- A10 Prospects estimates are much lower than the 1.3 s.d. gap obtained from NLSY97 administered at about the same time. In other words, estimates for the income-achievement gap for cohorts born within a couple of years of 1980 vary by no less than 0.6 s.d. Measurement error is the most likely explanation for this spread in estimates made at close to the same time.
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- A13 reading estimated by NLSY97 is no different from the one observed twenty years earlier. Over the twelve years between the administration of ECLS-K and ECLS-K2010, the 90-10 math achievement gap, as reported by Reardon and Portilla (2016), declines by 0.13 s.d. and the gap for reading drops by 0.21 s.d.49 Neither set of observations reveals any increase in the income-achievement gap. Reardon (2011b) concedes that “the income achievement gap as measured in the NLSY97 cohort is virtually identical to the gap in the NLSY79 cohort, born twenty years earlier†(p. 96). But, he says, “the NLSY cohort was born in the early 1980s, just as the trend†upward is about “to begin†once more. This survey was administered too soon to discern “a rising gap among the 1980s and 1990s cohorts.†The ECLS data, analyzed in Reardon and Portilla (2016), removes uncertainty about whether or not the NLSY comparison was simply due to observations outside the relevant range.
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- A6 Appendix B: Comparison with Reardon (2011b) Our results differ from those reported by Reardon (2011b), who finds rapidly growing SES gaps when SES is measured with parental income indicators. In this Appendix, we reconcile our findings with his by showing that the difference in results is due to systematic measurement errors in his analysis. When a trend line is estimated from the studies in his analysis less prone to measurement error, no upward trend in the SES-achievement gap is detected.
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- A7 gap has grown by roughly 40 to 50 percent …, a very sizeable increase†(p. 97). Elsewhere, he describes this increase as “roughly 30 to 40 percent†(p. 93). Unfortunately, his analysis does not reflect the overall impact of the data problems, many of which he himself identifies in an appendix (Reardon (2011a)). There are two strands of evidence indicating that the perceived trends are not real but instead are a function of measurement error. First, in a significant portion of constructed gaps household income is very poorly measured; in another portion the test instruments themselves are quite suspect; and in a final set survey sampling and missing data become serious issues. When surveys at high risk of serious measurement error are excluded, no upward trend in the incomeachievement gap is observed. Second, comparisons of gap differences among psychometrically matched observations that cover the relevant period of supposed steep gap increases reveal no upward trend.
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- According to U.S. Department of Health and Human Services (2018), the study recruited ten hospitals willing to participate as recruiting grounds for mothers willing and available to participate in a multi-year study. The sample description explicitly says its “data are not representative in the statistical sense, and therefore inference to the nation as a whole is not possible. Comparisons to other databases, national or otherwise, should be made with extreme caution.â€45 The website for SECCYD identifies use of the Woodcock-Johnson Tests, which are designed to be IQ tests. It is not clear how these might translate into the reading or math achievement tests found in the other surveys. In any event, the survey does not meet the criterion of being nationally representative.
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- Add Health provides low estimates of the income-achievement gap in reading for students born between 1978 and 1983 when that gap is alleged to be much lower than in later years.
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Alvaredo, Facundo, Lucas Chanel, Thomas Piketty, Emmanuel Saez, and Gabriel Zucman, eds. 2017. World Inequality Report 2018. Paris: World Inequality Lab.
- An alternative approach, applied by Reardon (2011b), Chmielewski and Reardon (2016), and Chmielewski (2019) (see section 2.2), is to extrapolate achievement from the observed range to points farther in the tail of the distribution. It is just the shape of the SES-achievement relationship in the tails of the SES distribution that is the object of the overall analysis. We do not use this extrapolation approach because it necessarily involves making strong assumptions about the shape of the SES-achievement distribution that cannot be verified by the data.
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- Appendix Figure A1 replicates the Reardon analysis of estimated 90-10 incomeachievement gaps in math and reading for the birth cohorts 1961-2005 using only the highquality surveys.47 All of these data come from well-regarded, nationally representative surveys that obtained income information from parents rather than students. One striking fact emerges from this figure: Simple linear regressions that estimate trends in math and reading from the ten observations taken from these surveys show perfectly flat trends with no significant change in the income-achievement gap over this time period.
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Cheng, Albert, and Paul E. Peterson. 2019. "Experimental Estimates of Impacts of Cost-Earnings Information on Adult Aspirations for Children’s Postsecondary Education." Journal of Higher Education 90, no. 3: 486-511.
