The Mean Is Not Enough: Using Quantile Regression to Examine Trends in Asian–White Differences Across the Entire Achievement Distribution
by Spyros Konstantopoulos - 2009
Background: In recent years, Asian Americans have been consistently described as a model minority. The high levels of educational achievement and educational attainment are the main determinants for identifying Asian Americans as a model minority. Nonetheless, only a few studies have examined empirically the accomplishments of Asian Americans, and even fewer studies have compared their achievement with other important societal groups such as Whites. In addition, differences in academic achievement between Asian Americans and Whites across the entire achievement distribution, or differences in the variability of the achievement distribution, have not been documented. However, this is an important task because it provides information about the achievement gap for lower, average, and higher achieving students.
Purpose: The present study examines differences in academic achievement between Asian American and White students in average scores (e.g., middle of the achievement distribution), in extreme scores (e.g., the upper and the lower tails of the achievement distribution), and in the variability of the achievement distribution. The main objective of this study is to determine the achievement gap between Asian American and White students in the lower and upper tails of the achievement distribution to shed some light on whether the achievement gap between the two groups varies by achievement level.
Participants: I use data from four national probability samples of high school seniors to examine Asian American–White differences in achievement from 1972 to 1992. Specifically, I used data from the base year of the NLS (NLS:72), the base year of the High School and Beyond (HSB) survey of 1980, the first follow-up of the HSB survey in 1982 (that is HSB:80, HSB:82), and the second follow-up of NELS (NELS:92).
Research Design: The study is correlational and uses quantile regression to analyze observational data from the 1970s, 1980s, and 1990s.
Findings: The findings indicate that the Asian American–White gap is more pronounced in mathematics than in reading. In 1992, the gap in the middle and the upper tail of the mathematics distribution is greater than one third of a SD, which is not a trivial gap in education. In reading, the gap is overall smaller, and nearly one third of a SD in 1992 in the upper tail (favoring Asian students).
Conclusions: It appears that Asian American students are indeed a model minority group that performs not only at similar levels but also at higher levels than the majority group, especially among high achievers in mathematics (and reading in the 1990s).
Over the last two decades, Asian Americans have been consistently described as a model minority. This praise stems mainly from what is perceived or documented as their remarkable success in educational achievement, educational attainment, and occupational status. In particular, the high levels of educational achievement and educational attainment are typically considered the main determinants for identifying Asian Americans as a model minority.
Nonetheless, it is noteworthy that only a few studies have examined empirically the accomplishments of Asian Americans, and even fewer studies have compared their achievement with other important societal groups such as Whites. Specifically, no study thus far has examined empirically differences in academic achievement between Asian Americans and Whites across the distribution of achievement test scores, or differences in the variability of the achievement distributions, and how these differences have changed over time. This is an important task because it will provide evidence about the race/ethnic gap for lower, average, and higher achieving students.
The present study examines differences in academic achievement between Asian American and White students in average scores (e.g., middle of the achievement distribution), in extreme scores (e.g., the upper and the lower tails of the achievement distribution), and in the variability of the achievement distributions using national probability samples of high school seniors. The main objective of this study is to determine the achievement gap between Asian American and White students in the lower and upper tails of the achievement distribution. Although Asian American students have, on average, comparable achievement with that of White students, according to recent reports by the National Assessment of Educational Progress (NAEP), the race/ethnic gap for higher and lower achieving students has not been well documented. It is possible, for example, that although the achievement gap between the two groups is not that visible on average, it may be considerable for higher and lower achievers. In addition, the gap in the tails of the achievement distribution may be qualitatively different. That is, Asian Americans may outperform their White peers at higher achievement levels, whereas Whites may outperform their Asian peers in lower achievement levels.
Note that in this article, I treat the Asian American and White student groups as general race/ethnicity categories because I am interested in examining the achievement gap between Asian American and White students as whole groups. This is common practice in research on group differences in achievement or earnings, in which the groups of interest typically are defined generally as whole groups. Examples in education include the work by Hedges and Nowell (1995, 1999), in which the authors treated Black, White, and male and female students as general groups. Examples in economics include the work by Card and Krueger (1992) on the BlackWhite gap in earnings. In addition, reports by the NAEP, the Institute of Education Sciences, and the National Center of Education Statistics (NCES) typically present findings about the achievement gap using general categories for race/ethnic or gender groups (e.g., Blacks, Hispanics, Whites, Asians, males, females). I acknowledge that the composition of Asians and Whites most likely changed over time and that this may affect the estimates of the achievement gap between the two groups in this study. This is possibly a limitation of the study that I discuss in later sections.
