Grades in Germany

In Germany, the organisation of education is the responsibility of the federal states, resulting in 16 different education systems. Despite their differences, these systems share some organisational similarities. After kindergarten and primary school (in grade four or grade six depending on the federal state), students in Germany are selected into different secondary school tracks. In most federal states this system is three-tiered and consists of a track with lower requirements (Hauptschule) for years 5 to 9, a track with higher requirements (Realschule) for years 5 to 10 and an academic track (Gymnasium) for years 5 to 12 or 5 to 13 depending on the federal state. Typically students go to separate schools depending on their track. Alternatively, it is also possible for students to go to the same school up until year 10 (Gesamtschule), with some continuing on to the academic track. Successful completion of the academic school track is a requirement for admission to a university (of applied sciences). Students are graded on a scale from 1 for excellent to 6 for insufficient achievement at their respective levels, i.e. depending on their track.

Existing evidence of grading bias

Numerous studies across various contexts and subjects (mostly mathematics and languages) have found that girls receive better grades than boys for the same standardised test performance (for Israel [43]; for Denmark [52]; for Spain [30, 51]; for the US [10, 25]; for Czechia [11]; for Germany [12]; for Italy [49, 50]; for France [9]; for Switzerland [27]; for Greece [46]; for Portugal [47]; for New Zealand [35]). However, there are also studies that do not find such a bias (for Sweden [64]; for India [26]). A study using the same data from Germany as we use here, but examining younger children, finds a grading bias in favour of girls in German and in favour of boys in mathematics [17]. Moreover, the results of some experimental studies suggest that math teachers rate boys more favourably [48]. In an experiment on gender bias regarding STEM subjects in Germany, Austria, and Switzerland, a clear pattern of bias against girls emerges. However, in this experiment, the teachers’ biases disappears as they gain more experience teaching. Furthermore, no evidence was found for gender bias in the subject German [44]. Other experimental studies in Germany and Spain find no gender bias in teachers’ evaluations of essays [31, 65].

Furthermore, quite a number of studies have documented grading bias or discrimination by ethnic origin, minority status or migration background (e.g. for Italy [13, 28]; for Brazil [34]; for UK [32]; for Spain [30, 31]; for the US [25, 38]; for Germany [12, 33, 37]; for New Zealand [35]). However, there are also studies suggesting that—given the same standardised test scores—(some) ethnic minority students are even given more favourable grades than ethnic majority students (for Denmark [52]; for the UK [32]) or graded similarly (for Germany [17, 65]; for Switzerland [27]).

Compared to the body of research on grading bias due to gender and ethnicity or migration background, there are significantly fewer studies on the influence of social background and weight status. Several studies indicate the existence of grading bias against socially disadvantaged children, more frequently observed in languages than in mathematics (for Italy [28]; for Switzerland [27]; for Germany [17]; for Spain [30, 31]; for India [26]; for the US [25]). In a German survey of teachers, children, and parents it was shown that teachers subconsciously gave higher grades to children from higher social classes than was justified by their actual competence levels. This overestimation was caused by teachers perceiving these pupils as “more talented, more willing to achieve and better equipped with parental resources than children from lower social classes” [29, p.1]. In another experiment where teachers grade essays, no evidence was found for discrimination in grading across gender, ethnicity and social class. However, teachers were found to have lower expectations of lower class and minority pupils’ future performance in the case of higher-quality essays [65]. There also appears to be a bias against pupils who are overweight or obese (for the US [40–42]; for Sweden [39]; for Germany [17]).

Potential mechanisms explaining grading bias

There are two dominant related explanatory approaches for grading bias: student behaviour in the classroom [11, 54, 55] and the stereotypes teachers hold of different groups [29, 37, 53].

