Reference group effects and parental educational expectations: can big-fish-little-pond effects explain immigrant parents’ high expectations? Open Access

It is a well-established finding that immigrant parents often have higher educational expectations compared with nonimmigrant parents (e.g., Feliciano and Lanuza, 2016; Glick and White, 2004; Lawrence, 2015). At first glance this may appear surprising, given that parents of low socioeconomic backgrounds tend to show lower parental expectations (e.g., Davis-Kean, 2005; Glick and White, 2004; Yamamoto and Holloway, 2010), and that immigrant parents often occupy lower socioeconomic positions than their nonimmigrant counterparts, are less familiar with the education system, and may be less proficient in the instructional language (Antony-Newman, 2019).

While a substantial body of research on immigrant parents’ educational expectations has proposed potential explanations for immigrant parents’ higher expectations (e.g., self-selection, immigrant optimism; for an overview see Becker and Gresch, 2016), direct tests of the proposed theoretical mechanisms are rare (Becker and Gresch, 2016, pp. 89–90). One potential explanation for these higher parental expectations could also be related to the context in which education takes place: via reference group effects, if parents compare their children's achievement to those of their children's classmates. The same level of achievement tends to be evaluated less favorably when students are in a high-achieving context (e.g., school class), whereas it tends to be evaluated more favorably when they are in a low-achieving context. In education research, such mechanisms are known as the ‘big-fish-little-pond’ effects (Dai and Rinn, 2008; Marsh, 1987). Big-fish-little-pond effects have generated considerable research interest, and they have been found to shape not only students’ academic self-concept (Fang et al., 2018; Seaton, Marsh, and Craven, 2009) but also external evaluations of a student's abilities (e.g., among teachers; Rothenbusch et al., 2016; Boone et al.2018; Bergold, Weidinger, and Steinmayr, 2022). However, we do not know whether this mechanism also plays a role in the formation of parental educational expectations. Since immigrant students are more likely ‘to swim in a little pond’, that is, attend a low-achieving context (e.g., Borgna, 2016), reference group effects could lead their parents to systematically develop higher expectations for their educational outcomes.¹

Thus, this paper addresses the above-mentioned gap in the literature and investigates (a) whether big-fish-little-pond effects play a role in the formation of parental educational expectations and (b) whether these effects can (partially) explain why immigrant parents often have higher educational expectations. To investigate these questions, we draw on nationally representative data from the German part of the Progress in International Reading Literacy Study 2016 (PIRLS 2016) (Hußmann et al., 2020), which surveyed children and their parents in the fourth grade, just before the first school transition into different educational tracks, and conducted multilevel (mediation) analysis in combination with a multiverse analysis across 4,608 model specifications.

Educational expectations (i.e., realistic educational aspirations) are often distinguished from aspirations (i.e., idealistic educational aspirations), even though definitions differ between studies (Haller, 1968; Morgan, 2007; Seginer, 1983; Zimmermann 2020, pp. 66–67). While educational aspirations refer to (parents’) wishes for (their children's) educational outcome, educational expectations refer to the predicted educational outcome when considering resources and obstacles that support or hinder educational outcomes.

This implies that educational expectations result from parents considering different factors that affect their children's educational process. Thus, a rational choice perspective provides a useful framework for understanding parental educational expectations, as it posits that individuals formulate educational decisions, or in our case, educational expectations, based on costs-and-benefits considerations (e.g., Breen and Goldthorpe, 1997; Erikson and Jonsson, 1996). According to this theoretical approach, parents consider three factors when forming their educational expectations for their children: (a) the expected benefits of an educational path, such as of attaining an academic degree; (b) the perceived costs of obtaining this degree; and (c) the perceived probability of success. Therefore, all else being equal, if parents assess their children's academic achievement as (comparatively) low, they develop less ambitious educational expectations for their children, since assessed achievement plays a central role in assessing the probability of educational success. Conversely, parents are more likely to have higher expectations if they evaluate their children's abilities more positively and, consequently, perceive a greater probability of their success. Differential perceptions and assessments of their children's academic achievement will therefore result in differences in parents’ educational expectations.

The apparent paradox with immigrant parents is that they display high educational expectations although they often have fewer resources and may face higher costs, and their children tend to perform less well than their nonimmigrant classmates. In this vein, a large body of research has found higher educational expectations among immigrant and ethnic-minority parents compared with nonimmigrant and ethnic-majority parents (e.g., Lawrence, 2015, for the US; for contrasting results and differences between ethnic minorities, see Yamamoto and Holloway, 2010; Brinbaum and Cebolla-Boado, 2007, for France; Cebolla-Boado, González Ferrer, and Nuhoḡlu Soysal, 2021, for Spain). Higher educational expectations of immigrant parents have also been documented in Germany (Becker and Gresch, 2016; Relikowski, Yilmaz, and Blossfeld, 2012; Roth and Salikutluk, 2012)—despite the often lower achievement levels among immigrant children. Previous work on the underlying mechanisms has pointed to several potential explanations for immigrant parents’ higher educational expectations, many of which resonate with parents’ cost-benefit considerations (for a review of previous research, see Becker and Gresch, 2016, p. 82 ff.). These explanations include immigrant optimism (Cebolla-Boado, González Ferrer, and Nuhoḡlu Soysal, 2021; Kao and Tienda, 1995), information deficits (Cebolla-Boado, González Ferrer, and Nuhoḡlu Soysal, 2021; Relikowski, Yilmaz, and Blossfeld, 2012), discrimination and blocked opportunities (e.g., Morgan, 2004; Tjaden and Hunkler, 2017), social capital and ethnic networks (Roth and Salikutluk, 2012), status maintenance with respect to the country of origin (Engzell, 2019; Feliciano and Lanuza, 2017), and differences in context of achievement (Becker and Gresch, 2016).