Asian American students have typically demonstrated high levels of academic achievement compared with students of other race and ethnic groups. Some studies have reported that Asian Americans perform academically as well as or better than White students on average (Mau, 1995; Maxwell, 2007) and that they are overrepresented among high achievers (Konstantopoulos, Modi, & Hedges, 2001) and underrepresented among low achievers (Williams, 1992). Evidence from the NAEP suggests that Asian American and White fourth- and eighth graders have similar average achievement that is much higher than that of Black and Hispanic students. According to the U.S. Bureau of the Census (1996), nearly 40% of Asian Americans age 25 and older have a college degree or higher. Such investments in human capital formation typically yield sizable economic and social rates of return (Becker, 1964). In addition, previous work has documented that Asian Americans are overrepresented in high-status occupations compared with other minority groups (see Flynn, 1991). Other studies however, have reported that Asian Americans have levels of achievement comparable with other student groups (Wong, Lai, Nagasawa, & Lin, 1998).
High levels of family socioeconomic status (SES) have been consistently found to be significantly associated with high levels of academic achievement for all students since the Coleman Report (Coleman et al., 1966; White, 1982; White, Reynolds, Thomas, & Gitzlaff, 1993). Previous work that examined the performance of Asian Americans has also attributed their success to observable characteristics such as high family SES and high rates of intact families (Hawkins, 1993; Hurh & Kim, 1989; Kao & Thompson, 2003). For example, Hawkins found that once SES variables such as parental education and family income are taken into account, differences in achievement between Asian Americans and other groups become insignificant. In the same vein, Kao and Thompson argued that one major advantage in Asian Americans accomplishments is their high parental educational levels. Other researchers have attempted to identify parental practices that might explain the higher levels of Asian Americans in academic achievement and attainment (Mau, 1997; Sue & Okazaki, 1990). For example, educational success is viewed in Asian families as the best means for upward mobility. Finally, recent work that used representative samples of students has documented significant differences in average achievement between Asian Americans and Whites that favor Asian students (Kao, 1995). However, Kao found that differences in family background explain group differences in achievement scores. This finding provides additional support to the notion that SES and family structure are important predictors of Asian American students achievement.
The present study examines whether the achievement gap between Asian American and White students varies by achievement level. Although overall, Asian American students are considered high achievers, it is not obvious that their achievement levels are similar to those of White students for all types of students (e.g., average, low, and high achievers). I address this issue using methods that allow the assessment of the race/ethnic achievement gap in the middle and in the extremes (upper and lower tails) of the achievement distribution, and in achievement variability. Determining the Asian AmericanWhite gap at different quantiles across the achievement distribution will provide a much clearer picture of the race/ethnic achievement gap. Specifically, it will shed light on whether the race/ethnic achievement gap is small and uniform for all kinds of students (average, low, and high achievers), or whether the achievement differences between the two groups vary by achievement level. In addition, determining differences in the variability of the achievement distribution for Asian American and White students will help to better explain the achievement gap between the two groups in the tails of the achievement distribution (see e.g., Hedges & Nowell, 1995, 1999).
THE IMPORTANCE OF THE TEST SCORES
Although achievement test scores are often used as indices of somewhat different constructs in social science research, their importance in individuals advancement and prosperity is indisputable. Whether achievement scores are regarded as a proxy of ability, intellectual functioning, learning, or skill, their significant role is widely acknowledged. Since Coleman et al. (1966), achievement scores have become the official measure of school outputs and have been used as indicators of learning and school quality. In the human capital model, achievement scores also have a pivotal role because they are hypothesized to affect educational and occupational attainment, as well as labor market performance. In the economic literature, achievement scores have been shown to affect individuals earnings even after controlling for social class (Constant & Konstantopoulos, 2003; Murnane, Willett, & Levy, 1995).
There has been a long debate among social scientists with respect to whether test scores measure achievement or ability, and some researchers have argued that such distinctions are rather difficult to make (Anastasi & Urbina, 1997). Nonetheless, there is a consensus among researchers that test scores are influenced by innate ability (nature) and learning from the environment (nurture; see Neisser et al., 1996). The effects of the environment include experiences from various social conditions, family, and schooling. The relative contribution of such factors in test scores, however, is not empirically demonstrated. Finally, some economists contend that test scores represent a general skill or knowledge of the individual (Heckman, 1995). Regardless of the meaning of test scores, they play a significant role in our society. For example, college and graduate school admissions and financial aid, as well as employment opportunities and labor market success, are partially determined by individuals performance in achievement tests. Hence, detecting and discussing differences in test scores for important population groups is crucial for determining the improvement of student groups.
