these districts are summarized in Table 18. Hispanic enrollments are found in the majority of districts in most states in the Southwest (and Texas), and the average proportion of Hispanic students within districts in these same states is generally higher than elsewhere. Hispanic enrollments in the Northeast tend to be concentrated in a few of the larger districts (i.e., with higher average enrollment), while in the West they are dispersed among many smaller districts. The "average bilingual percentage" is the average percentage of the districts' Hispanic population enrolled in bilingual education classes. On a nationwide basis the average district provides bilingual classes for about 12 percent of its Hispanic enrollment; however, the larger districts in the Northeast have consistently greater portions of Hispanic students in bilingual education. The distribution of EMR disproportion is summarized in Table 19. The average disproportion for Hispanic students in these districts is positive for each of four size intervals and is especially high among small districts. However, it is striking that there are numerous large positive dispropor- tions (i.e., many more Hispanics than nonminorities) in each size interval and also numerous large negative disproportions (i.e., more nonminorities than Hispanics). IJnlike disproportion for all minorities combined or for blacks in particular, the small Hispanic-nonminority difference for the nation as a whole is an average of many sizable disproportions in both directions. It has been hypothesized that disproportion in Hispanic EMR place- ment is smaller in districts with substantial black enrollments, as His- panic students may come to be perceived as less prominent in terms of

Patterns in Placement as Revealed by the OCR Surveys 369 their minority status. To investigate this hypothesis and to examine the simple relationship of Hispanic enrollment to disproportion, districts were classified according to the percentage Hispanic enrollment (0-20, 20-40, 40-60, 60-80, 80-100), by percent black enrollment (0-25, 25-50, 50-75, . and 75-100), and by geographic region. The mean disproportion index was tested for main effects and interactions In a ~nree-way nxca-e~ec~s least-sauares analysis of variance for unequal cell frequencies. Separate ~ ~. ~· . . ~· ~_ ~_ 11 _ 17~ _ _ 1 _ ~ . analyses were conducted for districts with fewer than 1,000 students, districts with 1,000-9,999 students, and districts with 10,000 or more stu- dents; the designs were incomplete, since not all combinations of Hispanic and black enrollments were present in the data and thus some interactions could not be tested in each analysis. The mean disproportion scores representing districts in each minority ^. _ composition category are presented in Table 20. For the smallest districts (N = 124) there is a strong trend for districts with a higher proportion of Hicnnni~ Relent to have larger EMR disproportions; the differences among these means are stat~st~ca~y significant when p < .01. The same trend does not appear for medium-sized districts (N = 474) or for districts with 10,000 or more students (N = 1671. Further, Hispanic enrollment does not interact significantly with geographic region, substantiating the fact that the mean difference is general to small districts, regardless of locale. The mean EMR disproportion for Hispanic students decreases mono- tonically as the percentage of black enrollment increases among large districts but not among small or medium-sized districts. The difference for large districts is statistically significant when p < .01; furthermore, the difference does not interact significantly with Hispanic enrollment or with geographic region in any district size interval. Thus, there is a trend among large school districts and only among large districts for the relative proportion of Hispanic students in EMR classes to decline as the black enrollment increases; at the extreme, when the black enrollment ex- ceeds 75 percent, substantially fewer Hispanic than nonminority students are classified as EMR. The original hypothesis is substantiated for large school districts, although the perceptions and mechanisms through which the effect is created are not addressed by the survey data. Bilingual education classes are fairly common among schools with His- panic populations, although they tend to be more prevalent in larger dis- tricts. Over half of small districts (fewer than 1,000 students) have no Hispanic students in bilingual programs. At the other extreme, among districts enrolling 10,000 or more students, about 78 percent have some formal bilingual education, and 18 percent have one fourth or more of

