Interdistrict Comparisons of Intradistrict School Performance Inequality in Louisiana: 2001-2009 Lead Author: Mark J. Schafer, LSU Agricultural Center Co-author: James M. Fannin, LSU Agricultural Center Abstract The No Child Left Behind (NCLB) Act was enacted in 2001 to reduce the performance gap in educational achievement across various subgroups within the United States. Most scholars agree that the act has led to significant systemic changes within education systems. Certainly, some schools have shown substantial improvement under NCLB. However, school improvement varies significantly across schools. One study conducted in Louisiana found that one in five schools failed improve or performance actually declined from 2001 – 2004, and that this was not only typical of the state as a whole, but also of various regions and school districts (Schafer 2007). To understand this issue better, this paper first develops a measure of intradistrict school performance inequality—a school district level measure--to assess variation in school performance across like schools within the same school district. Second, school and district level data are used to compare intradistrict school performance inequality across Louisiana’s school districts at the beginning of the No Child Left Behind Act in 2001 (N=66). Third, we examine changes in intradistrict inequality over time by using the latest available data for the 2008-2009 school year (N=69). Fourth, the paper will examine relationships between district level characteristics and intradistrict school performance inequality. Fifth, and finally, the paper will discuss implications for theory, research, and policy of broad-based policies that have potentially drastically varying consequences for schools that are differentially placed within a performance-hierarchy within their school districts. This paper has been prepared to be presented at the Annual Meeting of the Southern Regional Science Association, March 26, 2010, in Washington D.C. This research was made possible through funding by a cooperative agreement with the Minerals and Management Coastal Marine Institute. We used data made publicly available by the Louisiana Department of Education. I. Introduction This research seeks to understand the extent to which No Child Left Behind-style accountability achieved its stated objective—to reduce the gap in educational achievement---in one rather particular sense in a state that is heavily influenced by the Oil & Gas Industry, Louisiana. As the title of the law implies, the objective of No Child Left Behind is to reduce student-level achievement gaps. In practice, however, states and school districts seek to improve students’ test scores by holding schools accountable for their students’ academic progress. Therefore, much scholarship has focused on schoollevel achievement gaps. Within the nested hierarchy, our focus moves up an additional level to the school district. Specifically, we are interested in developing a district-level method that can be used for district-level comparative analysis, in which the focus is on the extent of school-level performance variation or inequality within districts. Louisiana is an idea state within which to conduct a cross district comparison of within-district school performance inequality. First, its school districts are nearly coterminous with its parishes (counties), so comparisons very likely reflect other parishlevel inequalities. Second, the southern half of the state has long been influenced by the development, expansion, and changes that have occurred within the offshore oil and gas industry, while the northern portion of the state has not been particularly influenced by oil and gas. Hence, the state offers the opportunity to conduct a natural experiment of the resource-dependent and resource-independent parish school districts. Third, racial inequalities in educational performance can be traced back in history to segregation and urbanization, and these inequalities persist in both urban centers and rural communities. Racial disparities, however, may have more to do with East/West than with North/South 1 differences within the state. Fourth, Louisiana’s parish/school districts range from small, isolated rural districts with fewer than 10 schools to large urban districts with over 100 schools, creating the possibility of comparing within-district performance inequalities across a range of district-types. We hope the interdistrict comparisons of intradistrict performance outcomes will help policy-makers in Louisiana and similarly situated states. We begin this paper with a discussion of why we expect districts to vary with respect to their internal, school-level performance disparities. From there we move on to our approach to developing meaningful measures of intradistrict inequality. We then use those measures to present descriptive performance inequality data for Louisiana’s school districts in 2001 and 2009, the beginning and current point in the No Child Left Behind era. After that we present finding from cross-sectional and panel analyses, and we conclude with