In this study, we focus on the role of the context of achievement, that is, the class achievement level, in shaping parental educational expectations. We argue that systematic differences in the context of achievement between immigrant and nonimmigrant parents contribute to systematic differences in educational expectations, since the context of achievement affects how parents assess their children's abilities and success probabilities, and consequently, shapes parents’ educational expectations.

According to comparison theories, people evaluate their abilities and performance in comparison to a reference performance, so-called frames of reference. Different types of reference frames have been identified in the literature (Möller and Marsh, 2013). For example, people evaluate their current performance in comparison to previous performance (‘temporal comparison’; Albert, 1977), in comparison to a substantive criterion, such as scoring on a standardized test (‘criterion-oriented comparison’; Bergold, Weidinger, and Steinmayr, 2022; Rheinberg, 1983), or comparing their performance in two dimensions, such as in two school subjects (‘dimensional comparison’; Möller and Marsh, 2013). The social or external frame of reference (Festinger, 1954), the focus of the current study, applies when people evaluate competencies or performances in comparison to that of others, that is, the reference group. This means that the evaluation of one's own competencies and performances depends on the reference group's abilities or achievements.

In education research, one of the most common examples of this reference group effect is the so-called big-fish-little-pond effect: When people evaluate their competencies, they tend to compare their competencies and performances with those of their reference group (e.g., their classmates). They therefore come up with a relative assessment of their competencies. Equally able people will evaluate their own competencies and performances more positively when comparing their abilities with a low-performing reference group than with a high-performing reference group.² The big-fish-little-pond effect has attracted considerable empirical interest, particularly its impact on students' academic self-concept (e.g., Fang et al., 2018). Furthermore, the effect has been found all over the world and has earned the status of a pan-human phenomenon (Seaton, Marsh, and Craven, 2009).

Previous research indicates that such social comparison processes not only apply to the evaluation of one's own competencies and performances but are also relevant to the evaluation of others’ competencies and performances. The big-fish-little-pond effect has been found in the assessment of students by their teachers (Bergold, Weidinger, and Steinmayr, 2022; Rothenbusch et al., 2016; Trautwein et al., 2006). Bergold, Weidinger, and Steinmayr (2022), for example, show that teachers rate students’ abilities less favorably when the class-average ability is high. Given the occurrence of the big-fish-little-pond effect in the evaluation of one's own and other's competencies and performances, it is reasonable to assume that this mechanism is present not only among students and their teachers but also among students' parents.

Parents differ in one important aspect from students and their teachers with regard to big-fish-little-pond effects: Students and their teachers have direct information about a student's performance as well as their peers’ performance. That is, they know the average class performance, which is a necessary condition for the comparison mechanisms of the big-fish-little-pond effect to work. Do parents possess this information too?

It is reasonable to assume that they have a more or less accurate idea about the children's performance within the context of the class, as they rely on various sources of information to evaluate their children's (relative) academic performance (Sonnenschein, Stapleton, and Metzger, 2014). One of the primary sources of information is the school, where parents have access to their children's school reports and discuss their academic performance with teachers. In some federal states in Germany where the data of this study come from, parents are directly informed about the distribution of grades for their children's exams by being provided with the so-called Notenspiegel (e.g., Hessia, Hessian Ministry of Education, 2020). In other states the provision is voluntary (e.g., Bavaria, BayLfD, 2006; Brandenburg, MBJS, 2011), or it is not legally regulated (e.g., North Rhine-Westphalia, MSB, 2023).³ Other sources of information are the children themselves or other parents: Through exchanges with other parents of the child's school class, parents can obtain information about the performance of other children and assess their child's performance in comparison to their classmates. There is indeed evidence that parents engage in temporal, dimensional, and social comparisons when evaluating their children's competencies (Wolff et al., 2020; but see van Zanden et al., 2017).

These findings lead us to assume that parents evaluate their children's scholastic performance—and consequently their children's probability to follow a certain academic path and to attain a certain educational degree—not in a void but with respect to a significant reference group. Thus, parents’ evaluation of children's performance depends not only on the child's scholastic achievement but also on how a child performs compared with other children, with classmates constituting an important reference group.

