Educational Attainment and the Second Generation: A Meta-Analysis of Ethnicity

Transcription

1 Educational Attainment and the Second Generation: A Meta-Analysis of Ethnicity Jiangtao GOU First Year PhD student in Statistics Department of Statistics, Northwestern University Robert VARGAS Third Year PhD Student in Sociology Department of Sociology, Northwestern University December 11 th, 2009

2 Some [immigrant groups] move up by resisting assimilation others assimilate to values and behaviors of the American ghetto. That is what Jesselyn [a second generation Salvadoran American] said she and other poor streetwise Salvadorans had done: followed the example of poor streetwise blacks. They re like a role model, she said. We re a lot like them. This quote came from a New York Times article on the struggles of some second generation Americans. It puts forth the notion that the socio-economic mobility of the children immigrants depends on how they resist or assimilate into the cultures of poor African Americans, who tend to reside within or close to many immigrant enclaves in inner cities. The sociological theory driving this explanation in the article draws heavily from immigration scholars who have studied ethnic differences in outcomes (such as education, acculturation, and inter-marriage) amongst the second generation. Cultural explanations for these divergent outcomes, such as the one above, have been sought because of the consistent significance of ethnicity as a dummy variable in quantitative studies of the second generation. Immigration scholars have come to call this the black box of ethnicity (Zhou 2009). Numerous studies have shown, after controlling for socio-economic status, that ethnicity remains a statistically significant variable associated with educational outcomes. The statistical significance of the ethnicity dummy variable motivated numerous qualitative studies of immigrant communities, attempting to flesh out processes that quantitative analysis has not explained (Waters 1999; Zhou and Bankston 1998). Needed is a meta-analysis on the effects of ethnicity. While immigration scholars have used the statistical significance of ethnicity as a call to arms for qualitatively studying immigrant communities, not one scholar has looked at the average effect size of ethnicity across studies or what accounts for variation in effect sizes. This would enable 1

3 us to assess the following research questions: What is ethnicity really representing? Is the effect size large enough to warrant significant qualitative inquiry into culture that ends up in journalistic accounts? To answer these questions, we conducted several meta-analyses looking at the relationship between ethnicity and educational attainment. We break down ethnicity into two meta-analyses, one for Asians, the other for Hispanics. We calculate their average effect size, using standard difference in means, on the following educational outcomes: GPA, years of schooling, and high school completion. ETHNICITY AND THE SOCIOLOGY OF IMMIGRATION Portes and Rumbuat (2006) argue that three factors account for most ethnic differences in the trajectories of the second generation, human capital (monthly earnings, occupational status, annual incomes), family structure, and modes of incorporation. Despite the inclusion of these variables in models of educational attainment, arrests, incaraceration, and socio-economic mobility, ethnicity has continued to have a significant effect (Haller and Portes 2007; Portes and Rumbuat 2001; Portes 1995; Portes and Hao 2004; Rumbuat 2005; Zhou and Logan 2003). As a result, the current state of the debate centers upon what Zhou (2009, 9) calls unpacking the black box of ethnicity. Portes and Rumbaut (2001), interpret the effects of ethnicity as differences in the modes of incorporation, that is, the character and strength of ethnic communities and the hostile, neutral, or supportive ways in which immigrant groups are received by the U.S. government and society. Portes (1995) hypothesizes that the most significant characteristics of ethnic communities are the density of social networks, the multiplexity of social ties, and the 2

4 degree of bounded solidarity with the ethnic community. Depending on the extent of these factors, immigrant parents can call on co-ethnics to reinforce normative expectations vis-à-vis their offspring and to supervise their behavior (Portes 1995; 255). Furthermore, the ability of immigrant groups to build such tightly knit communities with high degrees of bounded solidarity depends on how they have been received by the U.S. government and society (Portes and Rumbuat 2001). Zhou offers a different interpretation of the ethnicity variable that emphasizes culture (Zhou and Bankston 1998; Zhou and Kim 2006; Zhou 2009). In their studies of Korean, Vietnamese, and Chinese communities, Zhou and Bankston (1998) see community as important protective factor from assimilating into the downwardly mobile segment of the native population. For immigrants children living in poor neighborhoods and attending inner-city public schools, Zhou and Bankston (1998) argue that assimilation might often entail adopting the adversarial outlook that characterizes the oppositional culture of domestic minorities (Fordham and Ogbu 1986). Therefore, retaining one s ethnic culture was interpreted as having a positive effect on the educational achievement of the Korean, Vietnamese, and Chinese second generation (Zhou and Bankston 1998; Zhou 2009). Although scholars have qualitatively shown cases of the second generation assimilating into the inner-city underclass (Waters 1999), one can doubt whether this accounts for a great portion of the ethnic differences in school performance among the second generation. Kroneberg (2008) offers the most convincing evidence in opposition to Zhou and Water s arguments. Using data from the Children of Immigrants Longitudinal Study, Kroneberg (2008) found no evidence for the hypothesis that a sizable 3