some discussions of the strengths and limitations of our work and suggest some potentially fruitful ways to carry this work forward in the future. II Intradistrict Outcomes Inequality: What is it? Why does it matter? Most studies of educational inequalities focus on (1) resources instead of outcomes and (2) cross district instead of within-district comparisons (Iatarola and Stiefel 2003). The research devoted to understanding resource inequalities across districts was spurred by interest in the effects of court-ordered educational finance reforms. Studies in the 1990s showed that these reforms led to increased spending in poor districts in states where they occurred (Murray, Evans, and Schwab 1998). The more recent focus on within-district comparisons has tended to focus on large urban school districts with large numbers of schools. These studies emerged in response to findings of increased equity in 2 cross-district educational resource distribution (Summers and Wolfe 1976). In Los Chicago (Rubenstein 1998), New York City (Iatorola and Stiefel), and other large urban school districts, scholars argued that interdistrict comparisons underscored the extent of resource inequities within these areas. A few studies have attempted to determine whether school-level resource disparities were greater within or between districts. Hetert (1995) compared per-pupil expenditures in California, Burke (1999) compared teacher-pupil ratios across large districts, and Owens and Maiden (1999) examined instructional expenditures in Florida. In general, these studies demonstrated that resource inequalities exist both within and between schools. Rubenstein (2006) provides an overview of a growing body of literature that focuses on the extent and type of resource inequalities within a single large district. He concludes that within district disparities are extensive and that they generally disadvantage the neediest schools, particularly with respect to quality teacher resources. This study complements this research on educational resources by shifting the focus to cross district comparisons of school-level outcomes. The research on educational outcome inequalities is less extensive. Berne (1994) analyzed outcome disparities across school districts in New York State, and found that for “outcome indicator after outcome indicator, New York City and the large urban school districts, the high poverty schools, and the high minority schools performed at substantially lower levels”. Several scholars have approached the study of outcomes from an efficiency perspective. In a review of the empirical findings, Belfield and Levin (2002) linked 3 outcomes to increased market competition among education providers. Other scholars have argue that when variable outcomes are achieved by like districts with similar inputs, the resulting measures can be seen as measures of inefficiency (Ruggiero, Miner, and Blanchard 2002). Policy makers can utilize this information to improve the efficiency of education delivery. Like input studies, research on educational outcomes tends to focus on individual student-level outcomes. Our focus is similar but slightly different. Our district-level analysis focuses on variations across district in school-level performance. Understanding inequities across schools within each district brings the focus to broader, parish level factors that support more equitable or inequitable school-level outcomes. We are particularly interested in the extent to which school-level inequities mirror broader socioeconomic inequalities within Louisiana parishes, and whether such inequalities are exacerbated or attenuated by linkages to the off-shore oil and gas industry. The next section discusses challenges to measuring outcome inequality, with a particular emphasis on the state of Louisiana. III Measuring Intradistrict Performance Inequality in Louisiana The state of Louisiana established a formula for each school to calculate a School Performance Score (SPS) based on a combination of test scores, attendance, and (for schools with grades 7 and up) dropouts. When accountability was initially established in 1998-1999 school year, Louisiana policy-makers established a 10-year bench mark for all schools to achieve a SPS of 100 or greater. The passing of the federal No Child Left Behind required policy-makers to add sub-group component scores, but the SPS formula 4 continued to be used and, thus, the state currently defines any school with an SPS over 100 as a “successful school”. In 2001, 223 schools (16.2%) had attained “successful school status and than number increased to 363 schools (28.5%) by 2009. In 2003 the state also implemented a “star” system, tied to the SPS and cost factors that ranged from 1 to 5 stars with 5 being the best schools. Schools earning only 1 star were seen as adequate, but barely, and risked having that state take more direct action if they failed to meet annual improvement goals. In 2009, 32% of all schools had earned only 1 star or worse, while nearly 40% of schools earned 2 stars and another 30% had earned 3 or more stars. Many studies of