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372 FINN TABLE 19 Distribution of EMR Disproportion for Hispanic Students Minimum Maximum Number of Standard District Size Districts Mean Deviation Log-Odds Q Log-Odds Q Fewer than 1,000 students 124 1.08 1.71 - 4.30 - .97 7.41 .99+ 1,000 to 2,999 students 242 0.66 0.99 - 2.13 - .79 7.67 .99+ 3,000 to 9,999 students 232 0.47 0.85 - 2.11 - .78 6.94 .99+ 10,000 or more students 167 0.35 0.63 - 3.35 - .93 2.17 .80 All districts 765 0.64 1.12 - 4.30 - .97 7.67 .99+ NOTE: Except for the number of districts, which is the actual number in the sample, all results are the weighted projections to nationwide values; weights are the inverse of sampling probabilities. their Hispanic student participating in bilingual instruction. At the same time the largest districts have the lowest EMR disproportion for Hispanic students (see Table 19~. To explore the relationship of bilingual education with EMR place- ments further, districts in each of four size intervals were classified by geographic region and by the extent of EMR disproportion for Hispanic students. Three levels of disproportion were formed. The high group is composed of those districts whose disproportion was greater than one standard deviation above the mean for all districts in the size interval; the low group is composed of those districts whose disproportion was less than one standard deviation below the mean; and the medium group contains those districts in between. Mean scores for the three groups were com- pared by fitting a two-way fixed-effects analysis-of-variance model to the data, with the percentage of students in bilingual education as the cri- terion measure. The results are summarized in Table 21. Among districts in two size intervals the percentage of Hispanic stu- dents in bilingual programs is significantly related to disproportion, and a similar trend is seen in the smallest districts as well. In each case, districts with the highest disproportion levels have the smallest proportion of stu- dents in bilingual programs. It is possible that Hispanic students with poor English proficiency are misclassified as EMR when bilingual pro- grams are not available. It is apparent from the nationwide results (Table 3) that Hispanic stu- dents are placed in SLD programs to a somewhat greater extent than are

Patterns in Placement as Revealed by the OCR Surveys TABLE 20 Mean EMR Disproportion for Hispanic Students, by District Racial/Ethnic Composition 373 Percentage Percentage of Black Enrollment of Hispanic Enrollment O to 25 25 to SO 50 to 75 75 to 100 All Fewer than 1,000 students 0 to 20 0.86 2.40 0.91 20 to 40 1.010.55 0.99 40 to 60 1.09 1.09 60 to 80 1.07 1.07 80tolO0 3.73 3.73 All 1.080.55 2.40 1,000 to 9,999 students 0 to 20 0.510.78 0.13 - 0.55 0.51 20 to 40 0.630.10 0.62 40 to 60 0.81- 0.43 0.76 60 to 80 0.59 0.59 80 to 100 0.57 0.57 All 0.580.62 0.13 - 0.55 10,000 or more students 0 to 20 0.43- 0.03 0.02 - 1.17 0.32 20 to 40 0.440.43 0.31 0.43 40 to 60 0.30 0.30 60 to 80 0.69 0.69 80 to 100 0.23 0.23 All 0.430.13 0.09 - 1.17 NOTE: Average log-odds index is the weighted projection to all districts in the particular size category. Empty cells indicate fewer than two districts in the sample with the particular ra- cial/ethnic composition. nonminorities. The state-by-state results (Table 18) show that while the Hispanic percentage in SLD is lower than the nonminority percentage in many states, the reverse is true in states with high concentrations of His- panics (Texas and the southwestern states exclusive of California3. The dynamics that create the SLD difference are not apparent from the OCR data. It does not appear that SLD placements substitute for EMR place- ments, since a few states have high average disproportions in both classifi- cations simultaneously (New Mexico, Texas, and Wyoming. In fact, the correlation of SLD with EMR disproportion among Hispanic students is Hit is important to recall that these data represent only the 1978-1979 school year. If pressure increases to reduce EMR enrollments, it is possible that programs for specific learn- ing disabilities will become an alternative placement.

