Appendix B.1. Outcome Variables (Y)
The outcome variables of this study are students “suffering from school bullying”, “suffering from relational bullying”, “suffering from verbal bullying”, and “suffering from physical bullying”, which are student-level variables. The PISA 2018 background questionnaire surveyed students’ experiences of bullying-related behaviors in school and measured three different types of bullying: physical bullying, relational bullying, and verbal bullying [
40]. PISA 2018 asked students “During the past 12 months, how often have you had the following experiences in school? (Some experiences can also happen in social media.):
“Other students left me out of things on purpose.” (Relational bullying),
“Other students made fun of me.” (Verbal bullying),
“I was threatened by other students.” (Verbal bullying),
“Other students took away or destroyed things that belonged to me.” (Physical bullying),
“I got hit or pushed around by other students. “ (Physical bullying),
“Other students spread nasty rumors about me.” (Relational bullying).
If a student chooses “Never or almost never” they receive 1 score, “A few times a year” receives 2 scores, “A few times a month” receives 3 scores, and “once a week or more” receives 4 scores. Add up the scores of six items to obtain the “suffering from school bullying” variable. The score ranges from 6 to 24 scores. Similarly, add the scores of questions 1 and 6, the scores of questions 2 and 3, and the scores of questions 4 and 5, respectively, to obtain the variables of relational bullying, verbal bullying, and physical bullying. The higher the scores are, the more serious the bullying is.
Since there is not necessarily a high correlation between the six measurement items of school bullying (for example, students may be suffering from relational bullying but not physical bullying), the measurement of school bullying should be a Formative Indicator. There is still no comprehensive way to test the reliability and validity of the formative indicators now, but most scholars believe that there should not be serious multi-collinearity problems among the combined indicators, which will reduce the reliability and validity of the measurement model [
41,
42]. Based on this, we carried out the multi-collinearity test of these six items. The result showed that the VIF values reflecting the severity of the collinearity problem were between 1.552 and 2.041, which met the standard of less than 3.3, indicating that there was no multi-collinearity problem among the 6 items. It means that the reliability and validity can be guaranteed. Similarly, the VIF values of relational bullying, verbal bullying, and physical bullying were 1.484, 1.203, and 1.270, respectively, none of which was greater than 3.3, indicating that there were no multicollinearity problems for the items in these 3 different types of bullying variables. Additionally, the reliability and validity can be guaranteed.
Appendix B.2. Predictor Variables (X)
The predictors at the student-level of students are as follows:
Gender. In this study, gender is a binary dummy variable, female = 0, male = 1. Studies found that the number of male students who suffered from school bullying was significantly higher than that of female students [
8,
14], so gender is an important factor that affects a student’s suffering from school bullying.
Grade (continuous variable). Students are all in grades 7 to 12. Research showed that the amount of school bullying decreases with the grades increasing [
8,
9,
43].
Education Type (two-category dummy variable), general education = 0, vocational education = 1;
Grade repetition (two-category dummy variable), no grade repetition = 0, grade repetition = 1;
Truancy (two-category dummy variable), no truancy = 0, truancy = 1;
Arriving late for class (two-category dummy variable), no lateness = 0, lateness = 1;
Family’s economic, social, and cultural status (continuous variable). PISA uses IRT technology to synthesize ESCS according to the parents’ highest educational degree (PARED) which selects the maximum value of parents, parents’ highest occupational status (HISEI) which is assigned based on the occupational prestige index in previous research [
44] and adopts the maximum value of parents, and home properties (HOMEPOS) which is based on the property condition reported by students of their family’s computers, books, musical instruments, internet, independent bedrooms, vehicles (cars), and other household assets, etc. Then, they are added up to obtain the individual overall household economic status score. Finally, the three variables of PARED, HISEI, and HOMEPOS were converted into standard Z-values and subjected to principal component analysis to obtain the ESCS value of each student. The average value of students in OECD countries is 0, and if the value is negative/positive, it is lower/higher than the average level of students in OECD countries. The higher the score is, the higher the family’s economic, social, and cultural status is.
The above 1 to 7 variables are not potential constructs, and they belong to the measurement of non-psychological constructs; there is no measurement error, so there is no need to discuss their reliabilities and validities.Teacher support (continuous variable). The variable measures the teacher’s cognitive and emotional support as perceived by the students for them in the classroom. There are four items for the question “How often do these things happen in your <test language lessons>?”:
“The teacher shows an interest in every student’s learning”;
“The teacher gives extra help when students need it”;
“The teacher helps students with their learning”;
“The teacher continues teaching until the students understand”.
The options are “Every lesson” for 1 score, “Most lessons” for 2 scores, “Some lessons” for 3 scores, and “Never or hardly ever” for 4 scores. For the sake of explanation, all the items are converted into reverse scores, and then we add these items to obtain the average for the index measurement of teacher support. The index range is 1 score to 4 scores. The higher the score is, the higher the teacher’s support for students’ learning is. The Cronbach’s alpha coefficient between the 4 items is 0.864, which indicates high internal consistency reliability.
- 9.
Parent support (continuous variable). The variable measures students’ perceived emotional support from their parents, including three items for the question “Thinking about <this academic year>: to what extent do you agree or disagree with the following statements?”:
“My parents support my educational efforts and achievements”;
“My parents support me when I am facing difficulties at school”;
“My parents encourage me to be confident”.