Following the first line of reasoning, teachers’ evaluations or grading is influenced by student behaviour in the classroom. For example, boys are often more disruptive, less self-disciplined, and less self-regulated than girls. This can result in lower grades [49, 66, 67] either through teacher perceptions and possible prejudice or by incorporating student behaviours in their grading schemes. Studies indicate that teachers give higher grades to students who are more well-adjusted and lower grades to students with more challenging behaviour [54]. Contrary to expectations, a study using data from Germany finds that overweight boys were more affected by bias than overweight girls. The authors suspect differences in classroom behaviour, which they could not account for, to be the reason for this result [17]. A study on gender-bias in grading using data from Czechia offers support for this hypothesis and suggests non-cognitive skills as an explanation for the grading bias in favour of girls across the performance distribution (math and native language) [11]. The authors argue that non-cognitive skills as well as in-class and homework behaviour confound teacher assessments but not test scores. This interpretation is further strengthened by evidence from a non-experimental study from the US in which the disadvantage of boys (after controlling for test scores) in reading, math and science mostly disappears, and under some specifications even leads to a bonus, when non-cognitive skills are taken into account [10]. This stresses the importance of conforming behaviour at school. Evidence from a factorial survey experiment on teacher recommendations for secondary school in Switzerland suggests that challenging behaviour in class may be especially harmful to girls precisely because it is gender stereotype non-conforming [68].

The second main mechanism behind grading bias is that teachers’ grading is influenced by stereotypes and thus expectations about children with different ascriptive characteristics. Implicit stereotypes have been suggested as the reason behind gender bias in the grading behaviour of math teachers to the detriment of girls in Israel [48] as well as in England, the US and Germany [8]. Similarly, in regard to language skills, boys have been found to be underestimated [8]. Research suggesting that gender bias against girls in STEM subjects disappears for more experienced teachers [44] speaks to the plausibility of this assumption.

In regard to ethnicity or migration background, it has been shown that teachers have stronger implicit stereotypes towards (Turkish) minority students (for Germany, [36, 69]) and have lower expectations of and less positive opinions about minority students (for the Netherlands, [53]). Teachers also seem to have higher expectations of European American and Asian American students compared to African American and Latinx students in the US [70], and teachers in Germany rate ethnic minority students who were described as stereotype-confirming lower in language proficiency but not in math in an experiment [71].

It has also been shown that teachers show a positive bias when evaluating the ability of students from more socio-economically privileged homes and are negatively biased in the case of less privileged pupils (experiment in the US: [24]). Furthermore, teachers’ implicit stereotypes could be influenced by pressure from high SES parents, potentially affecting their beliefs about the academic potential of the students [13]. In a German study, the overestimation of students from high SES families was explained by teachers’ more favourable perceptions of these pupils’ attributes and resources [29]. Moreover, research on track recommendations also shows a bias against children from lower social classes [72, 73].

When it comes to weight bias, one of the first studies suggesting that perceptions of ability might also be affected by physical appearance showed that students give higher ratings to (fictitious) other students’ essays if they are physically attractive and lower ratings if they are perceived as less attractive [74]. More recent studies have suggested that teachers’ prejudices may be responsible for the grading bias against overweight children [40, 75] with teachers believing that overweight children have to work harder for the same results, end up having lower grades, and require more support [42].

Grading bias from an intersectional perspective

To account for the fact that people can suffer from cumulative disadvantage by simultaneously facing obstacles on multiple grounds, or being unequally affected by different axes of inequality [76] depending on other aspects of their identities or group membership, we follow an intersectional approach [56, 77]. The term intersectionality was introduced by lawyer Kimberle Crenshaw in a discrimination lawsuit arguing that Black women had not been fired because they were women or because they were Black but specifically for being Black women [56, 77]. Similarly, research on educational inequalities is increasingly taking intersectionality into account to do justice to the fact that depending on their unique combination of ascriptive characteristics, students can face cumulative (dis)advantage on multiple grounds [57–61]. However, to date, empirical research on grading bias taking intersectionality into consideration has been scarce, which is why we aim to contribute to this line of research [17, 31, 52]. More broadly however, it has e.g. been shown that Black girls in US schools are confronted with specific persistent negative stereotypes by teachers [61], as are male Muslim boys in Germany [78]—this could translate into biased grading. Teachers also seem to evaluate obese girls more negatively than boys in the US [75], while the opposite is true for Germany, where teachers especially penalise overweight boys in math [17]. These results suggest that stereotypes towards people with one ascriptive characteristic (e.g. gender) can be amplified by the presence of another ascriptive characteristic (e.g. overweight).