But can big-fish-little-pond effects explain differences in expectations between immigrant and nonimmigrant parents? That is, are there systematic differences in the school context between immigrant and nonimmigrant students? Differences in average class performance, and thus in the reference groups, for immigrant and nonimmigrant students could lead to immigrant-nonimmigrant differences in parental expectations (depicted by paths a and b from class’ migration status via class’ achievement to parental expectations in Figure 1).

There are several reasons why immigrant students are more likely to attend a low-performing class than nonimmigrant students (and therefore have different reference groups). Immigrant children more often attend low-achieving schools because of residential segregation. Social and ethnic residential segregation affects school segregation (e.g., Böhlmark, Holmlund, and Lindahl, 2016, for Sweden; Boterman, 2019, for the Netherlands; Noreisch, 2007, for Germany), as parents usually choose schools in their neighborhood for practical or institutional reasons (e.g., mandatory catchment areas). Thus, the social and ethnic composition of the neighborhood is usually reflected in the student population of (elementary) schools, often causing children with a migration background to attend classes with a lower average socioeconomic status (SES). Because of social differences in scholastic achievement, that is, primary effects (Boudon, 1974), socially disadvantaged schools and schools with a high share of language-minority students are often associated with lower average school performances (Burger, 2019; Gresch, 2016, pp. 489–490).

Parental school choice further enforces the segregation of schools (Wilson and Bridge, 2019). According to Cebolla-Boado and Garrido Medina (2011) and Kristen (2008), parents’ school choice varies depending on their migration and socioeconomic status. Parents with a high SES and without a migration background more often choose a school with a lower proportion of socially disadvantaged or immigrant students (also referred to as ‘majority flight’ or ‘white flight’), which reinforces schools’ social and ethnic segregation (Gresch, 2016; Horr, 2016; Kristen, 2008; Parade and Heinzel, 2020). Owing to these effects of school choice and neighborhood segregation, we expect systematic differences in the class’ achievement level between immigrant and nonimmigrant families, leading to higher educational expectations among immigrant parents. Specifically, we expect that immigrant students are more likely to attend lower-performing classes than nonimmigrant students. Therefore, on average, immigrant parents compare their child's performance with a lower class’ performance than nonimmigrant parents, leading to a higher evaluation of their child's performance.

Our hypotheses therefore are the following: Big-fish-little-pond effects influence parents’ educational expectations (H1). First, we assume that average class performance affects parental educational expectations over and above their children's individual scholastic achievement (displayed as path b in Figure 1). High average achievement leads to lower expectations and low average achievement leads to higher expectations. Second, we assume that these reference group effects mediate the association between parental migration status and educational expectations (H2). We assume that immigrant students are more likely than nonimmigrant students to attend low-achieving classes (path a) and that these low-achievement contexts lead to higher educational expectations among immigrant parents, controlling for individual scholastic achievement (path b).

In the stratified German school system, the transition from elementary to secondary school, at which students are sorted into different school tracks, is a critical point regarding students’ future opportunities and development of educational inequalities (Neugebauer and Schindler, 2012). The most relevant distinction is between those tracks that lead to a school leaving certificate that opens up the path to tertiary education (the so-called Abitur or Fachabitur) and those that do not. This distinction is therefore central in framing parental educational expectations (Dumont, Klinge, and Maaz, 2019).

Since education falls within the responsibility of the federal states (hereafter Länder), school systems vary between them, in particular regarding how tracks are organized and when students are sorted into these tracks.⁴ In all Länder, students are sorted into different educational tracks at an early age: in most states after grade 4, in Berlin and Brandenburg after grade 6. During the last grade of primary school, teachers give a recommendation for secondary schooling and the school provides parents with a (mandatory) consultation and guidance on this decision. In these consultations, parents receive detailed feedback on their children's school performance and which secondary school teachers consider most suitable for them. The degree to which the recommendation is binding again varies between the Länder.

The primary education system in Germany is organized in school districts. Each elementary school has a catchment area that is mandatory in most areas. Thus, the composition of elementary schools reflects the neighborhoods’ ethnic and social segregation (Ditton and Krüsken, 2006; Horr, 2016; Parade and Heinzel, 2020). In all Länder, parents can nevertheless request to send their child to a school other than the designated one, an option that is used in particular by parents with a higher SES and nonimmigrant parents (Gresch, 2016; Horr, 2016; Kristen, 2008; Parade and Heinzel, 2020), thus reinforcing the social and ethnic segregation of elementary schools.

This section is structured as follows. The subsection Data provides information on the survey data we draw on. In the Multiverse analysis section, we elaborate the rationale of multiverse analyses, which test analytic specifications. These different specifications are described in the subsequent sections: the section Modeling strategy describes our decisions regarding model choice (for example, whether we estimated linear probability or logit models); the section Missing data and data exclusion describes which observations we excluded, and how we deal with missing data; the section Measures describes the operationalization of the variables and which covariates we included in our models.

