Antecedentes del compostaje en Colombia

The results from the joint measures approach can be interpreted in relatively simple language. Using the example of the 77 districts that are overrepresented at 3.00 standard errors threshold in the E-formula and at 4.00 or more in the Alternate Risk Ratio: for those racial/ethnic groups that are overrepresented in a specific disability category (or categories), not only is there a very high

probability31 _{that the differences between the proportions of individual racial/ethnic groups in their}

specific disability category (or categories) of overrepresentation and their corresponding general education proportions in the districts are true or real differences, the Risk for each of the same racial/ethnic groups in the same disability category (or categories) in these districts is more than 4.00 times the Risk of all other racial/ethnic groups combined in the state in the same disability category (or categories). As one can see, in the joint measures approach, the determination of disproportionality satisfies two sets of criteria, which makes the approach far more rigorous than either measure by itself.

5.1. Four Case Studies under the

Joint Measures Approach

What are the characteristics of a district when it is disproportionate in one measure but not in another? Under what circumstances does a district become disproportionate in both measures? To address these questions and to get an insight into the demographic characteristics of districts, we have identified four districts showing four different outcomes under the joint measures approach. Again, to keep the analysis simple, we will focus on overrepresentation in the six major disability categories, using 3.00 standard errors threshold in the E-formula and 4.00 in the Alternate Risk Ratio. The characteristics of the four districts are:

 District A, overrepresented in the E-formula, but not in the Alternate Risk Ratio  District B, overrepresented in the Alternate Risk Ratio, but not in the E-formula

 District C, overrepresented in the E-formula and in the Alternate Risk Ratio, but not in the same cell; and

 District D, overrepresented in both the E-formula and the Alternate Risk Ratioin the same cell, and therefore, is overrepresented under the joint measures approach.

All necessary data used in the calculations for the E-formula and the Alternate Risk Ratio for these districts are shown in Table 19. These data include enrollments in general education and in the six major disability categories in special education for the state and the four districts listed above, broken down by seven racial/ethnic groups. The results of the calculations are highlighted in the table and are discussed below.

Table 19. Enrollments and Results of the E-formula and the Alternate Risk Ratio Calculations in Four Districts

Native Asian Pacific Black Hispanic White Multiple Total

State Enrollments:

Total GE Enrollment (N) 44,927 683,318 37,014 424,518 3,119,111 1,673,567 96,792 6,079,247

Autism (N) 270 7,270 204 4,066 17,890 21,140 1,113 51,953

Emotional Disturbance (N) 315 712 102 5,102 7,370 11,438 500 25,539 Intellectual Disability (N) 271 3,128 213 4,319 21,616 9,166 445 39,158 Other Health Impairment (N) 431 1,843 215 6,513 17,606 23,342 749 50,699 Spec. Learning Disability (N) 2,301 8,782 1,238 34,908 166,458 67,520 2,668 283,875 Speech and Language (N) 990 12,049 743 8,808 71,283 44,360 2,371 140,604 District A:

Total GE Enrollment (N) 265 905 67 504 2,494 8,460 36 12,731

Autism (N) 0 4 0 4 11 91 3 113

Emotional Disturbance (N) 0 2 0 3 8 64 4 81

Intellectual Disability (N) 2 10 0 5 21 74 1 113

Other Health Impairment (N) 0 3 2 5 19 76 1 106

Spec. Learning Disability (N) 13 26 2 31 141 351 14 578

Speech and Language (N) 2 16 2 12 80 184 10 306

District B:

Total GE Enrollment (N) 45 217 26 123 974 2,391 230 4,006

Autism (N) 0 3 0 0 9 26 1 39

Emotional Disturbance (N) 1 0 0 2 6 42 4 55

Intellectual Disability (N) 0 0 0 0 6 8 3 17

Other Health Impairment (N) 0 0 0 1 6 29 1 37

Spec. Learning Disability (N) 0 0 3 9 41 122 4 179

Speech and Language (N) 1 6 1 4 34 49 4 99

District C:

Total GE Enrollment (N) 64 563 70 786 1,018 2,640 43 5,184

Autism (N) 0 1 0 4 6 23 2 36

Emotional Disturbance (N) 1 0 0 12 7 37 1 58

Intellectual Disability (N) 0 1 0 4 4 31 1 41

Other Health Impairment (N) 2 1 0 14 4 43 2 66

Spec. Learning Disability (N) 4 15 1 77 76 147 5 325

Speech and Language (N) 0 9 0 20 16 54 5 104

District D:

Total GE Enrollment (N) 29 3,932 66 90 3,993 1,420 189 9,719

Autism (N) 0 104 4 3 59 40 3 213

Emotional Disturbance (N) 0 2 0 2 7 12 1 24

Intellectual Disability (N) 0 22 0 1 17 5 0 45

Other Health Impairment (N) 0 11 1 11 42 46 3 114

Spec. Learning Disability (N) 3 29 1 3 152 29 5 222

Speech and Language (N) 0 107 1 4 125 49 10 296

GE = General Education

Bold = Overrepresentation in the E-formula at 3.00 standard errors threshold

Bold and Italics = Overrepresentation in the Alternate Risk Ratio at 4.00 threshold

District A

This is a district with 12,731 students in general education and 1,388 students or about 10.90 percent in special education (data not shown in table), with 1,297 students in the six major disability categories. In the E-formula, the district shows overrepresentation of White students in Autism disability category. It also shows overrepresentation of students with Multiple racial/ethnic backgrounds in Autism, Emotional Disturbance, Specific Learning Disability, and Speech and Language Impairment in the E-formula. In this district, none of the racial/ethnic groups are

overrepresented in the Alternate Risk Ratio. Note that all 42 cells (six disability categories multiplied

by seven racial/ethnic groups) for this district are used in the E-formula calculations, but only 11 cells (with cell size 20 or more) are used in the Alternate Risk Ratio calculations.

Let us take a closer look at the students with Multiple racial/ethnic backgrounds in District A. They constitute 0.28 percent in general education but 2.65 percent in Autism, which is 9.46 times higher than their general education percentage (data not shown in table). Even though the number of students in Autism is very small (only three), still at 3.00 standard errors threshold in the E-formula, the group shows overrepresentation, which however, disappears if the threshold is raised to 5.00 standard errors (data not shown in table). This group is not subject to the calculations in the

Alternate Risk Ratio due to the small cell size. (For the sake of academic interest, the Alternate Risk Ratio for the Multiple racial/ethnic group in Autism would be 9.81, if the group was not excluded from calculations. Note that the discrepancies in both measures for this group are extremely high.) White students in Autism disability category in the same district portray a slightly different picture. Because the cell size in this case is 91, they are subject to both the E-formula and the Alternate Risk Ratio calculations. White students constitute 66.45 percent in general education but 80.53 percent in Autism, resulting in overrepresentation at 3.00 standard errors threshold in the E-formula. However, they no longer remain overrepresented at 4.00 standard errors or beyond (data not shown in table). The Alternate Risk Ratio for White students in Autism is 1.54 (data not shown in table), which is far less than the 4.00 threshold, and therefore, they are not overrepresented in this measure.

Results from the joint measures approach should be interpreted in simple language so it is easily understood by the users of this approach. The results for White students in Autism can be stated as: there is a very high probability, perhaps more than 99 percent, that the difference between the proportion of White students in Autism and the proportion of White students in general education in the district is true difference (or, there is perhaps less than one percent probability that the

difference between the two proportions is due to chance) but the risk of White students in Autism in the district is only 1.54 times (far less than 4.00 times) as the statewide risk of students in all other racial/ethnic groups combined in Autism.

Based on the results of the two measures, as applicable for individual cells, District A is not overrepresented under the joint measures approach. If we used only one measure, the E-formula, the district would be overrepresented for more than one reason. But we must also take note that enrollments of the Multiple racial/ethnic group in Autism and Emotional Disturbance disability categories are quite small. A single family with two or three disabled children could easily create such a situation, raising an issue if a district should be identified as overrepresented because of such a small enrollment size for a group. Under the joint measures approach, situations such as this are avoided by combining the E-formula results with those of the Alternate Risk Ratio, which

excludes such cells from calculations. The only large cell with 91 White students in Autism that shows overrepresentation in the E-formula does not show overrepresentation in the Alternate Risk

Ratio at our selected thresholds. Since none of the cells in the district are overrepresented in both measures, the district is not overrepresented under the joint measures approach.