resource inequalities in education draw upon one or more of four measures of inequality: (1) the federal range ratio, (2) the coefficient of variation, (3) the gini coefficient, and (4) the McCloone Index. The first three are true measures of dispersion or inequality in a distribution while the last focuses only on the bottom half of a distribution and, therefore, may be better understood as a measure of adequacy. The choice of inequality measures, according to Kaplow (2005) depends on a combination of the conceptualization of the problem and the empirical facts in particular contexts. At this point in our exploration, we are less interested in the specific details of intradistrict inequality, but are concerned with (1) the range of school performance scores within districts, (2) the situation of the worst performing schools relative to the median performance in a particular district (McCloone Index), and (3) the extent to which all low performing schools are failing to meet federal and state required performance goals (we use the Percentage of Low Performing Schools). 5 For the first measure, we use the interquartile range rather than the range ratio. This is the only true measure of within-district school performance inequality. For the second measure we use the McCloone Index. This measure is best understood as a measure of within-district adequacy and, therefore, its interpretation is dependent upon the median school performance in the district. For example, if the median school performance is low then a high McCloone Index would simply mean that all schools in the district are relatively equitably weak. The third measure is not technically a measure of intradistrict inequality as it is a measure of the capacity of each district to provide quality educational services to its children. The combination of these three indicators provides a richer picture of both within and between district inequalities. IV. Intradistrict Inequality in 2001: The Beginning of Accountability Table 1 presents a descriptive picture of intradistrict school performance inequality in 2001. The indicators of performance, number of schools, inequality, and adequacy are listed in the left column. The next column lists overall averages for the state, and the following 4 columns compare intradistrict inequalities across MMS and nonMMS parishes (South and North) and large and small school districts, respectively. Several key findings from Table 1 are instructive. First, the typical school district in the state had a mean School Performance Score of 77.1 (the state defined schools with an SPS>100 as “successful schools”). In general oil and gas influenced (southern) and large school districts tend to have higher mean and median school performance scores. This finding challenges theoretical frameworks that suggest that urban and resourcedependent regions are disadvantaged. Second, the dispersion measures (IQR, S.D., CoV) 6 all show few differences between MMS and nonMMS parishes, but significant differences between large and small districts, but also differences within these broad categories. For example, among school districts with fewer than 25 schools, the interquartile range ranges from 6.1 across the eight schools in Iberville Parish to 46.2 across the eight schools in Point Coupee Parish. Third, the McCloone index shows that, within districts, the worst performing schools tend to do worse relative to the mean when the district is large. While this index is typically used to analyze equity in funding, here we can interpret the index is a specific way. Within all Louisiana school districts, schools that perform below the median SPS of 76.6, have an average SPS score of 85% of the median or 65.1. If the sample is limited to small school districts, low performing schools score on average at about 90% of the median score of 75.5 or 68.0, while the low performing schools in large districts only average 82% of the median score of 80.0, or about 65.6. Fourth, the typical school district in Louisiana had about 35% of its schools classified as “low performing” in 2001. That percentage was lower for MMS and large districts and higher for northern and small districts. In three districts, none of which were among the 33 MMS-defined districts, all the schools were low performing in 2001. Fifth, the school-level enrollment, percent minority, percent free and reduced lunch, and special education figures show broad similarities across both North and South Regions and across large and small school districts. Louisiana is unique in this respect, because its schools with large percentages of poor and minority schools are not isolated in large urban districts. 