LIMITATIONS OF PREVIOUS RESEARCH
The study of the social distribution of academic achievement has been of great interest in the social science literature. However, the quality of the empirical evidence has not always been satisfactory. First, the samples employed in various studies on group differences in achievement are typically not representative of a well-defined corresponding population. For example, the majority of the studies have used convenient or localized samples, and hence, the generality of the results to national populations is questionable. This is a concern that relates to the external validation of the findings (Cook & Campbell, 1979). A related issue is selection bias, and although the extent of the potential bias in these samples is unknown, it is conceivable that the estimates reported in studies that use convenient samples might be very different from their true population parameters. In other words, it is likely that some of the results reported in these studies are positively or negatively biased.
Nonetheless, there are some notable exceptions: for example, some early studies by Coleman et al. (1966) and Osborne (1982), who used data from the National Longitudinal Study of the High School Class of 1972 (NLS:72). More recent exceptions include studies by Bock and Moore (1986) and Herrnstein and Murray (1994), who used data from the National Longitudinal Study of Youth (NLSY); Grissmer, Kirby, Berends, and Williamson (1994), who also used NLSY data and data from the National Education Longitudinal Study (NELS); Kao (1995), who used NELS data; Campbell, Reese, OSullivan, and Dossey (1996), who used data from the National Assessment of Educational Progress (NAEP); and Hedges and Nowell (1999), who used data on achievement tests from all representative samples of high school seniors from 1965 to 1996 (including NAEP data).
Another shortcoming of prior studies is that they typically document average group differences in achievement using regular regression methods. Unfortunately, such methods do not provide any information on group differences at different points of the achievement distribution. For example, group differences in the tails of the achievement distribution might be qualitatively different from differences in the middle of the distribution. Such information is important for identification of low and high achievers within national population groups, especially for minority groups. That is, low-achieving Asian American students may be at a disadvantage compared with their White counterparts. A notable exception are the studies by Hedges and Nowell (1995, 1999), who documented group differences in achievement across the achievement score distribution. However, in their studies, Hedges and Nowell used different indexes to examine group differences in the middle and the tails of the achievement distribution. The authors used standard deviation units when reporting average group differences, and number ratios to determine the over- or underrepresentation of each group in the tails of the distribution. The current study uses the same index (standard deviation units) for group differences in achievement across the entire distribution and hence makes the results across different quantiles of the achievement distribution comparable.
Moreover, the majority of the previous studies have not examined group differences in the variability of the achievement distribution. Again, a notable exception is the studies by Hedges and Nowell (1995, 1999). Differences in variability can provide important information regarding group differences in achievement and a clearer definition of the distribution of achievement scores. Consider, for example, two groups and hence two distributions of achievement scores that have comparable means but different variances. The group with the higher variance will have more individuals in the low- and high-achieving categories mainly because of the difference in the variance.
The present study addresses the caveats of the previous research illustrated above by employing national probability samples of high school seniors and quantile regression methods that allow examining the achievement gap between the two race/ethnic groups across the entire distribution of achievement scores. In particular, I used information from four national probability samples of high school seniors to examine Asian AmericanWhite differences in achievement from 1972 to 1992. I used data from the base year of the NLS (NLS:72), the base year of the High School and Beyond (HSB) survey of 1980, the first follow-up of the HSB survey in 1982 (that is HSB:80, HSB:82), and the second follow-up of NELS (NELS:92). As mentioned earlier, the main objective of this article is to examine the Asian AmericanWhite gap in achievement scores, conducting cross-sectional analyses across the entire achievement distribution. I examined the unadjusted achievement gap between the two groups at each time point and then determined the effects of important covariates such as gender, SES, family structure, family size, and language spoken at home on the Asian AmericanWhite achievement gap at different quantiles and for each survey. Because I employd national probability samples, the results are more resilient to threats from selection bias and should have higher external validity (generalizability). The analyses involve statistical methods that provided estimates of the Asian AmericanWhite achievement gap at various quantiles (10th, 25th, 50th, 75th, and 90th) of the achievement distribution.
Data from four major surveys conducted over the last 30 years were used in the study. All these surveys tested nationally representative samples of students in America. In all data sets, I used the 12th-grade samples, and thus I investigated the Asian AmericanWhite differences in academic achievement of high school seniors who participated in each survey. All variables and coding procedures used were similar across all data sets.
