THE EFFECT OF CHARTER SCHOOLS ON STUDENT ACHIEVEMENT: A META-ANALYSIS OF THE LITERATURE CAMPBELL COLLOQUIUM EDUCATION PANEL, MAY 2012 Julian R. Betts and Y. Emily Tang, University of California, San Diego (jbetts@ucsd.edu, yetang@ucsd.edu) We are grateful to the Center on Reinventing Public Education, University of Washington, Bothell, for funding this research OUTLINE Introduction and Motivation Selecting Studies to Include Assessment of Alternative Methods of Evaluating the Impact of Charter Schools Challenges in Study Collection/Review Process Description of Methods Used in Review Results Future Research and Policy Implications 2 SOME BACKGROUND ON US EDUCATION Persistent concern over the performance of US public schools at the elementary and secondary levels Elementary Grades K-5 (ages 5-11) Secondary Middle: Grades 6-8 (ages 11-14) High: Grades 9-12 (ages 14-18) 3 THE US SPENDS A LOT (PER PRIMARY SCHOOL PUPIL) ON EDUCATION, OBTAINS AVERAGE EDUCATIONAL OUTCOMES Source: Gruber (2010) 4 THE US SPENDS ABOUT AVERAGE (% OF GDP) ON EDUCATION, OBTAINS AVERAGE EDUCATIONAL OUTCOMES Source: OECD (2011) 5 IN THE US THE SCHOOL THAT A STUDENT ATTENDS IS PRIMARILY DETERMINED BY WHERE HE/SHE LIVES San Diego Unified School District Elementary School Boundaries 2011-12 6 WHAT IS A CHARTER SCHOOL? Charter schools are a relatively new alternative to traditional neighborhood public schools ~ 20 years, substantial growth in the 2000s A succession of U.S. presidents has named charter schools as important agents of school reform 7 APPROXIMATELY 5% OF PUBLIC SCHOOLS ARE CHARTER SCHOOLS, THIS NUMBER IS GROWING Source: Lake and Gross (2011) 8 WHAT IS A CHARTER SCHOOL? Charter schools are publicly funded, governed by organization under contract with the state Charter schools are exempted from parts of the state education code, freeing them to innovate with respect to curriculum, pedagogy and hiring of teachers 9 CHARTER SCHOOLS ARE DIFFERENT FROM EACH OTHER, EXAMPLES FROM SAN DIEGO Albert Einstein Academy: “independent charter school that would have a dual instructional focus of German-English immersion within the context of a rigorous academic instructional model” Charter School of San Diego: initially developed from a state bill “designed to reduce the dropout rate by recovering students who had been out of school for more than 45 days” 10 SELECTING STUDIES FOR THIS LITERATURE REVIEW Scope: Include studies of US elementary and secondary charter school performance US public K-12 education is decentralized Most data on student performance are collected at the level of a US state, or the level of a school district (smaller than a US state) Outcomes: Include studies that use student performance on math and reading standardized tests as an outcome measure Methods: Include studies that use credible approaches to address selection bias 11 SELECTION BIAS: MAIN CONCERNS WITH ALTERNATIVE APPROACHES LEADING TO EXCLUSION Snapshots of average student achievement at one point in time can be misleading as they do not account for selfselection into schools US school attendance based largely on geographic residence. Students choosing to attend charter schools are likely different in observable and unobservable ways 12 UNOBSERVED CHARACTERISTICS CORRELATED WITH CHARTER SCHOOL ATTENDANCE Negative selection (downward bias) Example: An underprivileged, disadvantaged student without family support is at high risk of dropping out of school. She is advised by her high school counseling staff to transfer to a charter school, and she chooses to transfer. Problem: Underprivileged, disadvantaged students without family support are not likely to obtain high test scores in any school, traditional or charter. The estimate of charter school effectiveness based on comparison of charter school student performance and traditional school student performance would be biased downwards. 