7 V. Change in Intradistrict Inequality Table 2 presents descriptive statistics relating to the change in intradistrict inequality and adequacy from 2001-2009. First, Mean School Performance Scores increased by about 11.5 points overall, in both the North and the South, and in both large and small school districts. Notwithstanding that fact that four school districts saw declines in mean SPS during this period, the overall impression is that NCLB-style accountability led to school improvement throughout the state. We should also note that the overall improvement picture, and particularly that of large school districts is somewhat distorted by the major changes in Orleans Parish School district, which went from 116 schools in 2001 to 16 in 2009 (thus, technically becoming a small district) when the state took control of the vast majority of the schools after Hurricane Katrina in 2005. Second, the next two indicators in Table 2 show declines in two measures of intradistrict school performance inequality: about a 3 ½ point decline in the interquartile range and about a .06 point decline in the coefficient of variation. Again, these declines generally occurred across regions and district types. Third, the final two indicators of performance adequacy provide somewhat competing pictures of changes in adequacy. On the one hand, the McCloone Index increased from about .85 to .90, showing that the low performing schools in districts are earned school performance scores in 2009 that were closer to the median, on average, than the low performing schools in 2001. The bottom half is closer to the median than it was before. On the other hand, the percentage of state-defined low-performing schools (those with an SPS score of less than 70) declined only slightly overall, and did not 8 decline at all in nonMMS districts. The combination of these two findings support findings by Schafer (2007) that overall school improvement in the state masked the reality that about a third of all schools in the state, and within most regions and districts, saw stagnating or declining school performance from 2001 to 2005. VI. Determinants of Intradistrict Inequality at beginning of Accountability Table 3 presents an OLS regression analysis of determinants of intradistrict mean school performance, inequality, and adequacy in 2001. The explanatory variables listed in the left-hand column include district level measures of (1) size overall student enrollment; (2) student characteristics---percent at risk (defined as those eligible for free or reduced school lunch), percent minorities, and percent special education students; (3) district resources---pupil-teacher ratios, total revenues per student, total instructional expenditures per student, and percent of adults in the parish in poverty; and (4) district structural characteristics of being among the MMS-defined parishes or being a large district. The first model estimates the mean school performance score in the district. The results demonstrate the strong negative relationship between the percentage of minority students in a district and the mean school performance scores. The next two models estimate the two measures of dispersion, interquartile range and the coefficient of variation. Interestingly, the percentage of at risk students in a district is associated with a reduction in the interquartile range, while higher pupil teacher ratios are linked to wider range of school performance scores. This pattern does not hold for the coefficient of variation, which is positively associated with instructional 9 expenditures, poverty, and large school districts. To understand why greater instructional expenditures are associated with increased performance inequality across schools, it would be necessary to explore the allocation of these resources across the schools in the districts. One possibility is that greater expenditures are allocated toward special status magnet and gifted and talented schools (which are also more common in large school districts), but this is speculation at this point. The final two models explore the issue of adequacy. The results for the McCloone Index reveal that, relative to the median school in their own district, the lower performing schools fair better in districts with a higher mean SPS, more at risk students, and more special education students. On the other hand, the lower performing schools have a lower relative performance in larger versus smaller school districts. With respect to satisfying state-defined criteria for school performance, the findings mirror the findings for mean school performance. The key factor in explaining both mean school performance and percentage of low performing schools is the percentage of minority students in the district. VII. Determinants of Change in Intradistrict Inequality Table 5 presents OLS regression results for the change in intradistrict school performance inequality from 2001 to 2009. The first model shows that the increases in mean school performance were largely a result of the mean school performance in 2001; districts with high initial mean performances realized smaller increases. We included Orleans parish as a dummy variable due to its special circumstances resulting from Hurricane Katrina—the school district saw huge gains in its mean school performance, 10 but that is linked to the reality that it remained with only 16 of its initial 116 schools, the rest of which were taken over by the state. The second model shows two factors were associated with reductions