The NLS High School Class of 1972 (NLS:72) is a national probability sample of high school seniors designed to represent all 12th graders enrolled in public or private American high schools in the spring of 1972. Of the 16,860 seniors, a sample of 15,800 students who completed a 69-minute six-part battery measuring both verbal and nonverbal skills was used in the analyses. Only the reading and mathematics achievement test scores were used in these analyses. The reading portion required comprehension, analysis, and interpretation of information in the selected passages. In the mathematics achievement test, students were asked to indicate whether one of two quantities is greater than, less than, or equal to the other, or if the relationship between the two cannot be determined from the information provided. Specific knowledge of algebra, trigonometry, or geometry was not required for the math section.
In the spring of 1980, two cohorts of 10th- and 12th-grade students enrolled in public and private schools were surveyed for the HSB study (HSB:80). The sophomores were resurveyed in 1982, when they were seniors (HSB:82). I used data from the base year and the first follow-up. The base year sample included 25,069 seniors, and the first follow-up, 26,216 seniors. Students completed a 68-minute test battery similar in format to the battery used in NLS:72 but with slightly different content. I used reading and mathematics achievement test scores in both surveys.
The NELS of the Eighth Grade Class of 1988 (NELS:88) used a two-stage national probability sample of 24,599 eighth graders enrolled in public and private schools in 1988. These students were followed and resurveyed in 1992, when they were seniors. The sample I used consisted of 12,921 seniors of the second follow-up (1992). Students completed an 85-minute battery of four cognitive tests. The structure of the reading and mathematics tests, which were used in these analyses, were similar to those used in NLS:72 and HSB:80 and 82.
In all four surveys, I used reading and mathematics test scores as the dependent variables. The structure of reading and mathematics tests was comparable across all surveys (see following section). To put test scores from different time points in one common scale, I standardized them and constructed cross-sectional comparisons within each survey. Under the assumption that these tests are linearly equitable, a rather reasonable assumption for tests with comparable structure, standardization can provide reasonable indexes of group differences over time. In addition, linear test equating is hypothesized to perform well in large-scale testing situations in which the main objective is comparing groups of individuals (Kolen & Brennan, 1995; Petersen, Cook, & Stocking, 1983). I discuss the potential caveats of linear equating across test measures in the following section.
The main independent variable is race/ethnicity. I created a binary variable to examine the differences between Asian American and White students in achievement. Specifically, I included in the quantile regression a dummy for Asian American students, with Whites being the reference group. The coefficient of the Asian American category indicates the average difference in achievement between the two groups at various quantiles. The standardization of the outcome indicates that the regression coefficient of the Asian American category is expressed in standard deviation (SD) units. I also included predictors such as gender (female = 1, male = 0), SES (including information on income and parental educational attainment), language spoken at home (English vs. other language), family structure (intact vs. alternative-type family structures) and family size (number of siblings) as covariates to examine their effects on the Asian AmericanWhite achievement gap. Missing data dummies of all predictors of interest were also included in the regression to adjust for missing data effects. For comparability purposes, all independent variables were coded similarly, and I used the same set of explanatory variables in the quantile regression models across all data sets. I also included in the models interactions between race/ethnicity and the covariates to take into account possible differential effects (see analysis section).
COMPARABILITY OF MEASURES ACROSS SURVEYS
All data sets that were used in this study were acquired from three major studies (NLS, HSB, and NELS) that are part of the National Education Longitudinal Studies program instituted by NCES. One objective of this longitudinal program was to represent the educational experiences of our students in the 1970s, 1980s, and 1990s. NCES reports contend that cross-sectional time-lag comparisons for high school seniors in 1972, 1982, and 1992 are possible and that these data can be regarded as a series of repeated cross-sections of high school seniors (see Green, Dugoni, & Ingels, 1995). Although the sample designs of all three studies are similar, the achievement tests are not identical and may not be directly comparable. However, all achievement tests intended to capture the same domains of academic achievement (e.g., mathematics, reading) and tap parallel abilities (see Glick & White, 2003; Hedges & Nowell, 1995, 1999). Some NCES reports indicate that there were common items in NLS and HSB, and HSB and NELS, for mathematics and reading, and hence there is some content comparability of the achievement measures across the different surveys (see Green et al., 1995; Rock, Hilton, Pollack, Ekstrom, & Goertz, 1985).
The use of equating methods that put mathematics and reading scores for high school seniors in 1972 and 1982 on a common scale have been previously demonstrated (see Rock et al., 1985). Rock et al. concluded that comparisons of test scores in NLS and HSB can reasonably indicate change along the same dimension over time. In this study, I used linear equating methods (e.g., creating z scores) to put mathematics, reading, and science scores on a common scale (see Glick & White, 2003; Hedges & Nowell, 1995, 1999).