5 portion of immigrant s children are at risk to adopt an oppositional culture from contact with native minorities. Kroneberg s (2008) study supports a conditional view of community effects on the educational performance of children. In fact, Kroneberg (2008) explained: In communities characterized by high levels of self-employment, education, and aspirations, students math and reading test scores were considerably higher if their interviewed parents socialized mainly with coethnics. In communities that ranked low on those indicators, parents insertion into ethnic communities was associated with lower test scores. By taking these relationships into account, it was possible to explain away the remaining differences between [ethnic] groups that had been especially resilient with regard to mathematics scores. Kroneberg shows how, after controlling for community variables, the ethnic dummy variable ceases to be statistically significant. With that in mind, were scholars correct to assume that the statistical significance of ethnicity reflected culture? To further question this body of work, we conduct meta-analysis of the effects of ethnicity on educational attainment amongst the second generation. METHODS Retrieval of Studies To retrieve an initial set of studies focusing on educational outcomes amongst the children of immigrants, we used a combination of techniques. We started by using the following computer data bases: JSTOR, Social Sciences Abstracts, Google Scholar, and Sociological Abstracts). Our keywords were ethnicity, education, and the second generation. Our searches yielded around 500 studies in total. To our surprise, the majority of these studies did not fit into our criteria for inclusion, as most focused on outcomes for immigrants, and not the children of immigrants. To be included in our meta-analysis, the studies had to have an educational outcome, had to have at least one ethnicity dummy variable, and have a sample (or reasonably sized sub-sample) of the 4

6 second generation. Most study characteristics fit our criteria with the exception of one or two important criteria, and as a result, we reached a sample size of 15 studies. This relatively low number of studies should not surprising given that few data sets explicitly sample from the population of the children of immigrants. Studies like Add Health or the National Educational Longitudinal Study (NELS) have ethnic variation, but not enough generational variation to warrant studies on the second generation. The few studies that did are included in this study. Aside from these datasets, most other studies utilized data from the Children of Immigrants Longitudinal Study (CILS). While we can t be certain if this is an accurate sample of studies education, ethnicity, and the second generation, we are confident that our search strategies produced the most accurate sample possible. Variation in Measures of Ethnicity Analysis of the 15 studies revealed inconsistency in the measures of ethnicity, as well as confusing overlap with racial categories. Often times, ethnicity is thought of as national origin (Chinese, Korean, Mexican etc.), while race is thought of in the categories of white, black, asian, or Hispanic. The variation in measurement of ethnicity, shown in table 1, forced us to make important choices for our meta-analysis. Table 1 - List of Ethnicity Measures in the Sample of Studies Number of Studies in Our Sample that Used This Measure of Ethnicity Latino 2 Hispanic 3 Mexican 8 Haitian 2 Puerto Rican 4 Other Hispanic 3 Native 1 5

7 American West Indian 1 American Indian 1 Other 1 Asian 6 East Asian 1 South Asian 2 Other Asian 1 Pacific Islander 1 Southeast Asian 2 Filipino 3 Chinese/Korean 1 Chinese 2 Japanese 3 Korea 3 Cambodian 2 Vietnamese 4 To deal with this variation, we chose to focus on two groups, Mexicans and Chinese. According to Rumbuat (2005), Mexicans comprise 60% of second generation Hispanics in the U.S., while the Chinese represent 23% of second generation Asians. As our sample of studies lack a consistency of ethnicity measures to warrant meta-analyses of multiple ethnic groups, we focus on studies with Mexican and Chinese dummy variables, while using studies with Hispanic or Asian dummy variables as proxies for Mexican and Chinese ethnicity. As Mexicans are the largest sub-group within the Hispanic population, using studies with a Hispanic dummy variable will upwardly bias estimates of Mexican ethnicity. However, as Mexicans are the largest sub-group, the majority of respondents of Hispanic descent are likely to be of Mexican descent. For the Chinese, the situation is a bit different. They do not comprise a large majority of their racial group (Asians). However, they are among the highest educationally achieving ethnic groups in the U.S. 6

8 Using Asian dummy variables as proxies for Chinese ethnicity is a bit more problematic, however, as Asian ethnic groups tend to perform well in school, we expect our estimates to be the best possible estimate of Chinese ethnicity. If measures of ethnicity were more consistent across these studies, we would not have this problem. However, one can only work with the data at hand, therefore, we conduct this meta-analysis more as an exercise in illustrating the methodological problems in the study of race and ethnicity, rather than using our results as an accurate reflection of these populations. Measures of Educational Attainment Studies in our sample also varied in the measurement of their outcomes. To make the meta-analysis more interpretable, we conducted separate meta-analyses of ethnicity on three types of educational outcomes, high school completion, high school GPA, and years of schooling. Some cases broke down their measures, such as GPA, into outcomes such as math GPA or reading GPA. Rather than combining the two measures, we simply included estimates of math achievement and excluded outcomes of reading achievement. As each educational outcome has different interpretations and measurements (continous versus dichotomous outcomes), we felt it was necessary to conduct smaller meta analyses, in addition to computing an overall effect size for Mexican and Chinese ethnicity. Missing Parameters In reviewing these articles, we found that a number of important parameters for conducting meta-analysis were missing from these studies. These included missing standard errors, and adjusted R squared measures. In our sample, only four studies did not report their standard errors, while two studies did not report their adjusted r-squared. Standard errors were import for calculating the average effect size, while the adjusted R 7