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- Each image plate contains 4 black-and-white drawings, one of which best represents the meaning of the corresponding stimulus word. … Starting in 1998, the administration of the PPVT-R was largely limited to 4- and 5-year-old childrenâ€.44 Reardon makes use of the results of Add Health’s PPVT scores for six of the 17 observations used to estimate the growth in the reading gap for cohorts born between 1974 and 2001. But PPVT asks respondents to point at a picture when told a word. No reading is involved.
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- Figure 1. Overall Achievement Dispersion among U.S. Students, Birth Cohorts 1954-2001 Notes: 75-25 (90-10): overall achievement difference between the students at the 75th and 25th (90th and 10th )
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- Figure 10. SES-Achievement Gap Calculated with Alternative Point Estimation Method, Birth Cohorts 1954-2001 Notes: Difference in achievement estimated at the 75th and the 25th percentile of the SES distribution based on cubic estimation function of the SES-achievement relationships. See Figure 2 for data and additional information.
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- Figure 11. Ordinal Analysis of Change in the SES-Achievement Distributions, PISA 2000 and 2015 Panel A: Bottom quarter vs. top quarter of the SES distribution Panel B: Bottom quarter vs. top half of the SES distribution Notes: Horizontal axis: students in the low-SES group lined up along their math achievement distribution. Vertical axis: share of students in the high-SES group who score at or below the respective math achievement of the low-SES percentile.
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- Figure 4. 75-50 and 50-25 SES-Achievement Gaps, Birth Cohorts 1954-2001 Notes: 75-50 SES-achievement gap: achievement difference between the students in the top quartile and the bottom half of the SES distribution. 50-25 SES-achievement gap: achievement difference between the students in the top half and the bottom quartile of the SES distribution. See Figure 2 for data and methods.
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- Figure 5. Achievement Levels of Younger and Older Students, Birth Cohorts 1954-2001 Notes: Average student achievement. Sample: 1954-2001 birth cohorts, all surveys, all subjects, all students.
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- Figure 7. SES-Achievement Gaps among White and Black Students Separately, Birth Cohorts 1961-2001 Notes: Achievement difference between the students in the top and bottom quartiles of the SES distribution (75-25 SES-achievement gap), by race. Sample: 1961-2001 birth cohorts, LTT-NAEP and Main-NAEP surveys, math and reading, white and black students. See Figure 2 for data and methods with national (common) SES distribution. White White White White Black Black Black Black 0 .25 .5 .75 1 1.25 1.5 1.75 2
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- Figure A1. Estimated 90-10 Income-Achievement Gaps from High-quality Surveys, Birth Cohorts 1961-2005 Panel A: Math Panel B: Reading Notes: Replication of the Reardon (2011b) analysis of the 90-10 income-achievement gap using only high-quality surveys, birth cohorts 1961-2005. See Table A5 for acronyms. Figure A2. Achievement Trends of the Top and Bottom Quartile in PISA based on PISA’s ESCS Index and our SES Index by Test Year Notes: U.S. student population in PISA. Each point represents roughly 400-700 students. Mean scores for the top and bottom quartiles in each index were averaged across math, reading, and science.
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- Figure A3. Trend in the SES-Achievement Gap with Confidence Interval, Birth Cohorts 1961-2001 Notes: Achievement difference between the students in the top and bottom quartiles of the SES distribution (75-25 SES-achievement gap). See Figure 2 for details. 0 .25 .5 .75 1 1.25 1.5 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 birth year 95% CI Fitted values Figure A4. LTT-NAEP SES-Achievement Gaps and Overall Achievement Dispersion Panel A: Math Age 13 Panel B: Reading Age 13 (continued on next page) Figure A4. (continued) Panel A: Math Age 17 Panel B: Reading Age 17 Notes: SES 75-25: achievement difference between the students in the top and bottom quartiles of the SES distribution. 75-25: overall achievement difference between the students at the 75th and 25th percentiles of the achievement distribution. Normalized achievement is measured in standard deviations (of the test closest to 2000).
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- Figure A5. Main-NAEP SES-Achievement Gaps and Overall Achievement Dispersion Panel A: Math Panel B: Reading Notes: SES 75-25: achievement difference between the students in the top and bottom quartiles of the SES distribution. 75-25: overall achievement difference between the students at the 75th and 25th percentiles of the achievement distribution. Normalized achievement is measured in standard deviations (of the test closest to 2000).