Furthermore, so far, research on intersectionality has mostly focused on cumulative (dis)advantage, which can be either additive in nature, or alternatively also entail an additional penalty or reward. However, it is of course also possible that the advantageous or disadvantageous effects certain aspects of one’s identity can have in regard to an outcome cancel each other out and thus lead to no deviations from the average. This is e.g. the case when having a high social status cancels out the negative effect of being a migrant. In a large-scale factorial survey experiment on stereotypes focusing on the five social categories: gender, sexual orientation, age, ethnic and social class background, the intersections between these categories were found to be responsible for a large part of the variation in warmth and competence ratings. While most of the variation was caused by main effects for competence stereotypes, the opposite was true for warmth stereotypes [79]. Similarly, research on gender and ethnic (5 groups: Asian Americans, Blacks, Latinos, Middle Eastern Americans and white Americans) stereotypes using a free-response procedure has shown that the “gender-by-ethnic stereotypes” were not the result of adding up the respective parts but often contained unique elements specific to the combination in question [80].

In the context of grading bias, next to cumulative disadvantage, it is also possible that teachers would try to compensate particularly or multiply disadvantaged children by using a more lenient grading scheme towards them [31, 52]. In any case, depending on the strength of the stereotypes of the single attributes in question and the unique combinations of social categories, there are many possible scenarios as to what the overall effect on grading bias could be (from additional penalties to neutralisation of penalties to reversal, in extreme cases).

Data

In this contribution, we use data from the fourth starting cohort (SC4, 13.0.0, first survey in year 9 in 2010) of the National Educational Panel Study (NEPS). Our data set thus consists of a nationally representative sample of more than 14,000 ninth graders attained by a cluster sampling strategy (strata, schools and classes). For a more detailed description of the sampling strategy and the study design see [81]. The NEPS is carried out by the Leibniz Institute for Educational Trajectories (LIfBi, Germany) in cooperation with a nationwide network [82, 83]. Next to the questionnaires (paper-pencil-interviews) completed by the pupils in their classrooms, their parents were also surveyed (computer-assisted-interviews). In our contribution, we use data from the first two survey waves (at the beginning and end of year nine).

The NEPS study is conducted under the supervision of the German Federal Commissioner for Data Protection and Freedom of Information (BfDI) and in coordination with the German Standing Conference of the Ministers of Education and Cultural Affairs (KMK) and—in the case of surveys at schools—the Educational Ministries of the respective Federal States. All data collection procedures, instruments and documents were checked by the data protection unit of the Leibniz Institute for Educational Trajectories (LIfBi). The necessary steps are taken to protect participants’ confidentiality according to national and international regulations of data security. Participation in the NEPS study is voluntary and based on the informed consent of participants. This consent to participate in the NEPS study can be revoked at any time. Participant consent was individually obtained for this study, with legal representatives providing consent for minors. The Leibniz Institute for Educational Trajectories in Bamberg securely archives all consent documentation. To safeguard respondents, data usage is strictly limited to scientific research and is effectively anonymised. Prior to data sharing, the institutional data protection officer ensures scientific use and adequate anonymisation or protection.

For our analyses, we used fully anonymised archived samples of the NEPS data. We accessed the data for research purposes from September 2021 to March 2024. The last time we accessed the data was on 15 March 2024. While accessing the data, we did not have access to any information that could identify individuals, we only had access to fully anonymised data.