District B

This district has 4,006 students in general education and 452 students or about 11.28 percent in special education (data not shown in table), with 426 students in the six major disability categories. The district is overrepresented in only one cell in the Alternate Risk Ratio for White students in the Emotional Disturbance (ED) disability category. None of the cells are overrepresented in the E- formula measure at our selected threshold (3.00 standard errors), and therefore, the district is not

considered overrepresented under the joint measures approach.

The results for this district can be stated as: although the risk of White students in the ED disability category in the district is 4.00 or more times as the statewide risk of students in all other

racial/ethnic groups combined in the ED disability category, but the probability is not sufficiently high that the difference between the proportion of White students in the ED disability category and the proportion of White students in general education in the district is a true difference. Therefore, the district is considered not overrepresented under the joint measures approach.

District C

This is a district with 5,184 students in general education and 654 students or about 12.62 percent in special education (data not shown in table), with 630 students in the six major disability

categories. In this district, several groups of students are overrepresented in the E-formula

calculations: (1) Black or African-American students in Specific Learning Disability, (2) White students in Intellectual Disability, and (3) students of Multiple racial/ethnic group in Autism and in Speech and Language Impairment. In the Alternate Risk Ratio calculations, only White students are overrepresented in Emotional Disturbance. Since none of the same racial/ethnic groups of students are overrepresented in the same disability category in both measures, the district is considered not overrepresented in the joint measures approach.

District D

This district has 9,719 students in general education and 961 students or about 9.89 percent in special education (data not shown in table), with 914 students in the six major disability categories. In this district, five groups of students are overrepresented in the E-formula: (1) Black or African- American students in Emotional Disturbance; (2) Black or African-American students in Other Health Impairment, (3) Hispanic students in Specific Learning Disability, (4) White students in Emotional Disturbance, and (5) White students in Other Health Impairment. In the Alternate Risk Ratio calculations, three groups of students are overrepresented: (1) Asian students in Autism, (2) White students in Autism, and (3) White students in Other Health Impairment. Only White students in the Other Health Impairment (OHI) disability category are overrepresented in both measures. Let us take a closer look at White students in the OHI disability category. First of all, the cell size for this group is 46, a reasonably large number that is considerably higher than the minimum 20, and therefore, is subject to the calculations in both measures. Second, in the E-formula measure, the discrepancy between special education and general education percentages for this group in the OHI

disability category is so large that the group remains overrepresented until the threshold is raised to eight standard errors (data not shown in table)! Third, in the Alternate Risk Ratio measure, the discrepancy between this group (White students) and the comparison group (all non-White students combined) is also so large that the group remains overrepresented even if the threshold is raised from 4.00 to 5.00 (data not shown in table).

In other words, not only is there a very high probability that the difference between the proportion of White students in the Other Health Impairment disability category and the proportion of White students in general education in the district is a true difference, but the risk of White students to be in the Other Health Impairment disability category in the district is also much higher than the

statewide risk of students in all other racial/ethnic groups combined to be in the same disability category.There would be little debate that this group is truly overrepresented in the district.

5.2. Recommendation

In selecting a measure or measures for examining disproportionality, one needs to keep in mind that each measure answers a different question on disproportionality and each has its strengths and weaknesses. The user must decide beforehand if a particular question, and therefore, a particular measure, addresses the needs of the districts and the state and incorporates the intent of the law. If a single question (and therefore, a single measure) does not capture all or most of the elements of disproportionality that one would like to see addressed, then using more than one measure to examine disproportionality should not be ruled out. The analysis in this paper provides helpful information to policy makers in the state in selecting a measure or measures.

Based on the analysis of various measures in this paper, we believe that a joint measures approach provides much better information on racial/ethnic disproportionality in special education than any single measure. Therefore, we strongly recommend a joint measures approach to examine

racial/ethnic disproportionality in special education. We also recommend that the E-formula and the

Alternate Risk Ratio should be the two measures of choice for reasons discussed in the preceding pages. The strengths of the E-formula (Differentiated Range of Tolerance for Disproportionality for Different Sized Districts, for example) compensate for the lack of them in the Alternate Risk Ratio, and the strengths of the Alternate Risk Ratio (Comparability of Results across Districts, for example) compensate for the lack of them in the E-formula.

The determination of disproportionality should be based on when a racial/ethnic group in a program category (a cell) is disproportionate in both measures – not just in only one of the measures. The thresholds in the two measures can be set based on empirical analysis of data, as shown in Table 18, and based on consensus among the stakeholders in the state (one such example is 3.00 standard errors in the E-formula and 4.00 in the Alternate Risk Ratio).