9 squared measure was important for calculating a rough measure of standard deviations in the study (for producing Hedges G). As the time-constraints of this paper prevented us from asking the authors of these papers for their missing parameters, we gave studies missing a standard error a measure that was 10% of their coefficient. We acknowledge that making this assumption will impact our results, however, we felt the best strategy would be to give the authors the benefit of the doubt, and give them precise coefficients. For studies that did not show an adjusted r-squared, we assumed each had an r-squared of 25%. This percentage was similar to the r-squared of other studies in our sample. In addition, a number of studies did not report the breakdown in the count of respondents belonging to each ethnic group. The overall sample size was reported, but for some studies, we had to assume that half of the population was white while the other half was Asian or Hispanic. We treated all cases missing these important parameters the same, dividing the overall sample by two, and putting an equal amount of ethnic respondents and reference category respondents in our calculations. Some other important changes were made to data. At times, studies reported t- ratios instead of standard errors. We converted these into standard errors by dividing the coefficient by the t-ratio. In addition, all coefficients from studies using logistic regressions were converted into odds ratios through simple addition and subtraction (1-x if it were negative) (1+x if it were positive). Even further, for one study, we had to standardize their odds ratios because they had coded their outcome differently (1=high school completion, whereas all other studies coded 1 as dropping out). For this we also did addition and subtraction (1.16 odds of dropping out =.84 odds of completing high school). 8

10 RESULTS To calculate the average effect size of ethnicity, we categorized our studies based on their outcome. We modeled our meta-analysis of continuous outcomes (GPA and years of schooling) using raw differences in means and standard errors, with the assumption of independent groups. For our meta-analysis of dichotomous outcomes (high school completion), we used a log odds ratio and standard error model. For a more detailed description of our calculations, please see the appendix. Table 2 - Effects of Chinese and Mexican Ethnicity by Type of Educational Outcome for the Second Generation Chinese Average Estimates Size N High School Completion High School GPA Years of Schooling Mexican High School Completion High School GPA Years of Schooling In table 2, we see that the effect size of Chinese and Mexican ethnicity are fairly large for high school completion, and small for GPA and years of schooling. However, the average effect size of high school completion should be interpreted with caution, as the studies in our sample used different reference categories. Some used native whites as the reference category, while others used immigrants or an average of the rest of their sample. Even further, Oropesa and Landale (2009) have shown that most studies of high school completion overestimate the effect of Mexican ethnicity. They argue that datasets tend to pool together first and second generation Mexicans, and since a large portion 9

11 young immigrant Mexicans never enroll in school, they get counted as drop outs when they really should not. For this paper, we considered conducting meta-regression to investigate whether the variation in these effect sizes can be explained by such study characteristics. However, the small number of cases do not make meta-regression possible. Nevertheless, in future drafts, as we collect more studies, we can hopefully investigate this issue. Aside from high school completion, the effect of ethnicity for Chinese and Mexican students on GPA and years of schooling appears small. For Mexicans, ethnicity only accounts for.22 of a difference. For Chinese, ethnicity only accounts for a.143 advantage. Thinking about this in terms of the grading scale, the effect for ethnicity, in generous terms, would only account for the difference between a B and B+. For years of schooling, ethnicity makes a difference amounting to just less than one year. With these average effect sizes in mind, we should question whether the cultural explanations offered by immigration scholars really are the correct interpretation for this ethnicity variable. If ethnicity, on average, has this small effect, should we be as concerned about culture as some have argued. Evidence from this meta-analysis indicates no. RANDOM EFFECT MODEL To further evaluate the effect of ethnicity, we pooled together all the studies in a random effects model to attain a general estimate of the average effect size of ethnicity on educational outcomes (a summary measure comprised of our three educational outcomes). Since we believe the difference between different ethnicities is not a constant (different measure may give different results), we choose to use random-effects model to do meta-analysis, which treats the distance between overall mean and the observed effect 10

12 in any given study as two parts, one is the true variation in effect sizes, and the other is sampling error (See Borenstein 2009, 71). That is Yi i i. (0.1) We estimated the between-studies variance and the within-studies variance following the method of (Borenstein 2009, 72), where is a method of moments; or, we could use the software CMA to compute. For the Chinese, there are 6 GPA studies, 6 High School Completion studies, and 3 Year of Schooling studies, totally 15 studies. Input the data to CMA, we have And the output given by CMA: 11