374 FINN TABLE 21 Mean Percentage of Hispanic Students in Bilingual Education Low Size of District Disproportion Medium High Disproportion Disproportion Fewer than 1,000 students 9.76 (11) 9.30 (101) 1,000 to 2,999 students 16.89* (29) 9.97 (184) 3,000 to 9,999 students 13.19 (37) 11.84 (166) 10,000 or more students 23.87* (18) 12.90 (123) 6.51 (12) 7.52 (29) 14.33 (29) 14.43 (26) NOTE: All percentages are the weighted projections to nationwide values; weights are the inverse of sampling probabilities. Actual sample sizes are in parentheses. *Significant differences among these three means at p < .05. +.33 for all districts combined,22 and close to this value for districts in each of four size intervals. Examination of the SLD rates for Hispanics and nonminorities (not shown) indicate that the correlation reflects dif- ferent placement rates for Hispanic students, while that for nonminorities is not related to EMR disproportion. The processes by which Hispanic students are referred and assessed for placement in both special programs need further investigation. In summary, the apparently similar EMR placement rates for Hispanic and nonminority students disguise enormous variation in practices among school districts. There are a number of districts in which Hispanic stu- dents are assigned to EMR programs in large proportions. They are dis- tinguished from other districts by having small enrollments that are of- ten but not always largely Hispanic; furthermore, they have small black enrollments, small or nonexistent bilingual programs, and high per- centages of Hispanic students in SLD classes as well. Among large dis- tricts with the greatest pool of resources, low EMR disproportion and low SLD disproportion occur where many Hispanic students participate in bi- lingual programs. Further research on factors affecting the availability and utilization of alternate programs for Hispanic students is certainly warranted. It would be important to determine to what extent specific learning difficulties are 22Statistically significant at p < .05, using a two-sided test.

Patterns in Placement as Revealed by the OCR Surveys 375 related to language or whether SLD programs, like EMR, may be used in some districts as a substitute for bilingual instruction. The criteria used for both EMR and SLD placements should be elucidated as well as the definition of these possibly amorphous categories and the actual instruc- tional programming that is provided. AMERICAN INDIANS OR ALASKAN NATIVES American natives comprise over 1 percent of the public school enrollment in 15 states, largely in the West. Their placement in EMR classes exceeds the rate for whites in all but three of the states; in Alaska the average log- odds index exceeds the 80th percentile value of 1.6. The largest racial dif- ferences in Alaska are in districts with fewer than 1,000 students, but the disproportion in larger districts is substantial as well. Also, higher degrees of disproportion are concentrated in districts of all sizes with 70 percent or more Alaskan-native enrollment. Other than in Alaska, the average log-odds index of disproportion is not sizable, and in several instances is zero or negative. In general, the dif- ference in the placement of American Indians and Alaskan natives in EMR classes is not large or even consistently positive throughout the states. For this group in particular, however, the OCR survey may not tell the complete story, since numerous American Indians are enrolled in special schools and special programs that are not represented in the usual public school sample. ASIAN OR PACIFIC ISLANDERS Students who are of Asian or Pacific Island origins are assigned to EMR programs at rates considerably below those of whites in 10 of the 12 states in which they comprise more than 1 percent of the school enrollment. The average log-odds index is negative in 8 of the 12 states, with most values substantially so. Thus, in general, overrepresentation of Asian or Pacific Island students in EMR classes is not a problem; these groups might even be studied to determine why their placement rates are low. Two states, however, have positive log-odds indexes of disproportion in excess of 1.6. In both Colorado and Nevada, larger disproportions occur in small school districts with low minority enrollment. Unfortunately, the OCR survey does not distinguish among Asian populations; it is possible that the students in these states are, for example, recent immigrants from Vietnam rather than Japanese or Korean children whose families have been established in the United States for longer periods of time. Newly ar