To test our hypotheses, we use the German data from the Progress in International Reading Literacy Study 2016 (PIRLS 2016) (Hußmann et al., 2020). PIRLS is a large-scale assessment study that monitors trends in fourth-grade students’ reading achievement. The German dataset comprises a nationally representative sample of 3,959 students from 208 primary schools, with an average class size of 18 students. The survey was conducted between May and June 2016. PIRLS utilized a two-stage random sample design, drawing a sample of schools at the first stage, and selecting one or more intact classes of students from each of the sampled schools at a second stage (LaRoche, Joncas, and Foy, 2017). About 20% of the students have an immigrant background, and the average immigrant share of school classes is 21%. Tables A4 and A5 in the online appendix provide an overview of additional sample statistics. PIRLS offers a variety of information about students’ background and school in addition to data on reading achievement in the fourth grade. PIRLS 2016 includes questionnaires for students (response rate of 88%), parents (response rate of 72%), teachers (response rate of 93%), and school principals (response rate of 93%) in addition to assessment tests regarding students’ reading achievement (participation rate of 95%) (Hußmann et al., 2017, p. 62). Since tracking in most German schools takes place after the fourth grade, the educational transitions are salient at the time of the survey. Therefore, it is likely that parents have already carefully considered their children's educational careers before answering the questionnaires.

Instead of a single set of models, we conducted a multiverse analysis (Simonsohn, Simmons, and Nelson, 2020; Steegen et al. 2016). Therefore, before describing the statistical models, the selection and operationalization of the variables, and further data analytic choices, we first outline the rationale of the multiverse analysis. The analyses were carried out in Stata 16 and Mplus Version 8.8. We programmed the multiverse analysis using nested loops in Stata (Simonsohn, Simmons, and Nelson, 2020) and ran each model in Mplus using the Stata ado runmplus (Jones, 2010).⁵

Multiverse analyses address the issue that all analyses are based on numerous and, at times, arbitrary data analytic decisions. This concerns study-centric (e.g., exclusion criteria), variable-centric (e.g., variable coding), or model-centric decisions (e.g., model choice) (Rijnhart et al., 2022). If researchers present the result of only one model that emerges from a chain of specific data analytic decisions, it remains unclear how robust this result is in relation to alternative reasonable data analytic choices. To address this problem, scholars recommend examining the robustness of one's findings across the multiverse of model specifications (Auspurg and Brüderl, 2021; Brinkmann et al., 2024; Simonsohn, Simmons, and Nelson, 2020; Steegen et al., 2016; Young and Holsteen, 2017). Therefore, in this paper, we make our data analytic decisions transparent and show how the results depend on these decisions.

It is important to note, however, that the results of a multiverse analysis can be only as good and meaningful as the assumptions on which they are based. Rerunning a misspecified model does not make the findings more meaningful, but would contribute to false certainty. For this reason, it is essential to make the model-specific decisions in addition to the theoretical considerations transparent. In the following, we describe the analytical decisions we made, and the reasonable alternatives to these decisions. Table 1 provides an overview of the model specifications. In the analyses section, we provide a discussion of our initial model—that is, the model we would present if we were to present only one specification or model—and subsequently a discussion of the results of the multiverse analysis. We start by discussing model choice.

Since our data are hierarchical (students nested in schools/classes), we estimated multilevel models (Rabe-Hesketh and Skrondal, 2012; Raudenbush and Bryk, 2002; Snijders and Bosker, 2012). Moreover, since our hypotheses assume mediations (Hayes, 2009), we estimated multilevel structural equation models (Preacher, Zyphur, and Zhang, 2010).⁶

As described below, the dependent variable is of binary nature, which we address with two model variants (Table 1, dimension I). First, for our initial specification, we estimated a linear probability model (LPM). LPMs often perform as well as other more complicated models, such as logit models, and have the advantage of being easily interpretable (Angrist and Pischke 2009; Hellevik, 2009). To account for the necessarily occurring heteroskedasticity in a linear model with a binary dependent variable, we estimated robust standard errors using a sandwich estimator (Muthén and Muthén, 1998–2017). Second, since LPMs may predict probabilities outside the 0–1 range (Angrist and Pischke, 2009; Hellevik, 2009), we also estimated a logit model in an alternative specification. We estimated the models using the maximum likelihood method with robust standard errors (MLR). Standard errors for the indirect effect estimates were obtained with the multivariate delta method (Raykov and Marcoulides, 2004).

Moreover, to address the complex sampling design and the hierarchical data structure, we use within-cluster weights (Rutkowski et al., 2010). That is, we use the combination of final school weights and the final class weights at level 2 (adjusted for nonparticipation) and the final student weight at level 1 (adjusted for nonparticipation) (LaRoche, Joncas, and Foy, 2017).⁷

We build our models in several steps. First, we investigate whether immigrant parents have higher educational expectations than nonimmigrant parents (M1). Second, we investigate whether big-fish-little-pond effects, that is, class achievement, influence parental expectations (M2). Finally, we investigate whether these effects mediate the relationship between immigrant status and parents’ educational expectations through a two-equation model (M3). Table A1 presents the equations for the initial models M1 to M3.