Of course, the standardization creates comparable indexes of achievement across surveys under the assumption that the tests are linearly equitable. Previous research has documented that, even though typically three-level item response theory (IRT) equating methods lead to greater stability of equating results, linear equating also performs well (when tests are comparable) in large-scale testing settings and is a good practical alternative to more complex methods (see Petersen et al., 1983; Petersen, Kolen, & Hooever, 1989; Petersen, Marco, & Stewart, 1982). Because previous work has indicated some content comparability in NLS and HSB, and HSB and NELS for achievement measures such as mathematics and reading (see Rock et al., 1985; Green et al., 1995), under the assumption of reasonable comparability, linear equating should work reasonably well. In addition, Green et al. (1995) argued that it is acceptable to use data from NLS, HSB, and NELS to examine changes in achievement gaps between important groups in the student population over time. Linear equating is also widely used by commercial test publishers, and it is known to provide reasonably good results. Further, linear equating methods have also been routinely used in social science research (see, e.g., Glick & White, 2003; Hedges & Nowell, 1995, 1999; Morgan, 1996).
Nonetheless, although NLS, HSB, and NELS were designed to be as similar as possible, as Green et al. argued (1995), caution should be exercised in comparing NLS-72, HS&B, and NELS:88 data (p. 125). In addition, a recent report issued by the National Research Council that discussed comparisons among different state and NAEP tests concluded that achieving comparability between different tests with a single linking scale may not be that feasible. Hence, I fully acknowledge the difficulty involved in making comparisons of tests that are not identical and that this is a potential limitation of the present study. I encourage the reader to exercise caution when comparing the results from different surveys. In addition, the items used to construct the independent variables of this study are very similar across all three data sets. I used the same coding methods for all independent variables to achieve comparability for all predictors.
Studies that investigate group differences in achievement have primarily relied on estimation methods such as linear regression or hierarchical linear models. These models typically compute average differences in achievement between groups. It is plausible, however, that group differences in achievement are not uniform across the entire distribution of achievement scores. For example, the race/ethnic achievement gap might be more or less extreme in the tails of the distribution and, in any case, different from the achievement differences observed in the middle of the achievement distribution. Specifically, it is possible that the Asian AmericanWhite achievement gap is wider for high achievers (favoring Asian American students) and reversed for low achievers (favoring White students). Only a couple of studies have examined achievement differences in the tails of the achievement distribution using proportion ratios to illustrate the gender or race achievement gap (Hedges & Nowell, 1995, 1999). However, these studies did not express the group differences in extreme scores in measures comparable with those used to capture average differences in achievement (e.g., standard deviations units). All achievement differences obtained in the present study are expressed in standard deviation units to simplify the interpretation of the estimates.
The analyses are based on a widely used econometric method called quantile regression (see Buchinsky, 1998; Koenker & Bassett, 1978), which allows the estimation of group differences in achievement at various points of the achievement distribution. It also allows the evaluation of the effects of covariates such as gender, SES, family structure, family size, and language spoken at home on the race/ethnic achievement gap at different quantiles of the achievement distribution. I used quantile regression to examine Asian AmericanWhite differences in achievement at different quantiles of the achievement distribution. For either reading or mathematics, it is possible that the Asian AmericanWhite achievement gap is more pronounced in the upper tail of the achievement distribution than in the middle or the lower tail, given that Asian American students are typically overrepresented in the high-achieving categories (Konstantopoulos et al., 2001). First, I examined the group differences in achievement without adjustments for covariates. Second, I investigated the race/ethnic achievement gap net of the effects of gender, SES, family structure, family size, and language spoken at home. Because it is possible that some covariates such as gender, SES, and family structure may have differential effects on the two race/ethnic groups, I also included in the quantile regression equation all possible (two-way) interactions between the covariates and the race dummy variable. This is common practice in the social science literature, especially when examining group differences in earnings (see e.g., Konstantopoulos & Contant, in press).