Operationalisation

The most important dependent variables are the students’ grades in all subjects. The data set supplies us with grades as well as achievement test results in German, mathematics, as well as the natural science subjects: biology, chemistry and physics. In Germany, the grading system uses numbers from 1 (excellent) to 6 (insufficient). For better readability, in our analyses we recode the grades so that the highest values signify the highest achievement and then z-standardise them. According to several studies in Germany, students self-report their grades fairly accurately [84, 85]. For the domain-specific competence in reading, mathematics, and the natural sciences, NEPS provides WLE-estimators. The tests were administered in the classroom and aim to measure competence over the life course (for more information on the competence tests, see [86]). Since the pupils perform the competence tests in different order, the WLE-estimators correct for the position of the respective test in the test booklet.

In addition, the NEPS also measures general cognitive basic skills as cross-domain competence using the DGCF (Domain General Cognitive Functions) test. In the data, the test results are available as sum scores for reasoning and perceptual speed.

To capture differences between students with and without a migration background, we use two different operationalisations. First, we distinguish between ethnic majority and ethnic minority students, without differentiating between the various ethnic origins of the minority students. We classify students as ethnic minority students if they are first to 3.5 minority generation (minority status). Second, following previous literature and due to the available case numbers, we differentiate between the following places of origin: (1) Turkey, (2) the former Soviet Union (FSU), (3) Northwestern and Southern Europe, (4) Central and Eastern Europe as well as (5) other countries (minority group). Assignment to minority status and group is based on the countries of birth of the parents and grandparents using the origin group variable provided by the NEPS.

To classify body weight, we calculate the BMI using the students’ height and body weight. This value is then assigned a percentile value from the Center for Disease Control and Prevention (CDC) classification table according to the age (in months) of the students [87]; for a similar procedure, see [17]. Students were classified as overweight if they had a percentile score of 85 to less than 95 and as obese if they had a percentile score greater than or equal to 95. Due to the small number of students meeting these criteria, we decided to create a binary indicator (overweight or obese) that takes a value of 0 if students have a percentile score less than 85 and a value of 1 if students have a percentile score greater than or equal to 85.

For the operationalisation of social origin, we used the highest ISEI [88] of the parents. The ISEI can take on values between 11 and 90. This variable is based on information the pupils gave about their parents’ occupations. For cases in which the pupils did not provide information about their parents’ jobs, we rely on the information from the parent interviews where possible. We primarily rely on the information the students provide because of the higher percentage of complete questionnaires compared to the parent interviews. For the descriptive analyses, we subdivide the student population into deciles of socio-economic status. For the regression analyses, we use the z-standardised highest ISEI of the parents. To control for psychological characteristics and in-classroom behaviour, we use the following variables: the “big five”, the Strengths and Difficulties Questionnaire scale (SDQ) [89], health satisfaction, the Sick, Control, One, Fat and Food (SCOFF) scale [90] and a binary indicator for class retention.

The big five scales were generated using the answers to two items respectively:

1. openness: 1) “I have a vivid imagination, I am an imaginative person.” 2) “I have little interest in artistic things.” (recoded)
2. conscientiousness: 1) “I am easy‐going and tend to be a bit lazy.” (recoded) 2) “I am thorough when completing my tasks.”
3. extraversion: 1) “I am quite cautious, reserved.” (recoded) 2) “I am out‐going and sociable.”
4. agreeableness: 1) “I trust other people easily, I believe in the good in people.” 2) “I tend to be critical of other people.”
5. neuroticism: 1) “I am relaxed and don’t get stressed easily.” 2) “I am considerate towards others, sensitive.”

The scale values were z-standardised for analysis. Furthermore, we use two SDQ scales: one for measuring prosocial behaviour and the other for measuring problems with peers. Both scales can take values between 0 and 10. An example of an item from the prosocial behaviour scale is: “I try to be nice to other people. I care about their feelings.” An example of an item from the problems with peers scale is: “I am usually on my own. I generally play alone or keep to myself.” Once again, the scale values were z-standardised for analysis. Health satisfaction was measured using the following item: “How satisfied are you with your health?” using a scale ranging from 0) “completely dissatisfied” to 10)“completely satisfied”. The scale values were also z-standardised for analysis. The SCOFF scale is a scale for measuring problematic eating behaviour [90]. One of the items is: “Do you make yourself sick because you feel uncomfortably full?”. This scale forms a sum score of the answers, taking values between 0 and 5, with higher values indicating problematic eating behaviour. The dummy variable for class retention is an indicator of whether a student repeated a grade at least once by the time of the survey.