376 FINN rived immigrant populations present a unique opportunity to monitor special education placement rates as they develop. SOCIOECONOMIC STANDING AND SUSPENSIONS FOR SPECIFIC MINORITY GROUPS General relationships between socioeconomic status and suspensions with disproportion in EMR placements for all minorities combined are given in preceding sections. Correlations for each minority separately are pre- sented in Table 22. Suspensions are not correlated with disproportionate EMR assignment for any individual racial or ethnic minority. The same correlations for all minorities combined (Table 13) are positive. While EMR disproportions are accentuated by students of one minority group, it may be students of a different minority classification who are suspended. Thus, only an associ- ation for all minorities together is observed. There is a significant negative relationship between racial disproportion and socioeconomic status for each minority group except Asian or Pacific Islanders. The relationship is strongest for American Indian and Alaskan native students and least strong for students of Hispanic origin. However, the correlations for these groups, and blacks as well, are consistently negative. That is, disproportions even within a minority group tend to be smaller in districts serving populations with higher income levels. This relationship is worthy of further exploration to address such questions as whether individuals with higher income tend to live in suburban districts with lower overall EMR rates and also lower disproportional and whether the same behavior and school performance are treated differently in mid- dle- and lower-income districts. The answers to these questions may differ for particular minority groups and the attitudes and values associated with lower income for that population. DISPROPORTION AND STATE EMR CRITERIA To determine the extent to which state guidelines are associated with disproportion, information was obtained for 37 states on whether adaptive behavior assessments are required for EMR classification and the max- imum IQ score a child may have and still be labeled EMR. The states were classified by region and by whether adaptive behavior assessments were 23The correlation of socioeconomic status with the proportion of all students in EMR pro- grams for the total sample is-.3l, suggesting support for this three-variable hypothesis.

Patterns in Placement as Revealed by the OCR Surveys TABLE 22 Correlations of Log-Odds Index With Suspensions and Socioeconomic Status for Separate Minority Groups 377 Number of Suspensions of Proportion Racial/Ethnic Group Districts All Students Full-Price Lunches American Indian/Alaskan Native 817 - 0.03 - 0. 17* Asian/Pacific Islander 936 - 0.05 0.07 Black 3995 0.04 - 0.15* Hispanic 2681 0.00 - 0.10* NOTE: Correlations are the weighted projections to nationwide values; weights are the in- verse of sampling probabilities. *Statistically significant at p < .01 (two-sided test). required, and mean differences were tested by fitting a two-way analysis- of-variance model to the data, with several different criterion measures. The results are summarized in Table 23. There is no statistically significant difference between states that re- quire and those that do not require adaptive behavior assessment for EMR placement on any of the measures listed, including average IQ cut- off score, average size of the states' EMR programs (in terms of percent TABLE 23 Comparison of States Requiring and Not Requiring Adaptive Behavior (AB) Assessment for EMR Placement AB Required (20 States) AB Not Required (17 States) Correlation Correlation Standard With Standard With Variable Mean Deviation IQ Cutoff Mean Deviation IQ Cutoff IQ cutoff score U 73.10 3.92 74.42 3.97 Percentage of all students in EMR 1.61 0.94 0.11 1.43 0.69 0.0 EMR disproportion for race/ethnicity (log-odds) 0.44 0.93 - 0.15 0.59 0.90 - 0.59h EMR disproportion by sex 0.45 0.15 - 0.37 0.40 0.15 - 0.31 Percentage of white enrollment 73.65 25.44 0.33 79.56 13.44 o.50b U From Patrick and Reschly (1982). b Significant at p < .05 (two-sided test).

378 FINN age of students labeled EMR), disproportion either by sex or by race or ethnicity, or in terms of the average proportion of minority or nonminority students enrolled. Further, there is no interaction of region with the adap- tive behavior factor, indicating no exception to this generalization in any part of the country; also, when further control was added by employing "percentage of minority enrollment" in the state as a covariate, no signifi- cant differences appeared. Thus, the imposition of a state requirement that childrens' adaptive behavior be assessed as a necessary condition for EMR placement does not have a statistically noticeable impact on any of the outcomes investigated. This is due at least in part to the relatively wide variations in practice including the use or nonuse of adaptive behavior ratings among districts within the states. It contrasts strongly with find- ings that adaptive behavior limits EMR programs within individual school districts (Fisher, 1977; Mercer, 1973~. Two of the measures have a significant correlation with the state IQ cut- off but only in those states not requiring adaptive behavior assessments. EMR disproportion by race or ethnicity is correlated negatively with statewide IQ cutoff scores. That is, on the average, the lower the IQ cutoff score i.e., the more stringent the EMR criteria the greater is the rela- tive assignment of minority students to EMR classes. This is predictable for states in which adaptive behavior assessments are not made regularly, since EMR placements become more nearly a function of children's IQ scores. When adaptive behavior is included as an additional required assessment, however, the correlation with IQ cutoff score is reduced to . . ~ nonslgnl~lcance. The statewide IQ cutoff score is also correlated with the percentage of white enrollment in states not requiring adaptive behavior assessments. While this reflects a trend for states with greater proportions of white students to set higher cutoff scores for EMR classification, the motivation for this practice is not revealed from the survey data. REFERENCES Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W. 1975 Discrete Multivariate Analysis: Theory and Practice. Cambridge, Mass.: MIT Press. Fisher, A. T. 1977 Adaptive Behavior in Non-Biased Assessments. Revised version of paper presented at the meeting of the American Psychological Association. ERIC Document Reproduction Service no. ED 150 514. Mercer, J. R. 1973 Labeling the Mentally Retarded: Clinical and Social System Perspectives oil Me''- tal Retardation. Berkeley, Calif.: University of California Press.

