Evaluating School Priorities for Equal Opportunity in Admission to Schools

Figures & data

Table 1. SDHC middle magnet program enrolled population and applications by race/ethnicity for the 2015–2016 academic year.

ID	School	Program	FDOE	Total enrolled	Enrolled population				Total all ranked	All ranked applications
			Theme	population	BLA	WHI	HIS	XOT	applications	BLA	WHI	HIS	XOT
S1	Stewart	Math/Science/Technology	MAT	857	34%	24%	35%	7%	1,011	27%	33%	27%	13%
S2	Dowdell	Environmental Studies	OTH	613	28%	19%	49%	4%	283	27%	36%	29%	8%
S3	Sligh	Health Professions	OTH	648	76%	4%	16%	4%	339	38%	32%	18%	12%
S4	Franklin (Boys) Magnet	Boys Preparatory Academy	OTH	419	42%	26%	24%	8%	480	44%	25%	23%	8%
S5	Ferrell (Girls) Magnet	Girls Preparatory Academy	OTH	405	42%	24%	26%	8%	581	43%	28%	19%	10%
S6	Orange Grove Magnet	Visual/Performing/Arts	ART	562	31%	33%	30%	6%	1,008	46%	26%	20%	8%
S7	Progress Village	Visual/Performing/Comm. Arts	ART	865	29%	36%	28%	7%	861	32%	31%	28%	9%
S8	Roland Park K-8 Magnet	International Baccalaureate	IB	763	28%	29%	27%	16%	563	22%	33%	24%	21%
S9	Rampello Downtown K-8	Cultural Arts & Humanities	OTH	766	32%	34%	29%	5%	210	37%	30%	25%	8%
S10	Walker Magnet	International Baccalaureate	IB	900	12%	42%	31%	15%	764	13%	23%	42%	22%
S11	Williams	International Baccalaureate	IB	798	29%	23%	19%	29%	779	33%	18%	22%	27%
S12	Young Magnet	Creative Science Center	MAT	561	52%	13%	30%	5%	919	48%	25%	18%	9%
Total magnet middle schools				8,157	2,816	2,171	2,355	815	7,798	2,692	1,911	2,141	1,054
					34%	27%	29%	10%		34%	25%	27%	14%
Total SDHC enrolled population				207,469	44,402	74,336	71,971	16,760
					21%	36%	35%	8%

Note: FDOE Theme Specialty: MAT (Sciences/Math), ART (Performing Arts), IB (International Baccalaureate), OTH (Other Theme Specialty);

Race/Ethnicity: BLA (Black), WHI (White), HIS (Hispanic), XOT (Other Race/Ethnicity).

Table 2. SDHC magnet middle school program characteristics and applications to Grade 6 for the 2015–2016 academic year.

School Program				School enrolled population		Applications to Grade 6
ID	School	FDOE School grade	Title-I school	Total school students	Free/ Reduced Lunch	All ranked applications Grade 6		Ranked first applications Grade 6		Seats Available Grade 6
S1	Stewart	A	YES	857	70%	875	13%	369	11%	351	13%
S2	Dowdell	C	YES	613	92%	240	4%	61	2%	100	4%
S3	Sligh	F	YES	648	95%	291	4%	74	2%	81	3%
S4	Franklin (Boys) Magnet	A	YES	419	68%	405	6%	203	6%	239	9%
S5	Ferrell (Girls) Magnet	A	YES	405	74%	509	8%	247	8%	293	11%
S6	Orange Grove Magnet	A	NO	562	48%	832	12%	365	11%	211	8%
S7	Progress Village	A	NO	865	55%	742	11%	414	13%	348	13%
S8	Roland Park K-8 Magnet	A	NO	763	42%	478	7%	195	6%	44	2%
S9	Rampello Downtown K-8	A	NO	766	45%	178	3%	61	2%	55	2%
S10	Walker Magnet	A	NO	900	38%	690	10%	550	17%	424	16%
S11	Williams	A	NO	798	38%	687	10%	452	14%	359	13%
S12	Young Magnet	C	YES	561	88%	785	12%	240	7%	211	8%
	Total			8,157	60%	6,712	100%	3,231	100%	2,716	100%

Note: FRL = Free/reduced price meals.

FDOE School Grading Scale: A = 62% of points or greater, B = 54% to 61% of points, C = 41% to 53% of points, D = 32% to 40% of points, F = 31% of points or less;

Table 3. Descriptive statistics for SDHC magnet middle applications to grade 6 for the 2015–2016 academic year.