13 UNOBSERVED CHARACTERISTICS CORRELATED WITH CHARTER SCHOOL ATTENDANCE Positive selection (upward bias) Example: An active, concerned, involved parent is dissatisfied with the traditional public school in his/her neighborhood. The parent decides to optout of the traditional school and enroll his/her child in a charter school. Problem: Students with active, concerned, involved parents are likely to obtain high test scores in any school, traditional or charter. Implication: The estimate of charter school effectiveness based on comparison of charter school student performance and traditional school student performance would be upwardly biased. 14 SELECTING STUDIES FOR THIS LITERATURE REVIEW National Charter School Research Project issued a White Paper (drafters: Betts and Hill, 2006) arguing that lottery-based studies and student-level longitudinal “value-added” studies were the two most credible approaches These methods more convincing than other methods. 15 METHODS MATTER Source: Hill (2006) 16 4 COMMONLY USED METHODS OF ANALYSIS IN THE INCLUDED STUDIES In the set of studies we include, there are four approaches used 1) Lottery-based studies 2) Fixed-effect studies, that compare a student’s gains in achievement in years attended a charter to his or her gains in years attended a traditional public school 3) Propensity score matching 4) Other types of matching (e.g. CREDO) 17 LOTTERY-BASED ANALYSIS Source: Waiting for Superman movie (2010) 18 LOTTERY-BASED ANALYSIS Obvious benefit: expected outcomes identical for lottery winners and losers if lottery conducted fairly But several weaknesses to this “gold standard” External validity Most charter schools not oversubscribed Mathematica study of charter middle schools: only 130/492 oversubscribed Could be bias from attrition 19 PROPENSITY SCORE MATCHING Assumes “selection on observables” If students in charter schools have unobserved variations in ability or motivation, will be biased Two major studies of KIPP (Knowledge is Power Program) schools have used this approach CREDO at Stanford has produced string of influential state-level studies. Uses a unique matching process. Not propensity score but has similar issue with “selection on observables” 20 STUDENT FIXED-EFFECTS Benefit: Avoids need to compare one student with another, instead comparing individual students’ trajectories in charter schools and traditional public schools But many elementary students never switch between the two types of schools – external validity issue Zimmer et al (2009) compare test-score gains of charter “stayers” and switchers and do not get clear-cut result. But in some cases “stayers” have higher test-score gains Suggests downward bias from using this method Zimmer et al (2009) also raise concerns about reversibility – are the effects of attending a charter dependent on the order in which a student attends the charter and the traditional public school? Find some evidence that this is the case. Unobserved heterogeneity may change over time. Fixed effects cannot solve 21 INCLUDED STUDIES 40 reports now available, with just under 100 estimates of effects for each of math and English Language Arts (reading) Lottery-based studies still quite rare: still only 8 papers that use lotteries, covering 90 charter schools We exclude studies using less rigorous methods, specifically, those that do not use student-level test score gains as outcomes. 