In order to include more encompassing information on parental status, we use the parent questionnaire. The parent questionnaire contains a substantial amount of unit non-response (27.3%), as not all parents completed and returned the questionnaire. We have to assume that this information is not missing completely at random (Bhaskaran and Smeeth, 2014; Enders, 2010; Little and Rubin, 2002). We use two alternative strategies to handle missing data in the LPMs (Table 1, dimension III): complete case analysis (listwise deletion) and full information maximum likelihood (FIML), which is well suited for the analysis of data that is missing at random (Enders and Bandalos, 2001) and can be applied in multilevel modeling (Grund, Lüdtke, and Robitzsch, 2019).⁸ While the results may still be biased if the missingness depends on the value of the missing variable itself or if the normality assumptions are violated (Muthén, Muthén, and Asparouhov, 2016), the approach is preferable to listwise deletion.

Furthermore, we vary the exclusion criteria (Table 1, dimension V). First, we vary whether we include or exclude students with special educational needs. While the reference group effect is also found among children with disabilities (Szumski and Karwowski, 2015), it may be conceivable that reference group effects do not similarly translate to the educational expectations of parents with children with special educational needs. Especially in so-called inclusive or integrative classes (classes with students with and without special needs in regular schools), it is conceivable that parents do not form their expectations compared with the class-mean performance. Second, we vary the minimum class size because we expect class means based on only a few students to be less reliable predictors than means based on many students (Schunck, 2016), at least when small classes result from missing observations. However, a disadvantage of excluding small classes is that we lose observations and risk possible bias in the sample, especially when small classes do not result from missing observations but represent an actually small class size.

In the following, we describe the different operationalizations of our measures. Table A2 provides an overview of these measures and operationalization variants for the multiverse analysis. Table A3 provides an overview of the assumed causal status of the covariates and the reasoning of including versus not including them in the models.

To measure parents’ educational expectations, our dependent variable, parents indicated the highest school degree they expect their children to achieve (question wording: ‘What do you think: What is the highest level of schooling your child will achieve?’). The answer categories are 0, ‘no school degree’ (.25% of all responses); 1, ‘Hauptschulabschluss’ (school degree after 9th grade; 6.7% of all responses); 2, ‘Realschulabschluss/Mittelschulabschluss’ (school degree after 10th grade; 24.95% of all responses); 3, ‘Fachhochschulreife’ (qualification to enter university of applied sciences; 10.79% of all responses); and 4, ‘Abitur’ (the general qualification for university entrance; 57.31% of all responses).

In the stratified German education system, the most relevant distinction in school degrees is between the (Fach-)Abitur and other degrees, as the (Fach-) Abitur is the highest school leaving certificate and qualifies students for university entrance. In the first version, we therefore coded the variable into a binary categorical variable with the value 1 indicating the expectation for the Abitur (academic track) and the value 0 indicating the expectation for a lower degree. In the second version, we coded the outcome variable to 1 when parents expected their children to obtain either the Abitur or the Fachabitur (‘Fachhochschulreife’), which allows students to study at universities of applied sciences, and to 0 when they expected a lower school degree.

For the main independent variable, the student's migration status, we distinguish between students with nonimmigrant parents (the reference category), and students with immigrant parents. We used two versions of this variable. In both versions, we use students with nonimmigrant parents as the reference category. In the first version, we coded children with one immigrant and one nonimmigrant parent as children with nonimmigrant parents. In the second version, we coded this group as children with immigrant parents.

To measure reference group effects, that is, contextual effect, we include both the individual and the class scholastic achievement in our models. When a variable is included as both an individual characteristic and a level 2 aggregate, the level 2 aggregate indicates the contextual effect (Enders and Tofighi, 2007). The contextual effect shows the difference in parental expectations if a student with the same scholastic performance would attend a higher-performing class.

We use three different versions of scholastic achievement, and use the class average as the contextual effect and the non-aggregated variable as the individual effect for each version (Table 1, dimension II). In the first version, we operationalize the individual scholastic achievement using the average of the five reading test scores (plausible values) of the literacy assessment test. The plausible values range from 73 to 798 (with an average mean of 540 and an average standard deviation of 74), and higher values indicate better reading proficiency (see Martin, Mullis, and Hooper, 2017, for the scaling methodology). Although we favor this operationalization of the reference group effect because it is unaffected by potential biases in the teachers’ evaluation of a student's performance, school grades provide valuable alternative operationalizations. Since it is likely to be more difficult for low-SES parents or parents unfamiliar with the German education system to assess their child's school performance, school grades provide important information on the child's chances in their further educational career. Thus, the second and third versions are based on the student's last midyear grade in German and math, respectively. The grades in the German school system range from 1 to 6, with 1 indicating the best grade. We reverse-scaled the variables, so that higher values indicate better school grades.

For better comparability and to facilitate interpretation, we min-max normalized all individual-level measures of achievement so that they range from 0 to 1, and then calculated the class average. The min-max normalization affected the performance of the logistic models and led to high standard errors of the odds ratios; therefore, we used the non-normalized achievement variables in the logistic models.

As illustrated in Figure A1, we furthermore control for several additional student and class characteristics in all models: the student's sex (Buchmann, DiPrete, and McDaniel, 2008), age, and both the SES of the students’ families and the SES composition of the school class. The reference category for the students’ sex is male (0, ‘male’; 1, ‘female’). The students’ age ranges from 8 to 14 years (mean age: 9.9).