ID	School	Ranked First Applicants	Race/Ethnicity				ESE	FEM	SIB	EMP	LUN	ENG	URB	TIT
			BLA	HIS	XOT	WHI
S1	Stewart	369	20%	40%	10%	30%	41%	20%	23%	5%	67%	64%	97%	67%
S2	Dowdell	61	25%	39%	3%	33%	28%	51%	28%	0%	80%	72%	97%	84%
S3	Sligh	74	31%	42%	11%	16%	32%	69%	15%	0%	78%	54%	100%	74%
S4	Franklin (Boys) Magnet	203	34%	33%	5%	28%	36%	0%	21%	8%	68%	80%	98%	67%
S5	Ferrell (Girls) Magnet	247	40%	31%	6%	23%	27%	100%	23%	4%	73%	79%	100%	77%
S6	Orange Grove Magnet	365	42%	27%	7%	24%	35%	73%	30%	5%	72%	81%	100%	72%
S7	Progress Village	414	26%	30%	10%	34%	28%	71%	27%	8%	59%	81%	98%	59%
S8	Roland Park K-8 Magnet	195	14%	42%	12%	32%	40%	47%	41%	7%	53%	64%	99%	56%
S9	Rampello Downtown K-8	61	28%	36%	3%	33%	33%	51%	49%	8%	59%	80%	98%	54%
S10	Walker Magnet	550	8%	22%	22%	48%	42%	48%	30%	8%	31%	77%	98%	18%
S11	Williams	452	25%	14%	37%	24%	55%	49%	32%	6%	37%	65%	98%	41%
S12	Young Magnet	240	55%	20%	7%	18%	35%	35%	31%	4%	83%	78%	98%	80%
	Total	3,231	27%	28%	14%	30%	38%	51%	29%	6%	58%	74%	98%	56%

Note: Applicant’s race/ethnicity: BLA: Black, HIS: Hispanic, XOT: Other race, WHI: White; ESE: Applicant is eligible for ESE (special education services); FEM: Applicant is female; SIB: Applicant has siblings; ENG: the English language is spoken at home; EMP: Applicant’s parent is an employee of SDHC; LUN: Applicant is eligible to free/reduced price (FRL) meals; URB: Applicant’s home located in an urban area; TIT: Applicant is assigned to a disadvantaged (Title-I) neighborhood school;

Figure 1. Sketch of the simulation strategy.

Table 4. Steps for calculations of the inequality measures.

Step 1: estimate a logistic regression model on whether a child $i$ has access to high-quality education, as a function of his or her personal $m$ circumstances, using the maximum likelihood method.

$Ln\left(\frac{P(I=1|x_1,\dots ,x_m)}{1-P(I=1|x_1,\dots ,x_m)}\right)=\sum _{k=1}^m{\beta }_k\left(X_k\right)$

From the estimation of this logistic regression, the coefficient estimates ${\hat{\beta }}_k$ are obtained.

Step 2: obtain for each child, the predicted probability of access to high-quality education ${\hat{p}}_i,$ based on the predicted relationship ${\hat{\beta }}_k$ and the vector of their circumstances $X_{ki}$.

${\hat{p}}_i=\frac{exp\left({\hat{\beta }}_0+{\sum }_{k=1}^m{X}_{ki}{\hat{\beta }}_k\right)}{1+exp\left({\hat{\beta }}_0+{\sum }_{k=1}^m{X}_{ki}{\hat{\beta }}_k\right)}$

Step 3: obtain the overall coverage rate for the service C. The coverage rate shows what fraction of the population has access to high-quality education. $C=\sum _{i=1}^n{w}_i{\hat{p}}_i,$

where $n$ is the total population, and $w_i=1/n$ or some sampling weights.

Step 4: the Dissimilarity Index (D-Index) $\hat{D},$ is calculated,

$\hat{D}=\frac{1}{2C}\sum _{i=1}^n{w}_i\left|{\hat{p}}_i-C\right|$

Step 5: obtain the penalty $P$ for inequality. $P$ refers to access to the service that was allocated unfairly. $P=C\times \hat{D}$

Step 6: calculate the HOI, discounting the penalty for improperly allocated opportunities from the overall coverage rate ($C$). $HOI=C-P$

Table 5. The link between school choice policy, dimensions, objectives, and decision variables chosen for the simulations.

Dimension	Objective	Id	Decision variable	Variable type
Geography	Minimize school transportation costs	GEO	Distance from applicant’s home to school	Continuous
Family and Community	Facilitate school logistics for parents	SIB	Sibling attending a school	Binary
		EMP	The parent is an employee from the school district	Binary
Socioeconomic Diversity	Foster social cohesion and social mobility	FRL	The applicant is eligible for free/reduced price (FRL) meals	Binary
		BLA	The applicant is of Black race/ethnicity	Binary
Academic Quality	Maximize expected academic excellence	TIT	The applicant is assigned (by default) to a disadvantaged (Title-I) neighborhood school	Binary

Table 6. Criterion weighting used in the scenarios.