13 Meta Analysis Study name Statistics for each study Hedges's g and 95% CI Hedges's Standard Lower Upper g error Variance limit limit Z-Value p-value Fuligni1997GPA Portes2001GPA Kao1995GPA KaoTienda1995GPA Mouw1999GPA PortesHao2004GPA Feliciano2006HSC Wojtkiewicz1995HSC PortesHao2004HSC Hirschman2001HSC White1997HSC White2000HSC Rong1992YS Chiswick2004YS Rumbaut2005YS Favours A Favours B Meta Analysis We see the Hedges g is 0.134, and the standard error is 0.031, Z-value reaches to 4.267, p-value is less than 0.001, so we may conclude that the average effect size of Asian is significant but relatively small. For publish bias, we draw the Funnel Plot (randomeffects model), the circles are the observed studies, and dots are the predicted studies given by software CMA. See the diamonds at the bottom, we know this meta-analysis nearly do not suffer from publish bias. 12

14 Standard Error Funnel Plot of Standard Error by Hedges's g Hedges's g For Mexicans, there are 4 GPA studies, 6 High School Completion studies, and 3 Year of Schooling studies, totally 13 studies. Input the data to CMA, we have And the output given by CMA: 13

15 Meta Analysis Study name Statistics for each study Hedges's g and 95% CI Hedges's Standard Lower Upper g error Variance limit limit Z-Value p-value Fuligni1997GPA Portes2001GPA KaoTienda1995GPA PortesHao2004GPA Feliciano2006HSC Wojtkiewicz1995HSC PortesHao2004HSC Hirschman2001HSC White1997HSC White2000HSC Rong1992YS Chiswick2004YS Rumbaut2005YS Favours A Favours B Meta Analysis We see the Hedges g is , and the standard error is 0.060, Z-value reaches to 3.670, p-value is less than 0.001, so we may conclude that Mexican ethnicity has a larger effect than Chinese. We draw the Funnel Plot (random-effects model), the circles are the observed studies, and dots are the predicted studies given by software CMA. So we know the results may suffer from the publish bias. See the diamonds at the bottom; metaanalysis indicates that maybe some cases proved Latino did not really have a good chance to be published; or, there is anther possible situation, we failed to collect these kind of studies. 14

16 Standard Error Funnel Plot of Standard Error by Hedges's g Hedges's g CONCLUSION As the meta-analysis showed small effect sizes of ethnicity, we can conclude that immigration scholars need to seriously re-consider their interpretation of the effects of ethnicity. Our results offer two scenarios. Either the ethnicity variable is not capturing the hypothesized cultural explanations put forth by immigration scholars, or, cultural explanations do not account for much variation in educational outcomes. If the average effect size of ethnicity is small, does this mean that ethnicity does not matter? Not necessarily, especially as our results do not rule out the possibility that ethnicity (if measured differently or regressed on different outcome) makes a difference. In either scenario, our analysis has a number of important implications for research on race and ethnicity. First, researchers need to theorize how we can develop alternative and consistent measures of ethnicity. It does not help when terms like East Asian and Chinese/Korean are used, as this makes meta-analysis (or any type of interpretation) very difficult. Second, researchers need to seriously think about the 15

17 definition of ethnicity. Is it national origin? Is it race? Is it pan-ethnic? When the definition is declared, it should be used consistently. REFERENCES Chiswick, BR and N DebBurman "Educational attainment: analysis by immigrant generation." Economics of Education Review 23: Feliciano, Cynthia Unequal origins : immigrant selection and the education of the second generation. New York: LFB Scholarly Pub. LLC. Fuligni, AJ "The academic achievement of adolescents from immigrant families: The roles of family background, attitudes, and behavior." Child Development 68: Hirschman, C "The educational enrollment of immigrant youth: A test of the segmented-assimilation hypothesis." Demography 38: Kao, G "Asian Americans as model minorities? A look at their academic performance." American Journal of Education 103: Kao, G and M Tienda "Educational aspirations of minority youth." American Journal of Education: Mouw, T and Y Xie "Bilingualism and the academic achievement of first-and second-generation Asian Americans: Accommodation with or without assimilation?" American Sociological Review 64: Oropesa, RS and NS Landale "Why Do Immigrant Youths Who Never Enroll in US Schools Matter? School Enrollment Among Mexicans and Non-Hispanic Whites." Sociology of Education 82: Portes, A and L Hao "The schooling of children of immigrants: Contextual effects on the educational attainment of the second generation." Proceedings of the National Academy of Sciences 101: Portes, A and D MacLeod "Educational progress of children of immigrants: The roles of class, ethnicity, and school context." Sociology of Education 69: Portes, Alejandro and Ruben G. Rumbuat Legacies: The Story of the Immigrant Second Generation. Berkeley University of California Press. Portes, Alejandro and Rubén G. Rumbaut Immigrant America : a portrait. Berkeley: University of California Press. Rong, XL and L Grant "Ethnicity, generation, and school attainment of Asians, Hispanics, and non-hispanic Whites." The Sociological Quarterly 33: Rumbaut, RG "Turning points in the transition to adulthood: Determinants of educational attainment, incarceration, and early childbearing among children of immigrants." Ethnic and Racial Studies 28: White, MJ "Generation status, social capital, and the routes out of high school." Pp , vol. 15: Springer. White, MJ and G Kaufman "Language usage, social capital, and school completion among immigrants and native-born ethnic groups." Social science quarterly 78: Wojtkiewicz, RA and KM Donato "Hispanic educational attainment: The effects of family background and nativity." Social Forces 74:

18 Zhou, M "Growing up American: The challenge confronting immigrant children and children of immigrants." Annual Review of Sociology 23: Zhou, Min Contemporary Chinese America: Immigration, Ethnicity, and Community Transformation. Philadelphia: Temple University Press. Zhou, Min and Carl L. Bankston Growing up American : how Vietnamese children adapt to life in the United States. New York: Russell Sage Foundation. APPENDIX A Meta-Analysis of Grades: Model and Computation In this appendix, we will briefly show how to construct meta-analysis for the studies measured by grades, or grade point averages (GPA s). We have totally 6 studies measured by grades. A.1 An Example Study: Fuligni s study in 1997 [Fuligni1997] Goal of this study: Determine the relative impart of family background, parental attitudes, peer support, and adolescents own attitudes and behaviors on the academic achievements of students from immigrant families, which vary considerably according to their ethnic background (See [Fuligni1997], pp ). Sample: Participating students attended the 10 th grade of two high schools and the 6 th and 8 th grades of two middle schools in a California school district with a large number of immigrant families. Nearly 84% of the enrolled students participated in the study, yielding a total sample of 1341 adolescents (10% were absent, 4% declined to participate, and 2% were excluded because of learning or language difficulties) (See [Fuligni1997], p. 353). The present study included 1100 students with Latino, East Asian, Filipino, and European backgrounds (See [Fuligni1997], p. 353). Actually the sample size varied from 1005 to 1072 in the multiple regression models (See [Fuligni1997], pp ), because of missing values, we guess. Measure of Academic Achievement: Students grades in mathematics and English ranged from A to F, changing to a 4.0 scale. Despite the differential enrollments, grades were not weighted in this study to account for course level (See [Fuligni1997], p. 354). Model: A series of multiple regression models were performed in mathematics and English respectively. What we concerned here was the No.4 model which included dummy variables about the ethnicity in (See [Fuligni1997], pp ). The multiple regression model is Y X X X. (0.2) K K Here is a random disturbance term, Y is the students performance in mathematics or English, X i s are the independent variables used in [Fuligni1997] s study (in [Fuligni1997] s No.4 model, K equals to 10), they are all dichotomous or polytomous variables as we observed. Fuligni reported all s in his paper (See [Fuligni1997], pp ). i There are three ethnicity variables in Fuligni s study: Latino, East Asian, and Filipino. We assigned the dummy variables X 1, X 2 and X 3 as these three ethnicity variables. For example, 1 1 X for a certain 17

19 student in the sample means the student is Latino, X1 0 means he is not. So if we got a simple regression model like then the estimator of 1 rest students. Y 0 1X1, (0.3) which is b ˆ 1 1 would show the difference performance of the Latino and the If all X i s are independent or nearly independent, we can use the estimator of 1 in (0.3) to estimate the coefficient 1 in (0.2), but we have to adjust the estimation of the standard error of 1 which was reported by Fuligni in [Fuligni1997] in order to get the estimation of the standard error of 1 which is what we want, otherwise we would underestimate the standard error of this study, since the multiple model assigned the error to all variables, not only the ethnicity ones. In order to get the correction multiplier, we need the correlation coefficient r of this model Y X X. (0.4) K K Then we can get the estimation of the standard error of 1 which is 1 ˆ SE ˆ 1 1 r SE. (0.5) Since r as the correlation coefficient of model (0.4) usually will not be reported in any report, so we take the correlation coefficient of model (0.2) instead 1, that is SE ˆ 1 ˆ r SE ˆ Surely working in this way will overestimate 1 here K is not small, so the overestimation may be slight. 2 SE. (0.6), it is a safe way to find the significance. Actually For example, for mathematics performance, let X 1 represents the dummy variable for Latino, so we get ˆ , SE 1 ˆ , and r 0.14, so SE ˆ SE ˆ r Similarly, we get the effect sizes and the standard errors 1 Prof. Hedges told us this way on 1st December 2009 after class, since we had got this problem to ask him. 18

20 Ethnicity Latino East Asia Filipino Mathematics Effect Size Standard Error English Effect Size Standard Error The effect size shows the difference between the students in a certain ethnicity group and the rest students. In order to process meta-analysis, we calculate the Hedges g and its standard error; here, we follow the way of independent groups (See [Borenstein2009], pp ). Take the comparison of mathematics grades between the Latino and the non-latino in Fuligni s study as a case in point. We need the within-groups standard deviation first. Since we know the standard error, and work without the finite population correction since the sample size is relatively small, and assume the independence between the Latino group and the non-latino group, we have So we can calculate 2 2 SLatino SnonLatino Swithin n n n n SE (0.7) Latino nonlatino Latino nonlatino 2 S within through (0.7). Here, S within SE n n Latino Then Cohen s d (See [Borenstein2009], p. 27) nonlatino The variance of d is given by ˆ 0.36 d Sˆ 1.67 within Correction factor J is Var d 2 nlatino nnon Latino d n n 2 n n Latino nonlatino Latino nonlatino So Hedges g is J df and the standard error is g J d , 19