We operationalized students’ SES using parental education and family income. For parental education, we include a measure of the highest education level attained by either parent of students. Parental education level has 5 categories and ranges from 1 (‘some primary, lower secondary, or no school degree’) to 5 (‘university degree’). Family income is the equivalized income to take into account differences in household size and composition. The families’ equivalized income ranges from €58 to €5,384 (mean = €1,661; standard deviation = €861). We divide the variable by 100 so that a one-unit change indicates an income difference of €100. The first version of multiverse specification includes only the parental education level, because of the high amount of missing data in the family income variable (42% missing; see Table A4). The second version includes both parents’ educational level and family income, and the third version includes only family income. In all three versions, we use the class average to measure the SES composition of the school class. We prefer the first version of operationalization, as we argue that parental education might pose a mediator-outcome confounder (see Table A3). That is, we expect that the SES composition affects both the class achievement level and the class average parental expectations. In the fourth version of the multiverse specification, we excluded both SES variables, because of the risk that a student's SES might mediate the association between migration status, scholastic achievement, and parental expectations.

Additionally, we control for students’ cognitive abilities and the teachers’ evaluation of the students’ work behavior as potential confounders (see Figure A1). The students’ work behavior was evaluated by their teachers. The variable ranges from 0 to 3, with higher values indicating a more positive evaluation. The students’ cognitive abilities were assessed using a figurative analogies subscale of a standardized test of cognitive abilities (Heller and Perleth, 2000). The test scores range from 0 to 69, with higher values indicating better cognitive abilities (mean = 49.7, standard deviation = 9.5). In addition, we estimate more parsimonious models by excluding these additional control variables in the alternative model specifications (see Table A3 for a description of the variables’ causal status).

In the following, we discuss the findings of the initial model specification. We assume that parental expectations are not only influenced by individual processes, but also shaped by the children's class context. This implies that parental expectations not only differ between individuals, but also vary between classes. We first investigate the intraclass correlation (ICC) to investigate whether there are indeed significant differences in parental expectations between classes. The ICC of parents’ educational expectations of .102 indicates that 10% of the total variance can be attributed to systematic differences between the class contexts.⁹ This suggests that a significant part of differences in parents’ educational expectations can be explained by the class context the children attend, which we further investigated in the following models.

Before we turn to the test of our hypotheses, models M1a and M1b reproduce the well-known finding that immigrant parents have higher educational expectations than nonimmigrant parents while taking individual-level factors into account (Table 2). Model M1a included students’ gender, age, parental education, work behavior, and migration status as predictors. Model M1a shows a significant main effect of the immigrant status on parental education expectations both on the individual and class level. Immigrant parents are more likely to expect their children to achieve a higher school degree than nonimmigrant parents (b = .056, p < .05). Since the estimate comes from a linear probability model, the effect size can be interpreted as the difference in expected probability: Immigrant parents are about 5.6 percentage points more likely to expect that their children pass the Abitur than nonimmigrant parents. Furthermore, classes with higher shares of immigrant parents tend to show higher average educational expectations, as estimated by the between effect of the share of immigrant students (b = .280, p < .001). The effects of the immigrant status become more pronounced if the students’ scholastic achievement is adjusted (within effect: b = .094, p < .001; between effect: b = .375, p < .001; Table 2, model M1b). Moreover, parents’ educational expectations are higher when their child attends a class with a higher share of students with a migration background compared with classes with a lower share of immigrant students (b = .280, p < .001; Table 2, model M1a), which is in line with previous research on the impact of class ethnic composition on parents’ educational expectations (e.g., Lawrence, 2015).

In model M2 (Table 2), we test whether class context plays a role in parents’ educational expectations. Akin to model M1b, we include parental education and a student's demographics, work behavior, and individual scholastic achievement as controls. We assess the direct effect of the class achievement level on parents’ expectations holding the child's individual achievements constant through the contextual effect. In line with hypothesis H1, we find a big-fish-little-pond effect: Parents’ expectations are less favorable when their child attends a high-achieving class compared with a low-achieving class (b = −.607; p < .01)—and vice versa—controlling for individual achievement (b = 1.130; p < .001) and several other influential student characteristics. This means that if a student were to change their class context so that average achievement (min-max normalized, ranging from .18 to .83; see Table A5) would increase by one unit, this would be associated with a decrease in parental expectations that their child would pass the Abitur by about 61 percentage points (contextual effect).