22 CHALLENGES IN STUDY COLLECTION/ REVIEW PROCESS Handling large weight (large number of students and large number of schools) studies Handling the different methods used in different studies Solution: Analyze with and without large weight studies Solution: Investigate whether method of analysis matters Some reports omit important information, e.g. number of schools in the sample Solution: Email exchange with authors 23 Introduction and Motivation Assessment of Alternative Methods of Evaluating the Impact of Charter Schools Selecting Studies to Include Challenges in Study Collection/Review Process Description of Methods Used in Review Results Future Research and Policy Implications 24 OUR METHODS OF ANALYSIS Fisher test – Is there evidence that no study finds negative effects; conversely, evidence of no positive effects? Formal meta-analysis provides overall estimated effect, its statistical significance and measures of how much true underlying variation there is across studies Histograms Show variability and the influence of weighting of studies Vote-counting as a way of assessing variation in results 25 HETEROGENEITY IS AN UNDERLYING THEME Look for variations in effect by: Subject area tested (math vs. reading) Grade span (E, M, H) Geographic location KIPP vs. non-KIPP Is there a systematic difference in results based on the method researchers use? 26 METHODS USED IN REVIEW Testing Whether Charter Schools in Any Study Increase or Decrease Achievement Relative to Traditional Public Schools Meta-Analysis of Effect Size Histograms and Vote Counting as Measures of Variation 27 METHOD #1: EVIDENCE OF NO POSITIVE EFFECTS, OR NO NEGATIVE EFFECTS? Fisher’s combined test k S 2ln( pi ) i1 S is distributed with df=2k Null hypothesis: No positive effects Null hypothesis: No negative effects 2 28 METHOD #1: EVIDENCE OF NO POSITIVE EFFECTS, OR NO NEGATIVE EFFECTS? We conduct this analysis 12 times: 6 ways of combining grades, and two subjects (math and ELA) First sign of heterogeneous effects of charter schools: in 9/12 cases there is clear evidence of BOTH negative and positive effects Three exceptions with evidence of positive effects but no evidence of negative effects: elementary and middle school ELA scores, and middle school math scores 29 PROBABILITY OF NO POSITIVE EFFECTS IN ANY OF THE STUDIES: ALMOST ZERO Grade-Span Reading Tests Math Tests Elementary <0.001 <0.001 Middle <0.001 <0.001 High <0.001 0.001 <0.001 <0.001 All <0.001 <0.001 Studies of All Grades or Largest Grade Span(s) If An All-Grade Study Not Available <0.001 <0.001 El’y, Middle, and Combined El’y/Middle 30 PROBABILITY OF NO NEGATIVE EFFECTS IN ANY OF THE STUDIES: ALMOST ZERO IN MOST CASES, AND QUITE HIGH IN 3 CASES Grade-Span Reading Tests Math Tests Elementary 0.987 <0.001 Middle 0.994 0.978 High <0.001 0.001 <0.001 <0.001 All <0.001 <0.001 Studies of All Grades or Largest Grade Span(s) If An All-Grade Study Not Available <0.001 <0.001 El’y, Middle, and Combined El’y/Middle 31 METHODS USED IN REVIEW Testing Whether Charter Schools in Any Study Increase or Decrease Achievement Relative to Traditional Public Schools Meta-Analysis of Effect Size Histograms and Vote Counting as Measures of Variation 32 METHOD #2: FORMAL META-ANALYSIS Assume charter school estimates are randomly distributed Therefore it is important to estimate both the mean and the variation Underlying “true” variation across studies is the extent to which variation cannot be explaining by sampling error (“uncertainty”) in individual estimates Omitted many studies of individual KIPP schools as they would have disproportionate influence Include KIPP schools in subsidiary analysis 33 THE MEAN EFFECT IS A WEIGHTED AVERAGE In a random effects meta-analysis, we take a weighted average of the effect sizes across studies. If Yi is the effect size for the ith of k studies, and Wi is the weight for each study, our overall estimated effect size M is : k M (1) W Y i 1 k i i W i 1 i 34 WEIGHTS DEPEND ON WITHIN-STUDY VARIANCE AND ESTIMATED ACROSS-STUDY (TRUE) VARIANCE The weight for each study is the inverse of the sum of the within-study variance (based on the standard error) and an estimate of the true between-study variance, T2: 1 (2) Wi 2 VYi T T2 based on a method of moments estimate of the variance of true effect sizes. Note that as T2 becomes large relative to the average withinstudy variance estimate, then we will tend toward equal weighting across studies; whereas as T2 becomes relatively small, the weights can become highly unequal with heavier weight given to studies with the lowest sampling variance. 35 AN ESTIMATE OF WHAT % OF THE VARIANCE ACROSS STUDIES IS TRUE Use the I2 statistic (Higgins et al., 2003) Provides estimate of the percentage of variation across studies that reflects true underlying variation 36 SAMPLE OF OUR RESULTS ON EFFECT SIZES Grade Span Reading Tests Math Tests E (Elementary) 0.022* (9-7), 77.7% 0.049* (10-8), 94.7% * Indicates statistically significant (5% level) 37 SAMPLE OF OUR RESULTS Grade Span Reading Tests Math Tests E (Elementary) 0.022* (9-7), 77.7% 0.049* (10-8), 94.7% * Indicates statistically significant (5% level) “On average, attending a charter school is associated with an increase in test scores in reading equal to 0.022 of a standard deviation per year.” 38 SAMPLE OF OUR RESULTS Grade Span Reading Tests Math Tests E (Elementary) 0.022* (9-7), 77.7% 0.049* (10-8), 94.7% * Indicates statistically significant (5% level) Nine studies covering 7 geographic areas 77.7% of the variation across studies represents true variation in charter school effects, rather than “noise” 39 OVERALL EFFECT SIZE ESTIMATES Grade Span Reading Tests Math Tests E (Elementary) 0.022* (9-7), 77.7% 0.049* (10-8), 94.7% M (Middle) 0.011 (9-7), 85.7% 0.055* (10-8), 92.0% H (High) 0.054 (7-5), 98.3% -0.015 (8-6), 98.6% Combined E/M -0.009 (15-12), 93.4% -0.012 (15-12), 97.9% E, M, and Combined E/M 0.002 (31-17), 90.3% 0.020* (33-18), 96.8% 0.008 (17-14), 98.4% 0.014 (18-15), 97.7% All 40 ELEMENTARY/MIDDLE SCHOOL MATH EFFECTS: MEANINGFUL BUT NOT HUGE Enough to move a student at the 50th percentile to the 52nd percentile after attending a charter for one year Elementary school reading impact is smaller: enough to boost a student from 50th to about percentile 50.8 41 ELEMENTARY SCHOOL READING EFFECT SIZES Study % ID ES (95% CI) Weight Boston 0.06 (0.01, 0.10) 8.73 California -0.00 (-0.01, 0.00) 25.00 Chicago 0.10 (0.03, 0.18) 3.70 Delaware 0.03 (0.00, 0.07) 12.45 NYC 0.04 (0.01, 0.07) 12.83 NYC 0.19 (0.02, 0.35) 0.88 National 0.01 (0.01, 0.01) 27.01 San Diego -0.08 (-0.17, 0.01) 2.61 San Diego 0.04 (-0.01, 0.09) 6.80 Overall (I-squared = 77.7%, p = 0.000) 0.02 (0.01, 0.04) 100.00 NOTE: Weights