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- Figure A6. TIMSS SES-Achievement Gaps and Overall Achievement Dispersion Panel A: Math Panel B: Science Notes: SES 75-25: achievement difference between the students in the top and bottom quartiles of the SES distribution. 75-25: overall achievement difference between the students at the 75th and 25th percentiles of the achievement distribution. Normalized achievement is measured in standard deviations (of the test closest to 2000).
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- Figure A7. PISA SES-Achievement Gaps and Overall Achievement Dispersion Panel A: Math Panel B: Reading (continued on next page) Figure A7. (continued) Panel C: Science Notes: SES 75-25: achievement difference between the students in the top and bottom quartiles of the SES distribution. 75-25: overall achievement difference between the students at the 75th and 25th percentiles of the achievement distribution. Normalized achievement is measured in standard deviations (of the test closest to 2000).
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- He uses a quadratic equation to estimate the trend for these SES-achievement gaps by subject over the entire time period and a linear equation to estimate the trend between 1974 and 2001. He finds that the “achievement gaps [between those at the 90th and the 10th percentiles of the income distribution] among children born in 2001 are roughly 75 percent larger than the estimated gaps among children born in the early 1940s†(p. 95).
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- Home possessions. To create ESCS, the OECD uses an index of home possessions (homepos) which is “a summary index of all household and possessions items†(OECD (2017b)).
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- If the income gap had truly increased, it should be evident in these two intertemporally linked surveys. But, at roughly 1.3 s.d., the average income-achievement gap in math and data, argue that these SES-achievement gaps are comparable to those for later ages in the other surveys because gaps do not change much over the school years. 47 The point estimates are estimated from observation of the points displayed in Reardon (2011b), Figures 5.1 and 5.2. Reardon and Portilla (2016) provide estimated gaps from the three ECLS surveys. 48 Household income is measured in the same way in the two surveys, and the non-response rate for NLSY97 is 3 percent, about the same as the 2 percent for NLSY79.
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- In TIMSS, it is twenty in the two waves of the 1990s and between eleven and thirteen in the subsequent four waves. In PISA, it is 38 in 2000, 28 in 2003, and between 44 and 46 in the 35 Because some home possessions variables are missing for some students, we also considered computing homepos as a ratio of owned items to known items. In this case, homepos would be the sum of items possessed divided by the number of non-missing items. We did not make this adjustment, as it had a slightly lower correlation with the ESCS index. A4 subsequent four waves (all reported numbers refer to the sum of possible item counts across the dichotomous and categorical questions; see Appendix Table A4 for examples).36 Construction of the index. Using homepos and hisced, we simply follow the ESCS construction process of performing PCA and assigning each student the first principal component as a composite score.
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- It is possible to use two subsets of Reardon’s data to investigate the potential impact of testing artifacts on the trend results. The first set of surveys relying on the same testing, NLSY79 and NLSY97, was administered to cohorts born as early as 1961 and as recently as 1981, a twenty-year interval.48 The second set, ECLS-K, ECLS-B, and ECLS-K2010, provides information on income and achievement for cohorts born as early as 1993 and as late as 2005, a twelve-year interval. Together, these two sets of studies overlap nearly half (28 of 59 years) of the entire time span covered by Reardon (2011b) and over half (15 of 26 years) of the period between 1974 and 2001 when Reardon is more confident of the accuracy of estimated gap growth, identified as at least “30 to 40 percentâ€.
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- National Longitudinal Study of 1972 (NLS) The National Longitudinal Study of 1972 was an early survey conducted by the National Center for Education Statistics. It was designed to follow a sample of high-school seniors of the Class of 1972 into the labor market and college. Like Talent, its parental-income measure came from sampling the students, who place estimated income into one of ten categories.40 Twentyone percent of the respondents chose not to respond to this question.
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- National Longitudinal Study of Adolescent to Adult Health (Add Health) Add Health contains no math achievement data, but the study contributes over a third of the post-1970 data points used by Reardon to estimate the trend in the reading gap. The observations cover students at the ages of 13 through 18 born between 1978 and 1983. The survey has been used for a wide variety of studies, but grades and GPA are the primary school outcome measures. As Rees and Sabia (2010) note, “the Adolescent Health study did not administer formal achievement tests such as are available in the National Education Longitudinal Survey of 1988.†Instead, it contains the Peabody Picture Vocabulary Test (PPVT), a commonly used test of receptive vocabulary. It is described on the NLSY79 website (which used this test along with reading and math achievement assessments) as follows: “The PPVT-R [an updated version of the original] consists of 175 stimulus words and 175 corresponding image plates.