Patterns in Placement as Revealed by the OCR Surveys 379 Patrick, J. L., and Reschly, D. J. In Relationship of state education criteria and demographic variables to school system press prevalence of mental retardation. American Journal of Mental Deficiency 86. U.S. Department of Health, Education, and Welfare 1978a Fall 1976 Elementary and Secondary School Civil Rights Survey. Final File Documentation. Office for Civil Rights. June. Washington, D.C.: U.S. Depart- ment of Health, Education, and Welfare. 1978b 1978 Elementary and Secondary Civil Rights Survey. Sample Selection. Office for Civil Rights. February. Washington, D.C.: U.S. Department of Health, Educa- tion, and Welfare. Zoloth, B. S. 1976 Alternative measures of school segregation. Land Economics 52:278-298. APPENDIX EXAMPLES OF SMOOTHING DATA FOR SMALL DISTRICTS The 1978 OCR survey indicates 11 districts in Georgia with fewer than 100 minority students enrolled or fewer than 100 whites. When the numbers of students in these districts are summed, the proportions of students in EMR and in no special programs are as follows: Minority White EMR No special program 0.0065 0.0131 0.1054 0.8751 In the following table the EMR odds for minorities is 0.0065/0.1054 = 0.0617 and for whites 0.0131/0.8751 = 0.0150. One specific district has the following numbers of students: Minority White EMR 1 11 No special program 31 922 The EMR odds for minorities is 1/31 = 0.0323; one additional EMR stu- dent would bring the ratio to 0.0645, and no value between the two is pos- sible. The odds for whites is 11/922 = 0.0119, and the difference is 0.0323 = 0.0119 = 0.0204. The smoothed frequencies for this district are as follows:

380 FINN Minority White EMR No special program 1.0393 1 1.0119 31.5270 921.4218 From these values the EMR odds for minorities is 0.0330 (a small degree closer to the statewide value of 0.0617) and for whites 0.0120. The dif- ference of 0.0330 - 0.0120 is 0.0210, which is close to the original value. Another of the 16 districts with small enrollment has the following num- ber of students: Minority White EMR 21 0 No special program 194 65 The EMR odds for minorities is 21/194 = 0.1082, for whites 0/65 = 0, and the difference is 0.1082. The zero value raises such questions as does zero of 65 students, for example, mean as much as zero of 100 or of 500 students? Would the number remain zero if the white enrollment were in- creased, as may happen from one school year to another, or is this value a stable zero? A partial answer may be provided by examining the larger statewide data set, in which the odds for whites is small but is nonzero (0.0150~. Smoothing the district's frequencies yields the following results: Minority White EMR No special program 20.9588 0.0079 193.6464 65.3870 The odds for minorities is 0.1082, for whites 0.0001, and the difference is 0.1081, which is close to the original value.,~While the original zero value did not allow calculation of the log-odds index, the adjusted values yield In (0.1082)-In (0.0001) = 6.80.

Patterns in Placement as Revealed by the OCR Surveys 381 The smoothing procedure used in this analysis involves obtaining "pseudo Bayes estimates" of actual population frequencies in the manner described by Bishop et al. (1975: Section 12.1.1~. This method has distinct advantages over the widely used practice of adding 0.5 to each cell count, especially when the total number of observations in one or both columns is . ~ small.

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