are from random effects analysis -.3 -.2 -.1 0 .1 .2 .3 42 ELEMENTARY SCHOOL MATH EFFECT SIZES Study % ID ES (95% CI) Weight Boston 0.02 (-0.03, 0.07) 11.44 California -0.03 (-0.04, -0.02) 16.26 Chicago 0.12 (0.04, 0.19) 8.51 Delaware 0.04 (0.01, 0.07) 14.25 Idaho 0.33 (0.03, 0.63) 1.10 NYC 0.09 (0.06, 0.12) 14.29 NYC 0.19 (0.02, 0.36) 2.89 National -0.00 (-0.00, 0.00) 16.50 San Diego -0.19 (-0.30, -0.08) 5.89 San Diego 0.29 (0.22, 0.37) 8.88 Overall (I-squared = 94.7%, p = 0.000) 0.05 (0.02, 0.08) 100.00 NOTE: Weights are from random effects analysis -.3 -.2 -.1 0 .1 .2 .3 .4 43 MIDDLE SCHOOL READING EFFECT SIZES Study % ID ES (95% CI) Weight Boston 0.17 (0.07, 0.27) 5.65 Chicago -0.06 (-0.14, 0.01) 8.49 Delaware 0.08 (0.04, 0.12) 13.58 NYC 0.04 (-0.02, 0.10) 10.00 National -0.10 (-0.23, 0.03) 4.21 National 0.02 (0.02, 0.02) 17.37 San Diego -0.08 (-0.12, -0.04) 13.69 San Diego 0.01 (-0.04, 0.06) 10.94 Texas 0.01 (-0.01, 0.04) 16.06 Overall (I-squared = 85.7%, p = 0.000) 0.01 (-0.02, 0.04) 100.00 NOTE: Weights are from random effects analysis -.3 -.2 -.1 0 .1 .2 .3 44 MIDDLE SCHOOL MATH EFFECT SIZES Study % ID ES (95% CI) Weight Boston 0.54 (0.39, 0.69) 4.81 Chicago -0.09 (-0.16, -0.02) 10.32 Delaware 0.09 (0.05, 0.13) 13.10 Idaho -0.05 (-0.18, 0.08) 5.88 NYC 0.24 (0.16, 0.31) 9.70 National -0.08 (-0.20, 0.04) 6.31 National 0.02 (0.02, 0.02) 14.66 San Diego 0.06 (0.03, 0.10) 13.15 San Diego 0.01 (-0.09, 0.11) 7.90 Texas -0.00 (-0.02, 0.02) 14.17 Overall (I-squared = 92.0%, p = 0.000) 0.05 (0.01, 0.10) 100.00 NOTE: Weights are from random effects analysis -.3 -.2 -.1 0 .1 .2 .3 45 HIGH SCHOOL READING EFFECT SIZES Study % ID ES (95% CI) Weight Boston 0.16 (0.02, 0.31) 11.60 Delaware 0.21 (0.16, 0.26) 16.18 National -0.02 (-0.02, -0.02) 16.98 San Diego 0.04 (-0.24, 0.33) 6.09 San Diego 0.03 (-0.01, 0.07) 16.33 San Diego 0.15 (0.10, 0.20) 15.97 Texas -0.16 (-0.18, -0.14) 16.84 Overall (I-squared = 98.3%, p = 0.000) 0.05 (-0.03, 0.14) 100.00 NOTE: Weights are from random effects analysis -.3 -.2 -.1 0 .1 .2 .3 46 HIGH SCHOOL MATH EFFECT SIZES Study % ID ES (95% CI) Weight Boston 0.16 (0.02, 0.31) 11.60 Delaware 0.21 (0.16, 0.26) 16.18 National -0.02 (-0.02, -0.02) 16.98 San Diego 0.04 (-0.24, 0.33) 6.09 San Diego 0.03 (-0.01, 0.07) 16.33 San Diego 0.15 (0.10, 0.20) 15.97 Texas -0.16 (-0.18, -0.14) 16.84 Overall (I-squared = 98.3%, p = 0.000) 0.05 (-0.03, 0.14) 100.00 NOTE: Weights are from random effects analysis -.3 -.2 -.1 0 .1 .2 .3 47 READING EFFECT SIZES FOR STUDIES THAT COMBINE ELEMENTARY AND MIDDLE SCHOOLS Study % ID ES (95% CI) Weight Arizona -0.01 (-0.02, -0.01) 7.96 Arkansas 0.02 (0.00, 0.04) 7.00 Chicago -0.04 (-0.06, -0.02) 6.85 Chicago 0.00 (-0.01, 0.01) 7.64 DC -0.01 (-0.02, 0.01) 7.10 Georgia 0.01 (-0.00, 0.01) 7.86 Massachusetts 0.00 (-0.01, 0.02) 7.50 Minnesota -0.02 (-0.03, -0.01) 7.46 Missouri 0.03 (0.01, 0.05) 7.05 NYC 0.09 (0.02, 0.16) 2.57 North Carolina -0.09 (-0.12, -0.07) 6.00 Ohio -0.08 (-0.12, -0.04) 4.74 Ohio -0.00 (-0.01, 0.00) 7.80 Texas 0.09 (0.06, 0.12) 5.61 Texas -0.08 (-0.10, -0.06) 6.85 Overall (I-squared = 93.4%, p = 0.000) -0.01 (-0.02, 0.00) 100.00 NOTE: Weights are from random effects analysis -.3 -.2 -.1 0 .1 .2 .3 48 MATH EFFECT SIZES FOR STUDIES THAT COMBINE ELEMENTARY AND MIDDLE SCHOOLS Study % ID ES (95% CI) Weight Arizona -0.04 (-0.05, -0.04) 7.60 Arkansas 0.05 (0.03, 0.07) 7.20 Chicago 0.02 (-0.02, 0.06) 6.23 Chicago 0.02 (0.01, 0.03) 7.53 DC 0.01 (-0.00, 0.03) 7.36 Georgia -0.01 (-0.02, -0.00) 7.59 Massachusetts 