21 g g J 2 d SE Var Var If we want to mix the performance of mathematics and English to form one score presented the overall performance, we may assume that the mathematics performance and the English performance are independent, so we will simple know the overall difference is the sum of the differences of two parts, and the variance is the sum of the variance of the two parts, so. Ethnicity Latino East Asia Filipino Overall Effect Size Standard Error Actually there is a way to assume the correlation between mathematics performance and English performance as 0.50 (See [Borenstein2009], p. 234), where they just sum the two variances and then subtract one, gives a lower variance than what we get based on the independence of the two performance, which is a relatively safe way to draw statistical conclusion. And then we can calculate Hedges g and its standard error. Using the software Comprehensive Meta-Analysis (CMA version ) (actually we could calculate them by hand), the results are summarized below. Ethnicity Latino East Asia Filipino Mathematics Hedges' g Standard Error English Hedges' g Standard Error Overall Hedges' g Standard Error A.2 Other Studies measured by Grades Here we gave brief results of other 5 studies measured by grades. A.2.1 Portes and Rumbaut s study in 2001 [Portes2001] A multiple regression model with 26 variables (or predictors, as Portes and Rumbaut called) whose 11 variables were about national origins (See [Portes2001], pp , model II) was based on the GPAs, as the indicator of achievement from school records in senior high school in the United States in 1995 (See [Portes2001], pp ). So the comparison here is between one certain national origin group and the 20

22 others in the sample. Since there is no information about the number of different national origin groups (we only know the total number is 4899), we just treat the 11 groups have the same number, or, 445 each. Surely this treatment will underestimate the number of the two groups, Chinese/Korean and Mexican which we concerned, and results an overestimate of variance of Hedges g. Nationality Chinese/Korean Mexican Difference in GPA Standard Error Sample Size of this Group (est) Sample Size of Others (est) Portes and Rumbaut did not give the standard error directly, but they said that the coefficient of Chinese/Korean has very strong effect, where the coefficient sextuples its standard error; and the coefficient of Mexican has moderate effect, where the coefficient doubles its standard error (See [Portes2001], p. 249). So we calculate the standard errors based on the information. Then Hedges g s are calculated. Nationality Chinese/Korean Mexican Hedges' g Standard Error A.2.2 Kao s study in 1995 [Kao1995] Kao presents the effects of background variables on grades for Asian and whites, and there are some other variables like family income, home resources, etc (See [Kao1995], p. 143). Kao used the National Education Longitudinal Study of 1988 (NELS88) to compare Asian and white eighth graders on grades (See [Kao1995], p. 121). NELS88 used a two-stage stratified probability design to select a nationally representative sample to schools and students, and got students (24599 students finally participated) from 1052 schools, and Asian students were over-sampled, resulting in 1527 (See [Kao1995], p. 129). We use the model two which has more variables than model one, and get the difference between Asian and white (See [Kao1995], p. 148, table 8) Ethnicity Asian Difference in GPA Standard Error Sample Size of Asian

23 Sample Size of white R square Adjusted Standard Error Then Hedges g and its standard error are calculated. Ethnicity Asian Hedges' g Standard Error A.2.3 Kao and Tienda s study in 1995 [KaoTienda1995] Kao and Tienda had built a regression model of effects of background characteristics and generational status on eighth grade performance measures. There were 12 variables, and three of them were ethnicity variables, which equal 1 if the certain ethnicity, and 0 otherwise (See [KaoTienda1995] table 1 and 2). The data was gathered from the National Education Longitudinal Study of 1988 (NCES, 1990). So the comparison here was between the certain ethnicity and the rest of the sample. Ethnicity Asian Hispanic Difference in Grades Standard Error Sample Size of Certain Group Sample Size of others R square Adjusted Standard Error Here the sample sizes are estimated based on other two papers 23 about the NELS88. Then Hedges g and its standard error are calculated. 2 Kao, G and M Tienda "Educational aspirations of minority youth." American Journal of Education: Vol. 106, No. 3 (May, 1998), pp Robert M. Hauser and Megan Andrew. Reliability of Student and Parent Reports of Socioeconomic Status in NELS-88. University of Wisconsin-Madison. July 6, URL: < 22

24 Ethnicity Asian Hispanic Hedges' g Standard Error A.2.4 Mouw s study in 1999 [Mouw1999] Ted Mouw and Yu Xie gave a regression model of Eighth Grade Grade-Point Average on 20 variables, 7 of them were ethnicity variables. Here we compare the Southeast Asians and other Asians (See [Mouw1999], p. 247, table 8, model 2). Since there is no clue for the sample size of Southeast Asians, we just simple divided the number of total cases by seven to estimate it. Ethnicity Southeast Asian Difference in GPA Standard Error Sample Size of Southeast Asians 118 Sample Size of other Asians 707 R square Adjusted Standard Error Then Hedges g and its standard error are calculated. Ethnicity Southeast Asian Hedges' g Standard Error A.2.5 Portes and Hao s study in 2004 [PortesHao2004] Portes and Hao showed us a regression of senior grades on 12 predictors, 3 of them are national origin predictors. They used the data from the Children of Immigrants Longitudinal Study (CILS95-96), which sampled 5266 children from Miami, Florida, and California. Totally 44 schools took part in this study, and 77 different nationalities were represented in the study (See [PortesHao2004], p ). Here they considered three groups: Chinese/Korean, Mexican, and Vietnamese; since in Portes and Hao s paper, only total number (N = 4900) was reported, we simply treat the three groups have equal sample size because of the lack of information. 23