Furthermore, we control for the different school types in the German education system: the secondary school track with lower (Hauptschule) requirements, the track with higher (Realschule) requirements, the academically oriented secondary school (Gymnasium) as well as the comprehensive schools (Gesamtschule).

Sample selection

Our analytical sample comprises 14,090 students who participated in the second wave of the survey NEPS SC4 at the end of grade 9 and are not attending a special school [81]. S1 Table in the Supporting Information (SI) documents the number of cases, panel attrition and missing values for key variables. Variables with the highest number of missing values are: ISEI (12.3%), BMI (15.5%) and school grades in physics (13.2%), chemistry (13.7%) as well as biology (18.7%). The high number of missing values in the grades for biology, chemistry and physics is due to the fact that not all students attend these subjects. Thus, all students who indicated that they did not receive a grade in a subject were excluded from the respective analysis. We end up with the following case numbers per subject: N_German = 14,005, N_mathematics = 13,964, N_physics = 12,956, N_chemistry = 12,898, N_biology = 12,207.

Multiple imputation

As shown in S1 Table, some model variables have a large proportion of missing values. We decided to deal with this problem by applying multiple imputation by chained equations to generate 50 multiple imputed data sets without missing values (predictive mean matching using burnin = 50). A separate imputation model was calculated for each sample/subject. In addition to all model variables, the imputation models also include the following auxiliary variables: school grades in the other subjects, domain-specific test scores for the other subjects, school grades in mathematics and German from wave 1 (beginning of 9^th grade), self-esteem scale, job aspirations for age 30 (ISEI), parental education (CASMIN), subjective interest in mathematics and German (wave 2), life satisfaction (wave 1), school satisfaction (wave 1), the sampling stratum, as well as the student and school weights.

Estimation strategy

Following other studies on this topic, we use the so-called grade equation approach [17, 63] to estimate grading bias. This means that we investigate to what extent ascriptive characteristics (BMI, gender, ethnic background, SES) have an influence on school grades while controlling for the results of standardised competence tests (here we use domain-specific as well as general cognitive tests) and potential mediator variables (psychological characteristics and classroom behaviour). This approach assumes that standardised competence tests are a more objective measure of domain-specific competence than school grades and that they thus provide an objective reference value for skills [12, 17]. A major advantage of using standardised achievement tests is that the results are obtained independently of the teachers who give the students their school grades. Additionally, the tests are evaluated by researchers who do not know the students. Thus, it can be assumed that there is no danger of bias by ascriptive characteristics in the standardised competence tests.

In our regression analyses, we proceed step by step. For each of the five different grades we calculate the following models: In a first analysis, we estimate how strong the grading bias is (model 1; see Eq (1)). In each of these models, we include the ascriptive characteristic of interest (e.g. gender or BMI status) as well as the respective domain-specific competence score (e.g. for mathematics, the WLE score in mathematics), the general cognitive ability test scores and the school track attended. However, it should be noted that for the subjects chemistry, biology and physics, we rely on a general competence test for the natural sciences. We thus obtain an estimator for the total effects of grading bias in each subject for the ascriptive characteristics of interest. Given the structure of our data, we estimate three-level multilevel models with the levels: students (i) nested within classes (j) nested within schools (j). To reflect possible contextual variations in grading, we include random intercepts at the school and class level in the models. Since we are interested in grading bias for 5 factors (gender, body-weight, social origin as well as minority status and group) in 5 subjects (German, mathematics, biology, chemistry and physics), we estimate model 1, depicting the total effects of grading bias, 25 times. (1) where

Y_ijk is the z-standardised school grade;

γ are the regression coefficients;

A_ijk is one of the five ascriptive characteristics;

X_ijk is a vector of the individual-level model variables, including domain-specific test scores, general cognitive test scores and attended school track;

u_0jk is the random intercept at the class level;

v_00k is the random intercept at the school level;

σ_ijk is the error term.