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- percentiles of the achievement distribution. All tests administered by LTT-NAEP, Main-NAEP, PISA, and TIMSS. 1954-2001 birth cohorts, all subjects, all students. Normalized achievement is measured in standard deviations (of the installment of the respective test series closest to 2000). Each marker indicates years where there are one or more underlying observations.
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- Perna, Laura W. 2006. "Studying College Access and Choice: A Proposed Conceptual Model." In Higher Education: Handbook of Theory and Research, edited by John C. Smart. Dordrecht: Springer Netherlands: 99-157.
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- Peterson, Paul E. 2010. Saving schools: From Horace Mann to virtual learning. Cambridge, MA: Belknap Press of Harvard University Press.
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- Project Talent Talent, the earliest survey, provides estimated gaps for four cohorts born in 1942-1945. It uses student-provided estimates of family income, employing five income categories.39 While there are questions about the sampling in the Talent survey, the largest concerns relate to nonresponse rates to the question concerning family income. No less than 54 percent of the freshmen, 50 percent of the sophomores, 45 percent of the juniors, and 39 percent of the seniors chose not to “guessâ€â€”the word used in the survey—the answer to the family income question. For the early Talent cohorts born in the early forties, Reardon reports income-achievement gaps in reading and math of approximately 0.75 s.d. Only Prospect, which has its own measurement problem (see below), reports gaps of a similarly low magnitude.
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- Putnam, Robert D. 2015. Our kids: The American dream in crisis. New York: Simon & Schuster.
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- Reardon (2011b) himself expresses concern “that the trend in the estimated gaps for the earliest cohorts, those born before 1970, is not as accurately estimated as the later trend. … Family income was reported by students rather than by a parent … [and they] are school-based samples of students in high school [that] exclude dropouts, who are disproportionately lowincome and low-achieving†(pp. 95-96). He is more confident that the trend has shifted upward for cohorts born between 1970 and 2001. Between 1974 and 2001, “the income achievement 38 Issues related to extrapolating the observed SES percentiles are discussed in Appendix C and present an additional component of measurement error.
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- Reardon, Sean F. 2011a. "Appendix to: The widening academic achievement gap between the rich and the poor: New evidence and possible explanations." (mimeo) Stanford, CA: Stanford University.
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- Reardon, Sean F. 2011b. The widening academic achievement gap between the rich and the poor: New evidence and possible explanations. In Whither Opportunity? Rising Inequality, Schools, and Children's Life Chances, edited by Greg J. Duncan and Richard J. Murnane. New York: Russell Sage Foundation: 91-116.
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- Reardon, Sean F., and Ximena A. Portilla. 2016. "Recent Trends in Income, Racial, and Ethnic School Readiness Gaps at Kindergarten Entry." AERA Open 2, no. 3: 1-18.
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Rivkin, Steven G., and Finis Welch. 2006. "Has school desegregation improved academic and economic outcomes for blacks?" In Handbook of the Economics of Education, edited by Eric A. Hanushek and Finis Welch. Amsterdam: North Holland: 1019-1049.
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Saez, Emmanuel, and Gabriel Zucman. 2016. "Wealth inequality in the United States since 1913: Evidence from capitalized income tax data." Quarterly Journal of Economics 131, no. 2 (May): 519-578.
- Share of high-SES students scoring at or below low-SES students Share of high-SES students scoring at or below low-SES students Low-SES students by score percentile Low-SES students by score percentile Figure 12. Ordinal Analysis of Change in the SES-Achievement Distributions, TIMSS 1995 and 2015 Panel A: Bottom quarter vs. top quarter of the SES distribution Panel B: Bottom quarter vs. top half of the SES distribution Notes: Horizontal axis: students in the low-SES group lined up along their math achievement distribution. Vertical axis: share of students in the high-SES group who score at or below the respective math achievement of the low-SES percentile. Share of high-SES students scoring at or below low-SES students Share of high-SES students scoring at or below low-SES students Low-SES students by score percentile Low-SES students by score percentile
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- Sirin, Selcuk R. 2005. "Socioeconomic Status and Academic Achievement: A Meta-Analytic Review of Research." Review of Educational Research 75, no. 3 (September): 417-453.