I am also interested in gauging race differences in the variability of the achievement distribution. It is conceivable that the variance of the achievement distribution for Asian American students is different from the variance of the achievement distribution for Whites. Notice that differences in the variance of the achievement distribution might explain race differences in achievement in the tails of the achievement distribution (see Hedges & Nowell, 1995, 1999). For example, if Asian American and White students have comparable average achievement but the distribution of achievement for White students has a larger variance, then one would expect to find higher proportions of White students in the lower and the upper tails of the achievement distribution. Previous work by Hedges and Nowell (1995) has documented that the achievement distribution of male students is much more spread out than that of female students. To quantify differences in the variance I employed methods discussed by Hedges and Nowell (1995, 1999) and created an index called the variance ratio. This ratio is simply the square of the ratio of the standard deviation of the achievement distribution for one group (e.g., Asian Americans) to that of the achievement distribution of another group (e.g., Whites). A ratio greater than 1 indicates that the variance of the achievement distribution for Asian Americans is larger than that of Whites, whereas a ratio smaller than 1 indicates that the variance of the achievement distribution for Whites is larger.
First, I present the unadjusted (no covariate effects) estimates of the Asian AmericanWhite achievement gap and then the estimates adjusted by covariate effects for reading and mathematics achievement. All coefficients are expressed in SD units. Positive coefficients indicate that Asian Americans performed higher than Whites, whereas negative coefficients indicate that Whites performed higher. The unadjusted estimates of the race/ethnic achievement gap for reading and mathematics are reported in Table 1. The upper panel of Table 1 shows the results for reading, and the lower panel shows the results for mathematics achievement. In reading in the middle of the achievement distribution, the gap was 1/20 of a SD in 1972, favoring Whites. The reading gap increased three to five times in the 1980s and decreased to virtually zero in 1992, indicating that the two groups reached parity in 1992. All estimates at the 50th quantile did not reach statistical significance at the .05 level. The Asian AmericanWhite reading achievement disparity favored White students in the lower tail of the achievement distribution. For example, in 1982 and 1992, the reading achievement gap in the bottom 10% of the achievement distribution was nearly 0.25 SD, favoring Whites, and was statistically significant at the 0.05 level. In 1992, all differences in the lower tail of the reading achievement distribution were negative and significant at the 10th quantile. In the upper tail, with the exception of HSB:80 and NELS:92, all coefficients were virtually zero, indicating that Asian American students performed as well as White students. In contrast with HSB:80, in 1992, all coefficients are positive and significant, and nearly one seventh of a SD, indicating that Asian American students outperformed White students in the upper tail of the reading distribution in the 1990s. In 1980 however, White students outperformed Asian American students by nearly 0.25 SD. Overall, these results indicate that across the entire distribution of reading achievement scores and over time, White students typically perform slightly better than their Asian American peers in the bottom half of the distribution and the top quartile in 1980, whereas Asian Americans outperformed Whites in the top quartile in 1992.
The unadjusted mathematics achievement gap in the middle of the achievement distribution was greater than 0.4 SD in 1972 and 1980, favoring Asian Americans. The gap decreased considerably in 1982 and 1992 to approximately 0.25 SD. Nonetheless, although the achievement difference decreased over time, it was still statistically significant and nontrivial in 1992. The Asian AmericanWhite mathematics achievement disparity followed similar patterns in the upper and lower tails of the achievement distribution. In the lower tail, the achievement gap remained relatively unchanged over time, and in 1992, it was significant and greater than 0.25 SD in the lower tail (10th and 25th quantile), favoring Asian Americans. In the upper tail, the mathematics gap was more pronounced in later years, especially in 1992, when Asian American students performed significantly higher than their White peers in mathematics. The achievement gap in the upper tail was greater than 0.4 SD in 1992 and nearly doubled in 20 years (since 1972). This indicates that over time, higher achieving Asian American students are increasingly more likely to have higher levels of mathematics achievement than Whites. Overall, these results indicate that across the entire distribution of mathematics achievement scores, Asian American students consistently outperformed their White peers.
The adjusted estimates of the achievement gap are reported in Table 2 for reading and mathematics achievement. The structure of Table 2 is identical to that of Table 1. The upper panel of Table 2 summarizes the group differences in reading achievement, controlling for all covariates (except language spoken at home in HSB:80) and two-way interactions between the covariates and the race/ethnicity dummy variable. The estimates for mathematics are summarized in the lower panel of Table 2. In reading, the median-adjusted achievement gap was small and insignificant in 1982 and 1992. In fact, all median estimates were not significantly different from zero. In the lower tail, the adjusted gap was somewhat smaller than the unadjusted gap (except 1980). In the upper tail, Asian American students still have an advantage in 1992, but the achievement gap is statistically significant only at the 75th quantile.