In a next step, we calculate models that also include the other ascriptive characteristics (taking into account either minority status or minority group) as well as all other control variables (model 2; see Eq (2)). Our goal is to assess to what extent psychological characteristics and behaviour contribute to the explanation of the observed grading bias. We estimate this model 10 times (5 times for each subject including minority status and 5 times for each subject including minority group). (2) where

Y_ijk is the z-standardised school grade;

γ are the regression coefficients;

A_ijk is a vector of the ascriptive characteristics;

X_ijk is a vector of the individual-level model variables, including domain-specific test scores, general cognitive test scores; and attended school track;

Z_ijk is a vector of the individual-level model control and mediator variables, including psychological traits and in-classroom behaviour;

u_0jk is the random intercept at the class level;

v_00k is the random intercept at the school level;

σ_ijk is the error term.

In a third step, we test for intersectional effects of social origin, gender, body weight, and minority status or group on grading bias using several approaches. First, we estimate a model based on model 1 that includes all main effects of the above ascriptive characteristics, but no interactions between them. Second, we estimate the same model as in the first step, but including all two-way interactions between the four ascriptive characteristics. Third, we estimate a model that includes all 4-way interactions between the four ascriptive characteristics. Based on the results of these models, we calculate predictive margins of grades for different groups of students with different combinations of ascriptive characteristics and then compute the differences. This allows us to account for potential intersectional disadvantages by e.g. comparing low SES (-1 SD) overweight/obese boys of Turkish descent with high SES (+1 SD) non-overweight/obese majority girls.

Grading bias

Fig 1 shows the average bivariate grade differences for the ascriptive characteristics: gender, BMI status, SES, minority status and minority group. Furthermore, it shows the results of two models: the total effects of the ascriptive characteristics (grading bias) on school grades (model 1) as well as to what extent this grading bias is influenced by psychological traits or in-classroom behaviour (model 2). The corresponding regression tables are shown in S2–S6 Tables. For a figure depicting the mean test score differences, see S1 Fig.

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Fig 1. Mean school grade differences and grading bias by students’ ascriptive characteristics across subjects.

Note: Red coloured icons indicate statistical significance. Regression coefficients based on three-level linear regression models. Model 1 adjusts for domain-specific competence, general academic competence and school track. Model 2 adjusts for all model variables (see S2–S6 Tables). Source: NEPS SC4 (based on m = 50 multiple imputed datasets); weighted data, our own calculations.

https://doi.org/10.1371/journal.pone.0305703.g001

Regarding the bivariate differences, we see that, in some cases, there are considerable differences in the absolute school grades between these groups. For example, girls have significantly better grades in German (0.44 SD) and biology (0.19 SD) than boys while boys have slightly better grades in mathematics and physics. There is no significant gender difference in chemistry grades. Furthermore, overweight/obese students have lower grades than non-overweight/obese students in all subjects. This effect is least pronounced in mathematics and most pronounced in German and biology. We also see a considerable difference in grades, to the advantage of the more privileged students, between the first and the tenth SES deciles in all school subjects. Moreover, minority students have lower absolute grades than majority students. While these effects are relatively similar for all subjects, they are once again most pronounced in German. Almost all minority groups show lower grades than majority students in all subjects (except the FSU in mathematics). Among minority students, those from Turkey have the lowest grades. We therefore see the largest difference to the majority group for students from Turkey.