25 National Origin Chinese/Korean Mexican Vietnamese Difference in Grades t-ratio Standard Error Sample Size of Certain Group Sample Size of others R square Adjusted Standard Error Then Hedges g and its standard error are calculated. National Origin Chinese/Korean Mexican Vietnamese Hedges' g Standard Error APPENDIX B Meta-Analysis of High School Completion: Model and Computation In this appendix, we will briefly show how to construct meta-analysis for the studies measured by high school completion. We have totally 6 studies measured by high school completion. B.1 An Example Study: Feliciano2006 [Feliciano2006] Cynthia Feliciano in his book gave the odds ratios of models of the determinants of high school graduation among second-generation persons 20 to 40 in the United States, (See [Feliciano2006], p. 110), which based on the data from March CPS, He offer the 1.5 generation results at the same time (See [Feliciano2006], p. 109), here we use the second-generation results. Feliciano offered three models, the first model focused on the ethnicity, and other two added other variables in. So we use the first model here. Here the odds ratio is the ratio of two odds, the certain group and the white (See [Feliciano2006], p. 106). Feliciano offered us a table from CPS (See [Feliciano2006], p. 107, table 5.5), and the data will allow us to estimate the variance of log odds ratios, although he did not directly show us. Ethnicity White Asian Latino High School Graduate Sample Size

26 And the odds ratios and the estimated numbers of each group are Ethnicity Asian Latino Odds Ratios Number of Graduates Number of Non-graduates Control group, Number of Graduates Control group, Number of Non-graduates Take Asia s odds ratio as an example. with approximate variance OddsRatio LogOddsRatio ln ln , (0.8) Var and approximate standard error LogOddsRatio T T C T n n n n Event nonevent Event nonevent , (0.9) LogOddsRatio LogOddsRatio SE Var. (0.10) Then Cohen s d and its standard error (See [Borenstein2009], p. 47) 3 d LogOddsRatio 0.534, (0.11) 3 SEd SE LogOddsRatio (0.12) In order to calculate Hedges g, we need to multiply a correction factor J, which is 1 3 J 4 df 1. For Asia, df = 1413, J = ; for Latino, df = 3194, J = The results of Asia and Latino are summarized below. Ethnicity Asian Latino 25

27 Odds Ratios Lower Limit of Odds Ratios (one sigma) Upper Limit of Odds Ratios (one sigma) Log Odds Ratios Standard Error of Log Odds Ratios Hedges' g Standard Error of Hedges' g If we use the model 3 (See [Feliciano2006], p. 110), which has eight variables, and the ethnicities are three out of eight, the result will be Ethnicity Asian Latino Odds Ratios Lower Limit of Odds Ratios (one sigma) Upper Limit of Odds Ratios (one sigma) Log Odds Ratios Standard Error of Log Odds Ratios Hedges' g Standard Error of Hedges' g B.2 Other Studies measured by High School Completion Here we gave brief results of other 5 studies measured by high school completion. B.2.1 Wojtkiewicz and Donato s study in 1995 [Wojtkiewicz1995] Wojtkiewicz and Donato gave a logistic regression of high school graduation on race/ethnicity, nativity, and background variables. We use the model 3 which contained 19 variables and 7 of them are ethnicity variables (See [Wojtkiewicz1995], p. 567, table 3). The comparison here is between the certain group and non-hispanic white. 26

28 Ethnicity Asian Mexican Difference in High School Graduation Rate Standard Error Sample Size of Certain Group Sample Size of Non-Hispanic white Note here the computation is similar with the way in appendix A. And Hedges g and the standard errors are Ethnicity Asian Mexican Hedges' g Standard Error B.2.2 Portes and Hao s study in 2004 [PortesHao2004] Portes and Hao also showed us a regression of drop-outs on 12 predictors, 3 of them are national origin predictors. Data information is just the same in section A.2.5. They used the data from the Children of Immigrants Longitudinal Study (CILS95-96), which sampled 5266 children from Miami, Florida, and California. Totally 44 schools took part in this study, and 77 different nationalities were represented in the study (See [PortesHao2004], p ). Here they considered three groups: Chinese/Korean, Mexican, and Vietnamese; since in Portes and Hao s paper, only total number (N = 4654) was reported, we simply treat the three groups have equal sample size because of the lack of information. Since they used drop-outs, we times minus one in order to present the school completion. National Origin Chinese/Korean Mexican Vietnamese Difference in Dropout (times (-1)) Z-ratio (times (-1)) Standard Error Sample Size of Certain Group Sample Size of others R square