Since class achievement varies only at the class level, we model the mediation at the class level (level 2). Specifically, we estimate the path of migration status on class achievement on level 2 (path a), and estimate the effect of class achievement on individual parental expectations as a contextual effect (path b). Figure 3 shows the specified paths of the mediation analysis. Supporting hypothesis H2, we find an indirect effect of migration background on parental education expectations via class achievement (indirect effect, path a × path b: b = .091, p < .01).¹⁰ The students’ migration background is negatively related to the average class achievement level (path a: b = −.149, p < .001). This effect is substantial considering that class achievement level ranges from .18 to .83 and has a standard deviation of .089. The average class achievement level in turn is negatively associated with parents’ educational expectations (path b: b = −.607, p < .01). Given that parents’ educational expectations is a binary variable with an overall standard deviation of .495, this effect is also substantial. This suggests that immigrant students are more likely to attend a low-achieving class, which in turn is related to higher parental educational expectations. However, we also find a direct effect of the migration status context (b = .231, p < .01), indicating that reference group effects can only partially explain the positive effect of immigrant status context on parents’ educational expectations (total effect¹¹ of the migration status context on individual parental expectations: b = .217, p < .01).

To investigate the robustness of our findings based on the reference group model M2 and the mediation model M3, we employed a multiverse analysis using a variety of model specifications (see Table 1 for an overview of the specifications). The different specifications result in 4,608 model variants of the initial models M2 and M3 discussed above (3,072 models based on LPMs; 1,536 models based on logit models). As the effect estimates are not comparable between LPMs and logistic regression models, we report results separately.

The multiverse analysis regarding model M2 indicates high robustness of the big-fish-little-pond effect estimates (hypothesis H1, path b) across the model specifications (Figure 4 and Figure A2 for the LPM models and Figures A3 and A4 for the logit models). Each point represents the estimated effect for each specification, with blue dots representing statistically insignificant coefficients and black dots statistically significant coefficients (p < .05). Figure 4 additionally depicts the 95% confidence intervals to visualize the statistical uncertainty of the estimated coefficient. The red circle depicts the estimated coefficient from the initial model specification discussed above. The dots in the lower part of the figure indicate the model characteristics of a given model, such as which additional covariates we included in the model and how we operationalized the variables.

The estimated coefficient is negative in 92.3% of the specifications and statistically significant in 67.9% of the linear probability models (p-value ≤ .05 in 2,084 out of 3,071 models) (See Table 4). For the logit models, the reference group effect is negative in 91.7% of the model specifications and statistically significant in 62.2% (p-value ≤ .05 in 955 out of 1,536 models). This indicates a high robustness of the initial findings in terms of sign stability and statistical significance. Figure 4 indicates that not controlling the potential confounder of family SES, controlling students’ work behavior, and using school grade compared with reading achievement scores results in smaller estimates of the big-fish-little-pond effects.

To investigate how the big-fish-little-pond effect changes with different model variables in more detail, we conducted a so-called influence regression (see Young and Holsteen, 2017). Figure 6 shows how each model variant, on average, affects the big-fish-little-pond effect on parents' educational expectations (path b). The negative big-fish-little-pond effect is on average smaller when using math or German grades compared with reading scores (initial specification). The influence regression further shows that mainly the exclusion of parents’ SES status as a potential mediator influences both the coefficient and the statistical significance of the big-fish-little-pond effect. Excluding students’ working behavior, on average, leads to a stronger big-fish-little-pond effect.

For the multiverse analysis regarding the mediating role of the big-fish-little-pond effect (hypothesis H2, path a × path b), we use the same specifications as above. Specifically, we tested the robustness of the indirect effect of the migration background on parental expectations mediated by class achievement (Figure 5).

In sum, the multiverse analyses suggest high sign robustness of our findings across model specifications regarding big-fish-little pond effects for parental expectations. However, the indirect effect of migration status on parental expectations via big-fish-little-pond effects appears to be less robust. Although the direction of the relationship is very consistent, the indirect effect reaches statistical significance in only about half of specifications.

This paper contributes to a better understanding of how parents form their educational expectations in general and why immigrant parents often have higher educational expectations than nonimmigrant parents by showing that the children's class appears to serve as a frame of reference for parental educational expectations.

In line with the big-fish-little-pond hypothesis, we assumed that parents’ educational expectations develop in reference to the (average) class achievement. While this mechanism is a well-known explanation for differences in students’ ability self-perceptions (Fang et al., 2018), and teachers’ student evaluations (Bergold, Weidinger, and Steinmayr, 2022; Faber, 2013; Neumann et al., 2010; Trautwein and Baeriswyl, 2007), it has not been investigated with respect to parental educational expectations. By applying a multilevel (mediation) analysis to a representative sample of German fourth graders and their parents, we were able to show that average class achievement affects parents' educational expectations beyond their child's individual achievement. Our findings suggest that parental expectations vary systematically with the achievement level of the classes their child attends: Parental expectations are lower if children attend high-achieving classes. Parental expectations are higher if children attend low-achieving classes—this holds for all parents, regardless of immigrant status. Moreover, we hypothesized that higher educational expectations among immigrant parents result from differences in mean class achievement. Our initial multilevel mediation model indeed indicated that class achievement mediates the relationship between immigrant status and educational expectations: Students with immigrant parents are more likely to attend a low-achieving school, which is associated with higher parental expectations.