We see from the results of model 1 (see Fig 1) that students with different ascriptive characteristics receive different grades through almost all school subjects, even when they demonstrate the same domain-specific as well as general cognitive competence. In more detail, we see grading bias by gender in all subjects except for chemistry and girls seem to have an advantage in German (0.37 SD), mathematics (0.06 SD) and biology (0.21 SD), while boys have an advantage in physics (-0.10 SD). Looking at the results for students with different body weight, we see that overweight/obese students receive lower grades through all subjects (from -0.21 in German to -0.07 SD in mathematics and physics). Similarly, students with higher parental SES receive higher grades in all subjects (from 0.08 in German to 0.04 SD in mathematics and chemistry). Furthermore, we see that minority students also have a disadvantage through all subjects (from -0.14 in German to -0.07 SD in chemistry) except biology. If we look at the minority groups separately however, we only find significant differences to the majority group in some cases and mostly in German, where we see a disadvantage for pupils from Turkey (-0.24 SD), the FSU (-0.19 SD) and “other” countries (-0.15 SD). In mathematics we see a disadvantage for pupils from Central-Eastern Europe (-0.11 SD) as well as from “other” countries (-0.12 SD), while in physics a disadvantage is found for pupils from North-Western and Southern Europe (-0.13 SD), as well as “other” countries (-0.14 SD). For chemistry, we find a disadvantage for students from North-Western and Southern European (-0.11 SD) as well as Central-Eastern European countries (-0.10 SD). No differences are found for biology.

A comparison of coefficients for girls and boys in model 2 (see Fig 1) shows that, in general, when controlling for personality traits and grade retention, boys seem to gain in grade points compared to girls. However, especially in German (0.29 SD) and biology (0.08 SD), we still see a large discrepancy to the advantage of girls. In mathematics there are no more significant differences in grades while in physics the advantage of boys is larger than in model 1 (-0.2 compared to -0.1 SD) and they now also have an advantage in chemistry (-0.09 SD). Regarding body weight, the inclusion of the personality traits and the indicator for grade retention reduces the disadvantages for overweight/obese students. Significant disadvantages remain only in German (-0.1 SD). However, the inclusion of the variables operationalising personality and behaviour does not affect grading bias by social origin. The advantages for socio-economically privileged students remain around the same magnitude in all subjects. Regarding effects of ethnic origin, we see that adding the additional variables leads to a reduction of the disadvantage for minority pupils. While, this reduction is not very pronounced for German and physics, the disadvantages for minority students in mathematics and chemistry are no longer apparent. However, in German, the disadvantages in school grades remain for all minority groups except for the European minorities—with the most pronounced disadvantage for students from Turkey (-0.22 SD). In the other subjects, disadvantages are still evident for pupils from Central-Eastern European countries (-0.08 SD) in mathematics, and students from North-Western and Southern European (-0.11 SD) as well as “other” countries (-0.12 SD) in physics. There are no (longer) any differences to be found by ethnic group in chemistry and biology. The results suggest that although psychological and behavioural factors do seem to have an impact on grading, the effect is not very large.

Intersectional disadvantage?

To further illustrate the intersectional effects of the ascriptive characteristics of interest, we calculate predictive margins based on the above models including no interaction effects, 2-way interaction effects, and 4-way interaction effects. Fig 2 shows how much lower grades are for female and male minority students or those with a Turkish background (since this is the minority group where we see the biggest disadvantage in Fig 1) for different combinations of body weight and social origin. The corresponding regression tables are shown in S7–S11 Tables. For a figure depicting the predictive margins of majority students compared to minority students, see S2 Fig.

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Fig 2. Predicted school grade differences for students with specific ascriptive characteristics across subjects and different models.