0.06 (0.05, 0.07) 7.48 Minnesota -0.03 (-0.04, -0.02) 7.44 Missouri 0.03 (0.01, 0.04) 7.24 NYC 0.12 (0.03, 0.21) 3.43 North Carolina -0.16 (-0.20, -0.12) 6.11 Ohio -0.18 (-0.26, -0.10) 4.01 Ohio -0.06 (-0.07, -0.05) 7.56 Texas 0.08 (0.06, 0.11) 7.00 Texas -0.12 (-0.16, -0.08) 6.23 Overall (I-squared = 97.9%, p = 0.000) -0.01 (-0.03, 0.01) 100.00 NOTE: Weights are from random effects analysis -.3 -.2 -.1 0 .1 .2 .3 49 METHODS USED IN REVIEW Testing Whether Charter Schools in Any Study Increase or Decrease Achievement Relative to Traditional Public Schools Meta-Analysis of Effect Size Histograms and Vote Counting as Measures of Variation 50 METHOD #3: HISTOGRAMS Another way of displaying the variation across studies Tried weighting each study equally and weighting studies by number of observations Latter approach gives heavy weight to CREDO studies Our formal meta-analysis is closer to weighting studies equally than weighting by observation 51 52 53 METHOD #4: VOTE COUNTING Categorize studies by sign of effect and whether statistically significant Method is problematic because it ignores fact that many statistically insignificant results all in the same direction may, taken together, suggest a statistically significant result We use mostly to highlight the heterogeneity Typically find that for most grade spans >50% of studies show positive effects, but this weakens and sometimes reverses if we weight studies by number of observations 54 RESULTS VARY BY METHOD Lottery results yielded the most positive results, followed closely by propensity score matching. These were followed by fixed effects and other matching methods (which are fairly similar with mixed positive and negative results) But it may not be the method that matters quite so much as the specific schools studied Example: Propensity score results are large but focus on KIPP schools 55 RESULTS VARY BY METHOD 56 RESULTS VARY BY METHOD 57 REPLICATION OF RESULTS USING DIFFERENT METHODS There are 3 studies/pairs of studies that replicate lottery results using more traditional “valueadded” methods They generally suggest that value-added models can get close to the lottery results (but in a few cases estimates slightly to meaningfully lower): Boston (Abulkadiroglu et al.) New York (Hoxby et al. and CREDO) San Diego Preuss School (McLure et al., Betts, Tang and Zau) 58 REPLICATION OF RESULTS USING DIFFERENT METHODS There are 3 studies/pairs of studies that replicate lottery results using more traditional “valueadded” methods They generally suggest that value-added models can get close to the lottery results (but in a few cases estimates slightly to meaningfully lower): Boston (Abulkadiroglu et al.) New York (Hoxby et al. and CREDO) San Diego Preuss School (McLure et al., Betts, Tang and Zau) 59 Introduction and Motivation Selecting Studies to Include Assessment of Alternative Methods of Evaluating the Impact of Charter Schools Challenges in Study Collection/Review Process Description of Methods Used in Review Results Future Research and Policy Implications 60 IMPLICATIONS FOR RESEARCH Evaluate individual schools Charters are meant to innovate; unlikely that all charters will have the same impact Charters should obtain permission from applicants to gather student records States and chartering authorities should regularly receive lottery data 61 IMPLICATIONS FOR RESEARCH Focus on successful schools to identify characteristics that may be working E.g. longer day/time, student population targeted, discipline