However, the multiverse analyses show that while this effect is very robust in terms of sign stability, it is less in terms of statistical significance. The indirect effect of the migration status reached statistical significance in only about 45% of the model specifications. Moreover, the big-fish-little-pond effect can only partially explain the relationship between immigrant parents and educational expectations. Thus, future research should test additional contextual mechanisms discussed in the literature. Promising starting points pose the immigrant optimism and the information discrepancy approaches (Salikutluk, 2016). Although these approaches have been primarily used to explain interindividual differences in educational expectations between minority and majority members, they could also apply to the study of class-level differences. For instance, parents’ expectations could be shaped not only by the context of class achievement but also by other parents' optimistic views.

Our findings are limited in several ways that might be promising starting points for future research. First, our analyses are cross-sectional and we therefore cannot draw conclusions about causality. Research using panel data that observes school changes could investigate whether transferring to a higher- or lower-performing class affects parents’ educational expectations. Second, we investigate differences between immigrant and nonimmigrant parents without distinguishing between different immigrant groups. Indeed, research in the US context suggests that parents’ expectations differ between ethnic groups (Yamamoto and Holloway, 2010). However, because of the small sample size of immigrant students, we could not distinguish between groups of immigrants. Third, our theoretical model and the interpretation of the results rest on the assumption that parents have information about the relative performance of the children, that is, that they know how their child performs with regard to the rest of the class. In the German case, in some federal states, parents are indeed informed about the distribution of grades within their children's classes. However, this does not hold for all federal states. Thus, in the absence of robust evidence that parents are aware of their children's relative performance compared with their peers, the results should be understood less as strong evidence of big-fish-little-pond effects than the absence of falsification. Fourth, we investigated whether parents’ educational expectations are influenced by the achievement level of the entire school class and did not examine whether parents’ comparison process is restricted to some classmates. Although it is argued that people tend to compare themselves to similar others (Festinger, 1954), studies that investigated whether specific subgroups of classmates are of particular importance for social comparison processes among students have yielded mixed findings (e.g., Jansen, Boda, and Lorenz, 2022; Thijs, Verkuyten, and Helmond, 2010). However, with the data at hand this is not feasible, as there are too many classes with too small a proportion of migrant-origin students for which we could not reliably estimate a class-mean performance. Whether the achievement of other immigrant children is more relevant to immigrant parents’ expectations than the achievement of the entire class thus remains an empirical question that goes beyond the scope of this study.

Furthermore, the causal status of several covariates is ambiguous (see Table A3), which significantly impacts our findings. Some covariates, such as students’ SES and work behavior, are mediator-outcome confounders and should therefore be controlled. However, the same covariates could also mediate the association between immigrant status and achievement, and should therefore not be controlled. For instance, the multiverse analyses show that our findings highly depend on whether we control for students’ socioeconomic background. While controlling for SES provides clear evidence for the big-fish-little-pond effect and its mediating role, the results become less robust when we do not include SES in our models. Consequently, the proposed mechanisms appear to hold only under control of SES. Lastly, our study focused on the German context only. Although the German case is especially suitable to investigate parents' educational expectations, future research should investigate whether our findings generalize across countries.

Although there is robust evidence from prior studies showing higher educational expectations among immigrant parents than among nonimmigrant parents, empirical tests of the underlying mechanisms are still scarce. The present research investigated one possible mechanism previously not examined: big-fish-little-pond effects. We used a representative sample of German fourth graders to test whether the classroom context affects parents’ expectations for their children's education. We showed that big-fish-little-pond effects shape parents’ educational expectations, for both immigrant and nonimmigrant parents. High average performance in a class leads to lower parental educational expectations and low average performance leads to higher expectations.

However, the school context can only partially explain why immigrant parents have systematically higher educational expectations for their children than nonimmigrant parents. While immigrant children are more likely to attend low-achieving classes, and parents' educational expectations of their children are higher in low-achieving classes, the indirect effect in the mediation analysis was not particularly robust, being statistically significant in only about half of the model specifications of the multiverse analysis.

AI tools were used to copyedit parts of the text, such as to check grammar, spelling, and sentence structure. They were not used for text-generating purposes. The analyses and data preparation were carried out without AI assistance.

The data underlying this article are available in the IQB – Institut zur Qualitätsentwicklung im Bildungswesen, at http://doi.org/10.5159/IQB_IGLU_2016_v1. The R scripts and the Stata scripts for the data preparations and analyses are available at the following link: https://osf.io/73b6q/?view_only=b46ae2827fd94e068fa405d458e86640.

The authors report there are no competing interests to declare.

This research study is exempt from ethical review as it solely involves the secondary analysis of data available to the scientific community. The survey underlying this study has been conducted by the International Association for the Evaluation of Educational Achievement (IEA) in cooperation with the Institut für Schulentwicklungsforschung (IFS) at the University of Dortmund (Hußmann et al., 2017). Consequently, the responsibility for data collection and protection lies with the original data collectors. The data are available in the IQB – Institut zur Qualitätsentwicklung im Bildungswesen, at http://doi.org/10.5159/IQB_IGLU_2016_v1.

This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG; project number: 430266278).

Supplemental data for this article can be accessed online at https://doi.org/10.1162/euso_a_00014.