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- Six of his twelve surveys are plagued with serious problems and clearly do not meet current scientific quality standards. Importantly, these surveys introduce systematic measurement error into the subsequent trend estimation based upon them. From the information provided in A8 Reardon (2011a, 2011b) and the online descriptions, these surveys do not provide reliable data points but nonetheless have a decided influence on the shape of the estimated trend line.
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Slesnick, Daniel T. 1993. "Gaining Ground: Poverty in the Postwar United States." Journal of Political Economy 101, no. 1 (February): 1-38.
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- Table A1. Surveys and Subjects by Test Date, 1971-2015 LTT-NAEP Main-NAEP PISA TIMSS 13-year-olds 17-year-olds 8th graders 15-year-olds 8th graders Math Reading Math Reading Math Reading Math Reading Science Math Science 1971 X X 1973 X X 1975 X X 1978 X X 1980 X X 1982 X X 1986 X X 1988 X X 1990 X X X X X X 1991 1992 X X X X X X 1993 1994 X X X X X 1995 X X 1996 X X X X X 1997 1998 X 1999 X X X X X X 2000 X X X X 2001 2002 X 2003 X X X X X 2004 X X X X 2005 X X 2006 X X 2007 X X X X 2008 X X X X 2009 X X X X X 2010 2011 X X X X 2012 X X X X X X X 2013 X X 2014 2015 X X X X X X X Notes: LTT-NAEP math data for 1973 are available for levels but not gaps.
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- Table A3. Racial SES Distribution over Time Test year Birth year Percent white Percent black Top 25 percent of aggregate SES 1978 1961 27 8 2012 1995 33 14 Bottom 25 percent of aggregate SES 1978 1961 20 48 2012 1995 14 31 Notes: Data source: LTT-NAEP.
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- Table A5. Acronyms for Sources of Data Analyzed by Reardon (2011b) Acronym Survey Talent Project Talent NLS National Longitudinal Study of 1972 HS&B High School and Beyond NLSY79 National Longitudinal Study of Youth 1979 NELS National Education Longitudinal Study Prospects The Congressionally Mandated Study of Educational Growth and Opportunity Add Health National Longitudinal Study of Adolescent to Adult Health NLSY97 National Longitudinal Study of Youth 1997 ELS Education Longitudinal Study SECCYD Study of Early Child Care and Youth Development ECLS-K Early Childhood Longitudinal Study-Kindergarten, 1997 ECLS-B Early Childhood Longitudinal Study, Birth Cohort Table A6. Correlation between SES Index and Family Income in ELS SES index 1987 income 1991 income Permanent income SES index 1 0.51 0.59 0.66 1987 income 0.51 1 0.75 0.94 1991 income 0.59 0.75 1 0.94 Permanent income 0.66 0.94 0.94 1 Notes: Data source: 1988 Education Longitudinal Study (ELS).
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- Taverise, Sabrina. 2012. "Education Gap Grows Between Rich and Poor, Studies Say." New York Times: February 9.
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- The correlation between the SES index and reported family income is displayed in Appendix Table A6. The two variables are strongly but not perfectly correlated. Interestingly enough, at 0.66 the SES index is more highly correlated with the average of the annual earnings estimates obtained in 1987 and 1991 than with either of the annual estimates, suggesting that the average is a better measure of permanent income, a concept similar to socio-economic status.37 37 Using 2002 ELS data, where family income is available only on the base year survey (2001 income), the correlation between the SES index and reported income is 0.503.
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- The inherent difficulties with this extrapolation can be illustrated with our SES-achievement data. Figure 8 in the text shows the SES histogram for Main-NAEP in 1990, incorporating student data on parental education and home-possession items. The top panel of Appendix Figure A10 presents this SES distribution in terms of the achievement distribution corresponding to the SES percentiles that are observed. The bars in the figure indicate the percentile ranges of the SES distribution covered by the categorical elements of the SES distribution along with the average achievement in the category. For example, the highest SES category identified in the data covers the top 26.5 percent of the distribution and has an average achievement of 278 scale points.