in the dispersion as measured by the interquartile range. Higher district-wide enrollments were associated with increases (or smaller decreases) in the interquartile range from 2001 to 2009, while districts with higher instructional expenditures realized greater reductions in the range of school performance inequality. The third model offers a slightly different picture of changes in school-level dispersion about the mean. MMS and Orleans parishes realized significantly greater declines in inequality than nonMMS parishes from 2001 to 2009, while declines were less pronounced in districts with high enrollments, more at risk students, and more special education students. (Note that the positive sign does not necessarily indicate increased inequality; it is possible that school performance inequality was reduced but these factors significantly reduced the rate of reduction). The fourth model demonstrates that the lower performing schools within each district improved their scores, relative to the median score, in districts with a higher percentage of at risk students. At the same time, districts with high percentages of minorities and more of the adult population in poverty saw more limited change in the relative performance of the weakest schools. Finally, the findings presented in the fifth model suggest that significantly larger reductions in the percentage of low performing schools occurred in Orleans and MMS parishes. Discussion This research sought to understand variation in school performance both within and across school districts in the state of Louisiana. We tempered our initial interest in 11 interdistrict comparisons of intradistrict performance inequality with a consideration of the issue of adequacy. On one extreme, a school district may have relative equity in performance across schools within the district while, at the same time, every school in the district is considered “low performing” by state-defined standards of student test scores. In such a case the question of intradistrict equity across schools would take a back seat to the larger question of why the performance is lacking throughout the district. On the opposite extreme, another district may have a relatively large internal differentiation in performance between its best and worst performing schools, but every school (even the lowest performing school in the district) is considered by the state to be “adequate”, meeting state and federally-defined minimum performance standards. In cases such as these, stakeholders may appreciate the fact that district leaders were able to bring all schools up to the minimum standards, yet still ask valid questions as to why there is considerable intradistrict inequality. Most Louisiana school districts lie somewhere in between these two extremes and, therefore, need to be cognizant of both the districts’ performance relative to other districts in the state and the various schools’ performances relative to each other within the district. Our results strongly suggest that intradistrict inequalities have declined during the accountability/NCLB era. Three of the four indicators of inequality used (interquartile range, coefficient of variation, and McCloone Index) suggest significant declines in both the overall dispersion of school performance within districts, but also improvements in the relative performance of schools at the bottom half of the range. At the same time, relative to state standards, school districts have seen very little change in the proportion 12 of low performing schools. By and large, districts with no low performing schools in 2001 also had no low performing schools in 2009, those with all low performing schools in 2001 also had all low performing schools in 2009, and the rest realized only marginal increases and decreases in the percentage of low-performing schools. A reasonable next step in this analysis would be to explore the relationship between outcomes and, to the extent it is possible to get good data, school-level inputs. The primary objective of this approach would be to use our knowledge of outcomes to describe the extent to which districts have the capacity to use inputs efficiently (or to spread them efficiently across schools). The data envelope procedure described by Ruggeiro et. al. (2002) would be useful in this regard. The procedure allows for more appropriate comparisons related to the efficient use of educational resources, because the input/outcomes relationships are mediated by differences in educational costs (e.g. large transportation costs in rural schools, high poverty costs, high proportion of students with disabilities, etc.). This kind of analysis seems like a fruitful way to provide educational policy and decision makers with valuable information rooted in cross district comparisons of within district processes. 13 References Belfield, Clive R. and Henry M. Levin. 2002. The Effects of Competition on Educational Outcomes: A Review of the US Evidence. National Center for the Study of Privatization in Education. Columbia University, New York. Berne, Robert. 