The median mathematics achievement gap adjusted for covariate and differential effects was nearly one SD in 1972 and decreased dramatically to about 0.3 SD in 1992, favoring Asian American students. The estimates in the 1970s and 1980s are large and resemble estimates reported by Hedges and Nowell (1999) on the BlackWhite achievement gap. The results in the upper and lower tails of the mathematics achievement distribution are comparable overall. In 1992, the adjusted achievement gap in the lower tail is overall greater than 0.3 SD, significant, and similar to the unadjusted gap for that year. The estimates of the adjusted achievement gap in the top of the distribution were overall similar to those estimates in Table 1 (unadjusted gap), and significant and greater than 0.3 SD in 1992.
Table 3 reports the variance ratios for Asian American and White students in reading and mathematics. Generally, all estimates are close to one that indicates that the achievement distribution of Asian American students is almost as equally spread out as that of Whites. In 1992, the variance ratios are greater than 1, indicating that the Asian American achievement distribution is becoming more variable over time. Overall differences in the variances of the achievement distributions do not seem to have affected the achievement gap in the tails considerably, because the variance ratios are very close to 1 in the 1970s and 1980s. However, in 1992, the differences in variance may indicate overrepresentation of Asian American students in the upper tail, given that the adjusted median achievement gap in mathematics is considerable in 1992. Indeed, following Hedges and Nowell (1999), I computed number ratios, a ratio of the number of Asian American to White students, and confirmed that Asian American students are somewhat overrepresented in the upper tails in 1992. In addition, the unadjusted and adjusted for covariate and differential effects variance ratios are comparable in magnitude.
Grade 10 analyses
Because the samples used in the analyses include high school seniors, individuals who are not in school at Grade 12 are excluded from the analyses. Hence, it is possible that the 12th-grade samples are selected and the estimates may be biased or different from their true population parameters. If, for each race/ethnic group, the students who drop out are not systematically different from those who stayed in school, then one would expect the potential bias to be close to zero. In this study, to obtain accurate estimates, it is essential that students who drop out within a group (e.g., Asian American) are similar, with respect to achievement, to those who stayed in school within that group, or that the dropout patterns are the same for Asian American and White students. Consider the case in which only the best Asian American students stay in school in Grade 12, whereas all types of White students (average, low, and high achievers) stay in school in Grade 12. This would result in a larger race/ethnic achievement gap in Grade 12 than in Grade 10 (favoring Asian American students) because of selection in the Asian American student population, other things being constant. Fortunately, some of the longitudinal samples provided data that permitted such an investigation of possible selection effects.
One way to examine the effects of possible selection bias empirically is to conduct analyses using samples of high school students before their senior year. Such samples of students are available for HSB and NELS, but unfortunately not in NLS. The underlying assumption is that these samples should not have experienced the same selection effects due to dropping out as the 12th-grade samples. In other words, selection effects should be smaller in earlier grades (e.g., Grade 10) than in Grade 12. Hence, if the results of the Grade 10 analyses are comparable with those from the Grade 12 analyses, this would indicate that dropout effects at Grade 12 are minimal. Alternatively, it could mean that the dropout effects are similar in Grades 10 and 12. HSB provided samples of 10th-grade students, and NELS samples of 8th- and 10th-grade students. For comparability purposes, I decided to use the 10th-grade samples for both HSB and NELS.
The results of these analyses are summarized in Table 4. The upper panel of Table 4 reports group differences in reading achievement for HSB and NELS, and the lower panel the achievement gap in mathematics for 10th and 12th graders. In HSB, the group differences in reading achievement in Grade 10 are typically larger than those in Grade 12. In NELS, the pattern is reversed in the top half of the distribution, with larger estimates observed in Grade 12 reading. In the lower tail of the distribution, the reading achievement gap is larger in Grade 10 than in Grade 12. The pattern for mathematics is similar in HSB, that is, the group differences in mathematics achievement in Grade 10 are typically larger than those in Grade 12. In NELS, the pattern is reversed, that is, the achievement gap in mathematics is typically larger in Grade 12. Overall, these results suggest that there may be differential dropout patterns in the two groups. For example, it is possible that in NELS, the Grade 12 samples included lower proportions of lower achieving Asian American students and higher proportions of higher achieving Asian American students, assuming everything else is constant. In HSB, the results may indicate a positive selection for White students in Grade 12, other things being equal. Overall, these results possibly indicate underestimation of group differences in HSB and overestimation of group differences in NELS in Grade 12. Because I could not conduct such analyses with NLS data, it is difficult to generalize these results to NLS. A selection effect in NLS is possible.