If for some reason one were to select only one measure for disproportionality calculations, then based on the data and analysis presented in this paper, the E-formula offers the most promising approach in determining racial/ethnic disproportionality in special education. It has the necessary strengths and fewest weaknesses among all measures of disproportionality that we have examined. The Alternate Risk Ratio would be a good second choice.

If a joint measures approach is used to examine disproportionality, it is also possible to weight the results of each measure in determining overrepresentation or underrepresentation for a district. The weighting factor will depend upon the relative importance of the questions associated with the

measures selected. In the example using the Alternate Risk Ratio and the E-formula, if comparability of districts is more important to the user than the differences in the racial/ethnic

composition between general education and special education, then the results of the Alternate Risk Ratio should be weighted more than the results of the E-formula. If, on the other hand, the

discrepancy between general education and special education among the various racial/ethnic groups is the dominant issue, then the E-formula would carry more weight than the Alternate Risk Ratio.

Prior to selecting measures (or a measure) for examining disproportionality and setting thresholds, one would need to review the results from the measures (or measure) in light of their implications for any monitoring and follow-up activities. If the districts showing overrepresentation or

underrepresentation are subject to on-site review by the state, then factors such as available resources, personnel, and the time necessary for monitoring should be taken into consideration in the selection process. However, these external factors should not drive the process of selecting measures or setting thresholds in examining disproportionality; these factors are secondary to the process that will identify districts that are “truly” disproportionate, based on the definitions of the individual measures. One must exercise caution so that the notion of a pre-determined number of districts to be selected is not viewed as a “quota”. Also, any pre-determined number of districts to be selected has the risk of excluding districts that may be truly disproportionate.

6. Significant Disproportionality

While the underlying purpose of examining disproportionality is to correct any racial/ethnic imbalance in special education in relation to general education and/or any discrepancy among various racial/ethnic groups, significant disproportionality takes this effort a step further.32 _{When a}

district is identified to have significant disproportionality (overrepresentation) for a racial/ethnic group in a program or disability category, it is required to spend 15 percent of its federal funds under IDEA during each year it remains significantly disproportionate (overrepresented) to redress the disproportionality issues. It is challenging enough for a district to address any disproportionality issues in general, but it is probably far less desirable to be in a situation of significant

disproportionality because it leads to difficult fiscal consequences plus additional monitoring and oversight from the state. Therefore, the definition of significant disproportionality could become a contentious item for districts that would be adversely affected by it.

There are no specific directions from OSEP on how to define significant disproportionality - only general guidelines. It is up to the states to define significant disproportionality in relation to disproportionality in general. However, any definition of significant disproportionality must be approved by OSEP before a state can use it with districts.

There are at least three aspects of racial/ethnic disproportionality based on which one can define

significant disproportionality. They are: frequency, severity, and persistency. Before we go further into the details, it would be helpful to set the context of disproportionality in which the definitions of these terms and the ways to define significant disproportionality would be meaningful.

Let us assume that a state adopts the joint measures approach to determine racial/ethnic disproportionality in special education and the measures of choice are the E-formula and the

Alternate Risk Ratio. Also assume that the thresholds for disproportionality (overrepresentation) are set at 3.0 standard errors for the E-formula and at 4.0 for the Alternate Risk Ratio. A district would be considered disproportionate for a racial/ethnic group in a program or disability category (cell) if both the E-formula and the Alternate Risk Ratio results for this cell (the same cell) cross these two thresholds. For the sake of clarity, we will call this situation simple disproportionality and distinguish it from significant disproportionality which we will define in this chapter. Within this framework and based on the concepts of frequency, severity, and persistency, as stated above, significant disproportionality can be defined in a number of ways, as described below.

6.1. Frequency

Frequency is the number of cells that are disproportionate (or have simple disproportionality) among all possible cells in a program category in a district in a given year. In disability categories, for

example, a district may be disproportionate in, say, three different cells (White students in Emotional Disturbance, African-American students in Intellectual Disability, and Hispanic students in Specific Learning Disability), out of 42 possible cells (six disability categories times seven racial/ethnic groups). It may also be expressed as the percentage of the cells that are disproportionate out of the total number of possible cells in a district. In the above district, 7.1 percent ((3/42)*100) of the cells