	GEOGRAPHY	ACADEMICS	FAMILY		SOCIOECONOMICS
Scenario #	GEO	TIT	SIB	EMP	BLA	FRL	FOCUS
1	0.750	0.083	0.042	0.042	0.042	0.042	Geography
2	0.083	0.750	0.042	0.042	0.042	0.042	Academics
3	0.083	0.083	0.375	0.375	0.042	0.042	Family
4	0.083	0.083	0.042	0.042	0.375	0.375	Socioeconomics
5	0.250	0.250	0.125	0.125	0.125	0.125	Equal weight
6	0.000	0.000	0.000	0.000	0.500	0.500	Socioeconomics
7	0.410	0.160	0.050	0.260	0.020	0.100	Geography
8	0.290	0.240	0.040	0.100	0.140	0.190	Geography

Notes: GEO: Distance from applicant’s home to school; TIT: Applicant is assigned to a disadvantaged (Title-I) neighborhood school; SIB: Sibling already attending a school; EMP: Parent is an employee of the school district; BLA: Applicant is of Black race/ethnicity;

FRL: Applicant is eligible for free/reduced price meals

Table 7. Settings used for the simulations performed to answer the research questions.

Simulation	Focus	Algorithm	Capacity
1. Variations in school priorities	Varying school priorities	DFA	100%
2. Variations in assignment algorithms	Geography	DFA, LOT, SLA	100%
3. Variations in capacity	Socioeconomics/equal	DFA	25% – 175%
4. Measuring family welfare	Socioeconomics	DFA	25% – 175%

Table 8. HOI for the opportunity in access to schools, with variations in school priority profiles.

		Access to a School of Any-Quality				Access to a School of High-Quality
Scenario	Focus	HOI	D-index	Penalty	Coverage	HOI	D-index	Penalty	Coverage
1	Geography	62.8	14.0	10.3	73.1	56.0	11.8	7.5	63.5
2	Academics	64.8	14.6	11.1	75.8	58.0	11.4	7.4	65.5
3	Family	63.9	15.3	11.6	75.5	57.5	11.9	7.8	65.3
4	Socioeconomics	64.7	14.8	11.3	75.9	58.3	11.0	7.2	65.6
5	Equal Weight	64.6	14.7	11.1	75.8	57.9	11.4	7.4	65.4
6	Socioeconomics	64.2	14.4	10.8	75.0	58.1	10.4	6.7	64.8
7	Geography	64.4	14.4	10.9	75.2	57.5	11.5	7.5	65.0
8	Geography	64.2	14.8	11.2	75.3	57.5	11.5	7.5	65.0

Notes: Algorithms: DFA=Deferred Acceptance Algorithm; LOT=Weighted Lottery Approach; SLA= Simple Lottery Approach. These simulations were run using only DFA, multiple focus in the priorities, and 100% capacity. HOI= Human Opportunity Index; D-Index: Dissimilarity Index; IOP= Inequality of Opportunity

Table 9. HOI for the opportunity in access to schools, with variations in assignment algorithms.

		Access to a School of Any-Quality				Access to a School of High-Quality
Scenario	Algorithm	HOI	D-index	Penalty	Coverage	HOI	D-index	Penalty	Coverage
1	DFA	62.8	14.0	10.3	73.1	56.0	11.8	7.5	63.5
7	DFA	64.4	14.4	10.9	75.2	57.5	11.5	7.5	65.0
8	DFA	64.2	14.8	11.2	75.3	57.5	11.5	7.5	65.0
1	LOT	76.8	1.9	1.5	78.3	67.3	1.8	1.2	68.5
7	LOT	75.7	3.5	2.7	78.4	67.1	2.2	1.5	68.6
8	LOT	74.5	5.2	4.1	78.6	66.3	3.3	2.2	68.6
9	SLA	76.6	2.1	1.7	78.2	65.5	4.0	2.7	68.3
10	SLA	77.6	1.7	1.3	78.9	65.5	4.2	2.9	68.4
11	SLA	76.5	2.2	1.7	78.1	64.8	4.4	3.0	67.8

Notes: These simulations were run using all the available algorithms, and 100% capacity.

Scenarios 1, 7 and 8 have a focus on geography, applicants who live close to school are prioritized for admission.

Algorithms: DFA=Deferred Acceptance Algorithm; LOT=Weighted Lottery Approach; SLA= Simple Lottery Approach.

HOI= Human Opportunity Index; D-Index: Dissimilarity Index; IOP= Inequality of Opportunity

Table 10. HOI for the opportunity in access to schools, with variations in capacity constraints.