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- The PISA Index of Economic, Social, and Cultural Status (ESCS) Across the different PISA waves, the OECD provides a measure of socio-economic status called the PISA Index of Economic, Social, and Cultural Status (ESCS). The ESCS, according to the PISA 2015 Technical Report, is “a composite score built by the indicators parental education (pared), prestige of the occupation of the parent with the highest occupational ranking (hisei), and home possessions (homepos) including books in the home via principal component analysis (PCA)…. The rationale for using these three components was that socio-economic status has usually been seen as based on education, occupational status and income. As no direct income measure has been available from the PISA data, the existence of household items has been used as a proxy for family wealth†(OECD (2017b)).
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- Those lower estimations could easily be due to serious measurement error driven by a test of reading skills that does not require the student to read. 44 https://www.nlsinfo.org/content/cohorts/nlsy79-children/topical-guide/assessments/peabody-picturevocabulary -test-revised [accessed January 15, 2020]. A11 Study of Early Child Care and Youth Development (SECCYD) Although Reardon says his surveys are nationally representative, SECCYD is not.
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- Trends from Two Sets of Psychometrically Linked Surveys One concern with the overall approach in Reardon (2011b) is that it compares test score gaps (measured in standard deviations) across a large number of structurally different tests. This kind of comparisons of trends across tests can give incorrect inferences even about the direction of change (Ho (2009); Holland (2002)). The problems of such comparisons are particularly severe when the tests have different designs and scales.
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- Trends in the SES-Achievement Gap from High-quality Surveys in Reardon (2011b) With reliance on SES-achievement gap data constructed from different birth cohorts found in large-scale surveys, it is natural to want to include as many different survey data sets as possible. As delineated above, however, six of Reardon’s choices do not meet current scientific quality standards. The three early surveys rely upon student reports of household income (Talent, NLS, and HS&B); three later surveys lack reliable test information and/or pertain to non-representative samples (Prospects, Add Health, and SECCYD). These error-prone data points yield gap estimates that are biased downward. Since they tend to relate to early birth cohorts, they distort the trends that are estimated when combined with higher-quality data available later.
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- U.S. Department of Education. 2013. Digest of Education Statistics 2012. Washington, DC: National Center for Education Statistics.
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- U.S. Department of Health and Human Services. 2018. NICHD Study of Early Child Care and Youth Development: Phase I, 1991-1994: Inter-university Consortium for Political and Social Research.
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- Washington, D.C. National Center for Education Statistics. 2013. The Nation's Report Card: Trends in Academic Progress 2012. Washington, DC: Institute of Education Sciences.
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- We estimate a revised trend line using Reardon’s data that restricts observations of gaps to the high-quality surveys in Reardon (2011b). These cover the birth cohorts 1961-2001 (NLSY79 [two cohorts], NELS, NLSY97 [three cohorts], ELS, ECLS-K, and ECLS-B). We supplement these limited observations with an additional observation added from Reardon and Portilla (2016) who update the SES-achievement gap analysis to include the ECLS-K2010.46 (The 45 https://www.icpsr.umich.edu/icpsrweb/DSDR/studies/21940/versions/V6/summary [accessed 2/1/2020]. 46 While the three ECLS data sets are included among the high-quality surveys, their outcome data are tests of kindergarten readiness in math and reading. Reardon and Portilla (2016), who specifically analyze trends in these A12 ECLS-K2010 observation became available subsequent to the publication of Reardon (2011b) and extends the birth cohorts available to 2005).
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- Weissmann, Jordan. 2012. "Occupy Kindergarten." Atlantic: Feb. 11.
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Wilson, William Julius. 2011. ""The Declining Significance of Race": Revisited & Revised." Daedalus 140, no. 2 (Spring): 55-69.
- Younger students are those between ages 13 and 15 or in 8th grade, depending on the test. For expositional purposes, younger students are referred to as 14-year-olds. Older students are those aged 17 or in 12th grade, depending on the test. See Figure 1 for data and methods. 17-year-olds 14-year-olds -.3 -.2 -.1 0 .1 .2 .3 Mean achievement 1950 1960 1970 1980 1990 2000 Birth year Figure 6. Achievement Gaps for Subsidized Lunch Eligibility and Black-White Achievement Gaps, Birth Cohorts 1954-2001 Notes: Samples: For free and reduced-price lunch, 1982-2001 birth cohorts, Main-NAEP surveys, math and reading, all students; for white-black gap, 1954-2001 birth cohorts, LTT-NAEP and Main-NAEP surveys, math and reading, black and white students. See Figure 2 for data and methods. Data on free and reduced-price lunch eligibility are only available for Main-NAEP tests, starting with the 1982 birth cohort.
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