1994. “Educational Input and Outcome Inequities in New York State.” Pp. 1-23 in Outcome Equity in Education, edited by Robert Berne and Lawrence O. Picus. Corwin Press Inc: Thousand Oaks, California. Hanushek, Eric A. and Woessmann, Ludger, Does Educational Tracking Affect Performance and Inequality? Differences-in-Differences Evidence across Countries (February 2005). NBER Working Paper No. W11124. Available at SSRN: http://ssrn.com/abstract=667166. Iatarola, P. and L. Stiefel. 2003. “Intradistrict Equity of Public Education Resources and Performance.” Economics of Education Review 22:69-78. Kaplow, Louis. 2005. “Why Measure Inequality?” Journal of Economic Inequality 3:65-69. Murray, S. E., Evans, W. N., & Schwab, R. M.. 1998. “Education-Finance Reform and the Distribution of Education Resources.” The American Economic Review: 88 789–812. Rubenstein, Ross. 1998. “Resource Equity in the Chicago Public Schools: A School-level Approach.” Journal of Education Finance 23, 4: 468-489. Ruggiero, John, Jerry Miner, and Lloyd Blanchard. 2002. “Measuring Equity of Educational Outcomes in the Presence of Inefficiency.” European Journal of Educational Finance 142:642-652. Schafer, Mark J. 2007. “School Accountability in Louisiana.” LSU Agricultural Center Bulletin Number 887. LSU Agricultural Center. 14 Table 1: Descriptive Statistics for Intradistrict School Performance Inequality in 2001: State, by Region, and by District Size (Large V. Small) Indicator State South North Large Small Mean SPS 77.1 80.2* 74.0 80.6 75.8 Low Mean 45.2 48.3 45.2 48.3 45.2 High Mean 102.3 102.3 98.4 102.3 98.4 Median SPS 76.6 79.8* 73.5 80.0 75.4 Mean Number Low Number High Number 21 3 116 28 6 116 13 3 64 48 26 116 10 3 20 Mean IQR Low IQR High IQR 20.8 6.1 51.2 20.1 6.1 31.6 20.7 6.6 51.2 25.8 12.6 51.2 15.5 6.1 46.2 Mean S.D. Low S.D. High S.D. 14.7 3.7 32.1 15.1 5.4 28.8 14.2 3.7 32.1 18.8 9.4 32.1 13.1 3.7 25.8 Mean CoV Low CoV High CoV .20 .05 .60 .20 .06 .60 .20 .05 .43 .25 .09 .60 .18 .05 .43 Mean McCloone Low McCloone High McCloone .85 .60 .97 .85 .72 .97 .85 .60 .94 .82 .72 .91 .90 .60 .97 Mean LP Schools Low LP Schoolsa High LP Schoolsb .35 0 1.00 .29 .41 0 1.00 .29 .37 0 1.00 0 .83 0 .83 Mean Enrollment Minority % At Risk% Special Ed.% 466 48.0 63.5 12.8 520 43.0 62.0 13.7 411 53.0 65.2 11.9 559 46.0 60.5 13.6 431 48.8 64.7 12.5 Num of Districts 66 33 33 18 48 *significant at p<.05 a Beauregard, Caldwell, Cameron, Catahoula, Jefferson Davis, LaSalle, Livingston, Plaquemines, St. Charles, St. Tammany, Vernon, West Carroll, Winn b Madison, St. Helena, Tensas 15 Table 2: Descriptive Statistics for Change in Intradistrict School Performance Inequality: 2001- 2009: Indicator State South North Large Small Mean SPS 2001 77.1 80.2 74.0 80.6 75.8 Mean SPS 2009 88.6 92.0 85.5 92.5 87.3 SPS Change 11.5 11.5 11.5 11.5 11.5 Low Change* -7.6 -7.6 -4.7 1.7 -7.5 1 High Change 52.5 52.5 24.9 52.5 24.9 Mean IQR 2001 Mean IQR 2009 IQR Change 20.8 16.5 -3.5 20.1 16.4 -2.7 20.7 16.6 -4.0 25.8 19.0 -4.6 18.5 15.8 -3.0 CoV 2001 CoV 2009 CoV Change .20 .14 .06 .20 .13 .06 .20 .14 .06 .25 .16 .08 .18 .13 .05 McCloone 2001 McCloone 2009 McCloone Change .85 .90 .04 .85 .90 .04 .85 .89 .04 .81 .89 .06 .86 .90 .04 LP Schools 2001 LP Schools 20092 LP Change .35 .33 -.02 .28 .24 -.06 .41 .41 0.0 .29 .27 -.02 .37 .34 -.03 Num of Districts 66 33 33 18 48 * Cameron, Union, and West Carroll districts Orleans Parish School District—due to loss of over half its schools to state takeover after Hurricane Katrina 2 In 2009, 17 districts had no low performing schools, while four had all low performing schools 1 16 Table 3: OLS Regression showing Determinants of Intradistrict School Performance Inequality: 2001: Indicator Mean SPS IQR CoV McCloone Low Performing Mean SPS 2001 -----.15 ---3.5** NA (-.97) (2.88) Enrollment 2001 8.71 -5.72 .03 -.04 -.07 (0.85) (-.47) (.30) (-.42) (-.28) At Risk 2001 -14.64 -33.17* -.23 .25* .43 (-1.21) (2.30) (-1.81) (2.16) (1.48) Minorities 2001 -44.06** 3.90 .23** .03 .91*** (-6.24) (.35) (2.93) (.33) (4.96) Special Ed 2001 .25 -28.13 -.59 .75* .45 (.02) (-.67) (-1.58) (2.20) (.52) Pupil-Teacher 01 -.05 4.09** .02 -.02 .01 (-.04) (2.82) (1.92) (-1.77) (.24) Revenues 01 3.91 -1.00 -.02 .01 -.00 (1.76) (-.43) (-1.25) (.41) (-.40) Expenditures 01 -1.81 16.1* .12* -.10 .00 (-1.11) (2.36) (1.99) (-1.75) (.29) Poverty 01 -6.32 31.14 .58* -.24 .18 (-.26) (1.1) (2.33) (-1.05) (.31) MMS -1.4 -2.15 .02 -.00 -.00 (-.64) (-.82) (1.07 (-.09) (-.00) Large 2.83 (1.27) Adj. R-Squared Number of Cases 6.5 (2.48) .73 66 .06* (2.43) .31 66 -.04* (-2.15) .50 66 -.03 (-.71) .33 66 .70 66 17 Table 4: OLS Regression showing Determinants of Intradistrict School Performance Inequality Change: 2001 - 2009 Indicator Mean IQR CoV McCloone Low Perf. Change change Change Change Change Lagged D.V. 0 Mean SPS 2001 Same 0 0 0 NA Enrollment 2001 0 + + 0 0 At Risk 2001 0 0 + + 0 Minorities 2001 0 0 0 0 Special Ed 2001 0 0 + 0 0 Pupil-Teacher 01 0 0 0 0 0 Revenues 01 0 0 0 0 0 Expenditures 01 0 0 0 0 Poverty 01 0 0 0 0 MMS 0 0 0 Large 0 0 0 0 0 Orleans + 0 0 Adj. R-Squared Number of Cases .67 66 .50 66 .81 66 .69 66 .37 66 18