		Access to a School of Any-Quality				Access to a School of High-Quality
Scenario	Capacity	HOI	D-index	Penalty	Coverage	HOI	D-index	Penalty	Coverage
5	25%	5.3	68.3	11.5	16.8	5.4	62.2	8.9	14.3
5	50%	19.0	47.1	16.9	35.9	17.7	42.1	12.9	30.6
5	75%	38.4	31.5	17.6	56.0	35.1	27.3	13.2	48.3
5	100%	64.6	14.7	11.1	75.8	57.9	11.4	7.4	65.4
5	125%	86.5	4.1	3.7	90.2	77.2	1.8	1.4	78.6
5	150%	92.4	2.1	2.0	94.3	81.2	1.8	1.5	82.7
5	175%	95.2	1.2	1.2	96.3	82.5	2.6	2.2	84.7
6	25%	4.4	68.5	9.6	14.1	4.0	67.2	8.2	12.3
6	50%	19.5	41.8	14.0	33.4	16.9	40.8	11.6	28.6
6	75%	38.2	29.7	16.2	54.4	34.7	25.9	12.1	46.9
6	100%	64.2	14.4	10.8	75.0	58.1	10.4	6.7	64.8
6	125%	86.9	4.0	3.7	90.5	77.1	2.3	1.8	78.9
6	150%	92.1	2.4	2.3	94.4	80.7	2.5	2.1	82.8
6	175%	94.9	1.5	1.5	96.3	82.2	3.0	2.5	84.7

Algorithms: DFA = Deferred Acceptance Algorithm; LOT = Weighted Lottery Approach; SLA = Simple Lottery Approach. These simulations were run using only DFA and several variations in school capacity.

Scenario 5 assigns an equal weighting to all the variables, while scenario 6 focuses on socioeconomic variables.

HOI= Human Opportunity Index; D-Index: Dissimilarity Index; IOP= Inequality of Opportunity

Table 11. Measuring family welfare for the opportunity to have access to a school.

			Access to a School of Any-Quality				Access to a School of High Quality
Scenario	Capacity	Algorithm	Ranked Third	Ranked Second	Ranked First	Total	Ranked Third	Ranked Second	Ranked First	Total
6	25%	DFA	10%	23%	67%	680	9%	23%	68%	582
6	50%	DFA	6%	15%	79%	1,362	6%	15%	79%	1,165
6	75%	DFA	3%	11%	86%	2,036	3%	10%	87%	1,742
6	100%	DFA	2%	8%	90%	2,680	2%	8%	91%	2,306
6	125%	DFA	0%	5%	95%	3,070	0%	5%	95%	2,678
6	150%	DFA	0%	3%	97%	3,145	0%	3%	97%	2,762
6	175%	DFA	0%	2%	98%	3,175	0%	2%	98%	2,794
1	100%	LOT	1%	6%	93%	2,716	1%	4%	95%	2,324
2	100%	LOT	1%	6%	93%	2,716	1%	4%	95%	2,324
3	100%	LOT	1%	6%	94%	2,716	1%	4%	96%	2,324
4	100%	LOT	1%	5%	94%	2,716	1%	3%	96%	2,324
5	100%	LOT	1%	7%	93%	2,716	1%	4%	95%	2,324
6	100%	LOT	1%	4%	95%	2,716	1%	2%	96%	2,324
7	100%	LOT	0%	6%	93%	2,716	0%	4%	95%	2,324
8	100%	LOT	1%	6%	94%	2,716	1%	4%	95%	2,324
9	100%	SLA	1%	6%	93%	2,716	1%	4%	95%	2,324
10	100%	SLA	2%	5%	94%	2,716	1%	3%	95%	2,324
11	100%	SLA	1%	6%	93%	2,716	1%	4%	94%	2,324
12	100%	SLA	1%	6%	93%	2,716	1%	4%	95%	2,324
1	100%	DFA	4%	9%	87%	2,716	3%	8%	88%	2,324
2	100%	DFA	2%	7%	91%	2,686	2%	7%	92%	2,309
3	100%	DFA	2%	7%	91%	2,691	2%	7%	91%	2,311
4	100%	DFA	2%	7%	92%	2,670	1%	6%	92%	2,297
5	100%	DFA	2%	7%	91%	2,686	2%	7%	92%	2,309
6	100%	DFA	2%	8%	90%	2,680	2%	8%	91%	2,306
7	100%	DFA	3%	7%	90%	2,702	2%	6%	78%	2,702
8	100%	DFA	2%	8%	91%	2,680	1%	6%	78%	2,680

Notes: Algorithms: DFA=Deferred Acceptance Algorithm; LOT=Weighted Lottery Approach; SLA= Simple Lottery Approach. Focus in the Scenarios: 1,7,8: Geography; 2: Academics; 3: Family; 4,6: Socioeconomics; 5: Equal weight.

Scenarios 9, 10, 11,12 were run with SLA, with no weights in the criteria; it is a completely random assignment.

HOI= Human Opportunity Index; D-Index: Dissimilarity Index; IOP= Inequality of Opportunity.