29 Adjusted Standard Error Then Hedges g and the standard errors are National Origin Chinese/Korean Mexican Vietnamese Hedges' g Standard Error B.2.3 Hirschman s study in 2001 [Hirschman2001] Hirschman s research in 2001 reported here is based on the analysis of educational enrollment among immigrant and native-born adolescents age 15, 16, and 17 from the Public Use Microdata Sample (PUMS) files of the 1990 U.S. Population Census. The sample sizes were shown in [Hirschman2001], page 321, table 1. The sample sizes of non-enrollment are estimated based on [Hirschman2001], page 323, table 2. Calculation follows the method in section B.1. Country of Origin China Mexico Odds Ratios of Non-enrollment/Enrollment Odds Ratios of Enrollment/Non-enrollment Number of Enrollment Number of Non-Enrollment The other group, Number of Enrollment The other groups, Number of Non-Enrollment And the results based on odds ratios are Country of Origin China Mexico Odds Ratios Lower Limit of Odds Ratios (one sigma) Upper Limit of Odds Ratios (one sigma)

30 Log Odds Ratios Standard Error of Log Odds Ratios Hedges' g Standard Error of Hedges' g B.2.4 White and Kaufman s study in 1997 [White1997] White and Kaufman reported the high school dropout percentage (See [White1997], p. 390), and six regression models (See [White1997], pp ). Since the lack of the information about sample size, we only list the results here, without some assumptions, we will not be able to count them in our meta-analysis. Ethnicity Asian Mexican Non-Hispanic white Dropout Percentage And the odds ratios of enrollment/dropout are (compare with non-hispanic white) Ethnicity Asian Mexican Odds Ratio The result is similar with the results in B.1 and B.2.3. In order to use this study, we may take the Hedges g s amount as its standard error. It will be safe compare with the result of B.1 and B2.3. Ethnicity Asian Mexican Hedges g B.2.5 White and Glick s study in 2000 [White2000] White and Glick gave a logistic regression of high school participation in The model 3 (See [White2000], p. 681, table 2) had 28 variables, and seven of them are race/ethnicity variables (vs. non- 29

31 Hispanic white). Here the authors only offered a rough rang of p-values, so we estimated the standard errors. Sample size could be gathered from [White2000], p. 680, table 1. Race/Ethnicity Asian Mexican Difference in School Participation Standard Error (est) Sample Size of Certain Group Sample Size of Non-Hispanic White And Hedges g and standard error are Race/Ethnicity Asian Mexican Hedges' g Standard Error APPENDIX C Meta-Analysis of Years of Schooling: Model and Computation In this appendix, we will briefly show how to construct meta-analysis for the studies measured by years of schooling. We have totally 3 studies measured by years of schooling. C.1 An Example Study: Rong s study in 1992 [Rong1992] Rong s study in 1992 explored immigrant generation effects (immigrant and native) on schooling attained for Asians, Hispanics, and non-hispanic whites, using Current Population Survey data (See [Rong1992], p. 625). He built up three multiple regression models for whites, Hispanics, and Asians, each model had three independent variables, one of them was a dummy variable, 1 = immigrants, 0 = other (children of immigrants and natives). So if we take the coefficients as effect sizes, they just show us the difference between the immigrants and the others in a certain ethnicity. And the computation is similar to the computation of Fuligni s study in 1997 in appendix A. The results are Ethnicity Asian Hispanics Difference in Years of Schooling Standard Error Sample Size of Immigrants

32 Sample Size of Native and Children of Immigrants R square Adjusted Standard Error Then Hedges g and standard errors are Ethnicity Asian Hispanics Hedges' g Standard Error C.2 Other Studies measured by Years of Schooling Here we gave brief results of other 2 studies measured by years of schooling. C.2.1 Chiswick s study in 2004 [Chiswick2004] Chiswick used current population survey (CPS) data to analyze the educational attainment by immigrant generation and among the foreign born by country of birth and age at immigration. Chiswick offered a summary statistics of educational attainment for the first generation (See [Chiswick2004], p.371). Country of Origin Chinese Mexican Average Educational Attainment Standard Deviation Sample size Use the procedure of two independent groups (See [Borenstein2009], p. 26, and [Cooper2008], p. 224), we have Country of Origin Chinese Mexican Educational Attainment Difference

33 Common Standard Deviation Sample size We may use the regression estimates of pooled sample (See [Chiswick2004], table 2, model 2) of the whole data (first generation (N = 7496), second generation (N = 4506), and native parentage (N = 56483), sample size is 68485) (See [Chiswick2004], p.369), and we use the data in [Chiswick2004] s table 3 to estimate the numbers of certain group, so Country of Origin China Mexico Difference in Education Attainment t-statistics Standard Error Sample Size of Certain Group (est) Sample Size of others (est) R square Adjusted Standard Error Then Hedges g and its standard errors are Country of Origin China Mexico Hedges' g Standard Error C.2.2 Rumbaut s study in 2005 [Rumbaut2005] Rumbaut gave a regression of years of education completed by , among young adult children of immigrants (See [Rumbaut2005], table 9). We use the model 5 there. Sample size are got from [Rumbaut2005], table 8. Ethnicity Vietnamese Mexican 32