LIMITATIONS OF THE PRESENT STUDY
The present study treats Asian American and White students as one general category, assumes homogeneity within each general group, and does not differentiate among subgroups of Asian Americans and Whites. I understand, however, that over time, the group of Asian American and White students likely comprises different proportions of Asian or White ethnic groups, respectively, and that there may be variability in achievement among these groups. Hence, treating the two race/ethnic groups as whole groups may be viewed as a limitation of the study if one is interested in differences among subgroups. It is noteworthy that only one of the data sets I used provides information about the origin of Asian American students, and hence, it would be difficult to conduct such analyses across data sets. In addition, dividing the Asian American student population into smaller groups results in very small subgroups of students, and statistical analysis is not that informative with such small samples. In addition, research on group differences typically treats the groups of interest as general gender or race/ethnic categories (see, e.g., Hedges & Nowell, 1995, 1999). In this study, I am interested in examining differences in achievement between Asian American and White students as whole groups following previous work that has examined the race/ethnic gap achievement or earnings (see Card & Krueger, 1992; Hedges & Nowell, 1999). As a result, I do not conduct comparisons among different Asian or White ethnic groups or between Asian groups and White groups. Such comparisons have been documented in other studies that used NELS data (e.g., Bireley & Genshaft, 1991; Blair & Qian, 1998; Kao, 1995; Konstantopoulos et al., 2001). For example, Kao found that Chinese, Korean, and Southeast Asian students performed higher in mathematics than their White counterparts. In addition, Konstantopoulos and colleagues found that South Asian students were overrepresented in the upper tail of the achievement distribution.
This article used three major national surveys conducted in the early 1970s, 1980s, and 1990s that provided information on student achievement and student background. I examined group differences in achievement between two important race/ethnic groups: Asian Americans and Whites. In particular, I examined the Asian AmericanWhite achievement gap in reading and mathematics achievement for low-, average-, and high-achieving high school seniors. Overall, the findings indicate that there are significant group differences in reading and mathematics achievement. These differences favor Asian American students in the 1990s, especially in mathematics.
The unadjusted group differences in reading indicated that overall, White students outperformed their Asian American peers. This is more evident in the lower tail of the reading achievement distribution, where the achievement gap is significant in the 1980s and 1990s. However, in the 1990s, Asian American students outperformed their White peers in reading in the upper tail of the achievement distribution (25th quantile). In addition, the median achievement gap was virtually zero in the 1990s. Group differences in reading, adjusted for important covariate and differential effects, are typically smaller in magnitude and insignificant. In 1992, the adjusted gap in reading was positive in the middle, and positive and significant in the upper tail of the reading distribution (25th quantile). This suggests that higher achieving Asian American students outperformed their White peers in 1992. Overall, in the 1990s, the gap is either small for lower achievers or larger for higher achievers, favoring Asian American students.
The unadjusted group differences in mathematics are somewhat different from those reported in reading and indicated that overall, Asian American students outperformed their White peers across the entire distribution and over time. The mathematics achievement gap became larger over time and was statistically significant in 1992 in the tails of the achievement distribution. In fact, the gap was somewhat more pronounced for high-achieving students, which is consistent with the findings in reading in 1992. The race/ethnic achievement gap for higher achieving students (e.g., 75th and 90th quantile) nearly doubled from 1972 to 1992, favoring Asian American students. This indicates that although in reading, the achievement gap is small overall, in mathematics, the achievement gap is alarming because it becomes larger, especially for higher achievers. Group differences in mathematics, adjusted by important covariate and interaction effects, are more pronounced in 1972 and 1980 but comparable in magnitude with the unadjusted differences in 1992. Specifically, in 1992, the adjusted gap in mathematics was positive and significant across the entire mathematics distribution and typically greater than one third of a SD, a nontrivial gap.
The results obtained from the sensitivity analyses suggest that there is a possibility that the dropout rates of the two groups in high school may have affected the estimates for high school seniors. However, the evidence is rather weak. Moreover, group differences in the variation of the achievement distribution are small but point to overrepresentation of Asian American students in the upper tail of the achievement distribution, especially in 1992. Overall, the distribution of reading achievement for Asian American students is as equally spread out as that for White students, and the same pattern is observed for mathematics achievement. In addition, differences in variability did not change much over time in reading or mathematics, but the estimates are slightly larger in 1992.
In sum, the Asian AmericanWhite gap is more pronounced in mathematics than in reading. In 1992, the gap in the middle and the upper tail of the mathematics distribution is greater than one third of a SD, which is not a trivial gap in education. In reading, the gap is smaller overall and nearly one third of a SD in 1992 in the upper tail (favoring Asian students). Hence, it appears that Asian American students are indeed a model minority group that performs not only at similar levels but also at higher levels than the majority group, especially among high achievers in mathematics.
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