policies, teacher management Obtain more details about charter school heterogeneity and study them Obtain more details about charter school closures 62 IMPLICATIONS FOR RESEARCH Probably important to examine more than results on math and ELA achievement. A handful of studies point to positive charter effects on graduation, college attendance and behavior. Expand focus to include outcomes other than math/reading test scores 63 WHAT WORKS CLEARINGHOUSE (WWC) FOR CHARTER SCHOOL RESULTS In the long run it would be good to have a nonpartisan group that collected and interpreted school-level charter results. 64 IMPLICATIONS FOR POLICY Status as a charter school vs. traditional public school unlikely to be (on its own) meaningful Promoting charter schools for sake of charter schools probably not productive path to comprehensive reform Continue expansion (no particular reason not to) Still only ~5% of traditional public school sector Renew focus on traditional public school reform Exploit flexibility of charter schools by using them as laboratories to learn what works 65 THANK YOU! Published version available at: http://www.crpe.org/cs/crpe/view/csr_pubs/467 Executive summary at: http://www.crpe.org/cs/crpe/view/csr_pubs/468 66 SUPPLEMENTARY SLIDES 67 ADDING KIPP STUDIES BACK IN HAS BIG EFFECT Grade Span Reading Tests Math Tests 0.070* (38-33), 88.3% 0.180* (39-34), 96.8% 0.034* (60-43), 90.8% 0.105* (62-44), 98.6% 0.096* (29-unknown), 82.7% 0.223* (29-unknown), 93.7% Including KIPP Schools M E, M, and Combined E/M Results Including Only KIPP Estimates M 68 SENSITIVITY TO EXCLUSION OF CREDO STUDIES CREDO (Stanford) has produced impressive string of mostly state-wide longitudinal student studies. Match each charter student to an average of several similar demographics and test scores Many charter students are matched based on their test scores AFTER they enter charter schools potential bias Hoxby (2009) has concerns about measurement error that may bias charter coefficient down CREDO offers partial rebuttal 69 RESULTS SOMEWHAT STRONGER IF OMIT CREDO STUDIES Grade Span Reading Tests Math Tests E 0.034* (8-6), 79.5% 0.072* (9-7), 95.2% M 0.010 (8-7), 87.2% 0.068* (9-8), 92.8% H 0.072 (6-4), 98.5% -0.002 (7-5), 97.5% Combined E/M -0.023 (6-5), 95.5% -0.041 (6-5), 96.9% E, M, and Combined E/M 0.008 (22-10), 92.0% 0.038* (24-11), 95.0% 0.016 (10-9), 86.6% 0.041* (11-10), 67.7% All 70 EFFECTS FOR URBAN DISTRICTS AND SCHOOLS LARGER THAN FOR ALL DISTRICTS Grade Span Reading Tests Math Tests E 0.046* (6-4), 61.8% 0.085 (6-4), 92.2% M 0.009 (5-4), 87.0% 0.139 (5-4), 94.8% H 0.101* (4-2), 78.2% 0.019 (4-2), 42.7% Combined E/M -0.003 (4-3), 86.2% 0.021* (4-3), 47.7% E, M, and Combined E/M 0.016 (15-5), 84.1% 0.077* (15-5), 92.4% All 0.008 (8-6), 63.2% 0.045* (8-6), 74.8% 71 VARIATIONS BY RACE/ETHNICITY Surprisingly few studies test for variation by race/ethnicity. CREDO studies an important exception Patterns not uniform, but overall, charter effects decline in the following order: black > Hispanic > Native American > white Results for whites typically negative, not always significant. Biggest exception is high school reading, with a positive and significant effect 72 VARIATIONS BY ENGLISH LEARNER, SPECIAL EDUCATION, MEAL ASSISTANCE Effects often insignificant, perhaps due to smaller sample sizes But some evidence of positive effects of charter schools on EL and special education students in both math and reading from studies of all grades and studies of middle schools 73