Note: Red coloured icons indicate statistical significance. Predictive margins at the means of all other model variables. Predictions derived from multilevel regression models (see S7–S11 Tables). No IE = models without interactions, 2-way IE = models with all 2-way interactions, 4-way IE = models with all 4-way interactions. Source: NEPS SC4 (based on m = 50 multiple imputed datasets); weighted data, our own calculations.

https://doi.org/10.1371/journal.pone.0305703.g002

The results suggest that the different models (no interaction effects, 2-way interaction effects, and 4-way interaction effects) lead to fairly similar predicted grade differences. Although the confidence intervals in the interaction models are significantly wider, making the predicted grade differences less likely to be statistically significant, the point estimates are often quite similar. These results suggest that the negative effects of ascriptive characteristics accumulate. Thus, we find evidence of an additive intersectional disadvantage, but no evidence of a significant additional penalty or strong compensation beyond the additive effects, since the interaction models yield very similar results to the models without interactions. This interpretation, based on the predicted grade differences, is further supported by the fact that very few of the 2-way or 4-way interactions are statistically significant (see, S7–S11 Tables). In German and mathematics, some combinations of girl and high-SES show a small positive effect. However, no consistent patterns can be derived from the few significant interaction effects.

To sum up, even though we do not find evidence of additional penalties or compensation effects beyond the sum of individual effects of gender, body weight as well as ethnic and social background, significant differences between groups are evident. Generally, the grade penalties are most substantial in the subjects German and biology. Moreover, the grade penalty is particularly pronounced for Turkish overweight/obese boys from socio-economically disadvantaged families compared to majority non-overweight/obese girls from advantaged families in German. With equal domain-specific and general proficiency scores, these students receive a German grade that is approximately 0.8 SD lower. We observe similar, though less dramatic, grade penalties across all subjects for Turkish overweight/obese boys and girls from socio-economically disadvantaged families. Looking at the predictive margins for all ethnic minority students compared to majority students (see, S2 Fig), similar patterns emerge. However, since the number of cases is much bigger (comparing all ethnic minority students to majority students), the confidence intervals are smaller and we find statistically significant differences for more combinations of ascriptive characteristics.

Robustness checks

To test the robustness of our results, we take a few measures. First, we transform our dependent variable (the school grades) differently. Instead of using z-standardised grades, we use the grade ranks of students within a class as the dependent variable and run linear regression models with clustered standard errors on the class level. We thus create grade ranks for each school class and standardise them to values between 0 and 1. To avoid possible biases that might occur in small classes where it might be difficult to create ranks, we restrict our analysis sample by only including students in classes with at least 10 pupils. While due to the smaller sample and the transformed value range (ranks take values between 0 and 1) we observe statistically significant results less often, the results for model 1 and model 2 are very similar to the results presented above using the z-standardised scores (see S3 Fig). Again, the effects are most pronounced in German. Furthermore, the gender effects seem to be very stable in all subjects.

Second, we let go of the assumption that the effects of the ascriptive characteristics of interest are constant across classes [52]. We therefore estimate random-intercept, random-slope models for model 1 (instead of random-intercept models), thus allowing the effects of the ascriptive characteristics to vary across classes. We chose to restrict our analysis sample based on relevant characteristics of the class composition: To be included, the class had to consist of at least 10 students, and there also needed to be at least one child with and one child without the specific ascriptive trait of interest per class, e.g. at least one boy and one girl. Since there are many classes without at least one child from each minority group, we do not estimate random slopes for the separate minority groups but use minority status instead. The models are computed using only complete cases (CCA), since it is not possible to display the distribution of random slopes in a multiple imputation (MI) framework. The switch from MI to CCA should not be a problem, since the effect estimates we are interested in are very similar in both approaches (see S4 Fig).

The patterns of the distribution of slopes across school classes in the random-slope models (see S5–S9 Figs) are worth noting. While there is not much variance across classes regarding the positive effects of a higher socio-economic background on grades through all subjects, the effects of the other ascriptive characteristics vary considerably in magnitude depending on the class. Especially in regard to gender and body weight, we see a large variance in effect size, while the differences are somewhat less pronounced for minority status. This means that the disadvantage some students face due to their gender, weight, socio-economic as well as ethnic background are stronger depending on where they go to school. However, without additional analyses, we cannot say what the cause of these differences is. All in all, the results of our robustness analyses are reassuring.