They receive 1 score for “Strongly disagree”, 2 scores for “Disagree”, 3 scores for “Agree”, and 4 scores for “Strongly agree”. Add up the scores of the three items and take the average to obtain the parent emotional support index. The index ranges from 1 score to 4 scores, and the higher the score is, the higher the level of parents’ emotional support for students is. The Cronbach’s alpha coefficient between the 3 items is 0.908, which indicates high internal consistency reliability. Relevant studies have shown that teachers’ support and parents’ support for students can influence their experiencing of school bullying [
25,
26].
At the school-level, there are two types of predictor variables: one type is the variables which are based on the overall construct, originate from the group level, and describe the characteristics of the group, including nine variables:
School location (categorical variable): divided into town schools and city schools, town schools = 0, city schools = 1. The areas where schools are located in villages (less than 3000 people), towns (about 3000 to 15,000 people), and county towns (about 15,000 to 100,000 people) are classified as town schools, and the areas where schools are located in cities (100,000 to 1 million people) and large cities (more than 1 million people) are classified as city schools;
School type (categorical variable): divided into public schools, which refer to schools directly or indirectly managed by the government or public educational institutions, and the leadership of the school is appointed or openly elected by the government, and private schools, which refer to schools directly or indirectly managed by non-government organizations, such as churches, unions, businesses, or other private institutions. Public schools are assigned the value of 0, and private schools as 1;
School size (continuous variable): the school size measures the total number of students enrolled in the school. When the total number of students is larger, it means that the school is larger in size;
Class size (continuous variable): class size refers to the average number of class members in the school, and the larger the value is, the larger the class size is;
Student–teacher ratio (continuous variable): the ratio of the total number of students to the total number of teachers in the school, and the larger the value is, the more students are supervised by each teacher;
Proportion of boys (continuous variable): refers to the proportion of the number of boys in school to the total number of students, and the larger the value is, the more boys in the school there are;
Proportion of special needs students (continuous variable): refers to the sum proportion of students whose native language is not Chinese, students with special educational needs, and students who are from families with financial difficulties. The larger the value is, the more of students with special needs there are;
Proportion of students without graduation certificate (continuous variable): refers to the proportion of the students’ number who leave the school without obtaining a graduation certificate to the total number of students. The larger the value is, the more students without a graduation certificate there are;
Similarly, the above (1) to (8) variables are not potential constructs, and they belong to the measurement of non-psychological constructs; there is no measurement error, so there is no need to discuss their reliabilities and validities
- 9.
Student behaviors and teacher behaviors that hinder learning at school (continuous variable): in the school questionnaire, we learned about student behaviors and teacher behaviors that hinder student learning by asking “In your school, to what extent is the learning of students hindered by the following phenomena?”
Student behaviors that hinder student learning include six items:
“Student truancy”,
“Student skipping classes”,
“Student lacking respect for teacher”,
“Students’ use of alcohol or illegal drugs”,
“Student intimidating or bullying other students”,
“Students not being attentive”.
Teacher behaviors that hinder students’ learning include five items:
“Teachers not meeting individual students’ needs”,
“Teachers’ absenteeism”,
“Staff resisting change”,
“Teachers being too strict with students”,
“Teachers not being well prepared for classes”.
If students choose “Not at all” they receive 1 score, “Very little” receives 2 scores, “To some extent” receives 3 scores, and “A lot” receives 4 scores. The higher the score is, the greater the impact that hinders students’ learning is.
Because there are not necessarily correlations between these behaviors of students and teachers (e.g., students who skip classes are not necessarily disrespectful to teachers, and similarly, teachers who are reluctant to change are not necessarily insufficiently prepared), the measurement models of the two variables are also combinedmeasurement index (Formative Indicator), and their reliabilities and validities are still tested by the existence of multi-collinearity. The multi-collinearity diagnosis results of the variable of student behaviors that hinder learning show that the first two items (Student truancy, Student skipping classes) have certain collinearity (VIF = 15.605 and 14.251), so the first item is deleted, and the sum scores of the five items left behind are used as the measurement of student behaviors that hinder learning. Then, the multi-collinearity diagnosis is carried out again, and results show that the VIF values of the 5 items are between 1.860 and 8.024. Although the VIF values of some items exceeds 3.3, according to Hair’s suggestion [
45], as long as the VIF is below 10, it is still an acceptable range, indicating that there is no collinearity problem, and the reliability and validity of the measurement model can be guaranteed. Therefore, the variable of student behaviors that hinder learning ranges from 5 to 20 scores. Similarly, the multi-collinearity diagnostic results of the variable of teacher behaviors that hinder learning show that the VIF values of the 5 items are between 1.881 and 4.179, which is also in an acceptable range, indicating that there is no collinearity problem between these items. The reliability and validity of the measurement model is good. The variable of teacher behaviors that hinder learning also ranges from 5 to 20 scores.
Another type of school-level variables are those based on shared constructs, including three variables as follows:
- 10.
School disciplinary atmosphere (continuous variable): it is aggregated from the mean value of the disciplinary atmosphere of the class perceived by students in the student questionnaire. The measurement of disciplinary atmosphere in the student questionnaire includes the following five items for the question “How often do these things happen in your <test language lessons>?”:
“Students don’t listen to what the teacher says”;
“There is noise and disorder”;
“The teacher has to wait a long time for students to quiet down “;
“Students cannot work well”;
“Students don’t start working for a long time after the lesson begins”.
Students choosing “Every lesson” receive 1 score, “Most lessons” for 2 scores, “Some lessons” for 3 scores, and “Never or hardly ever” for 4 scores. Add the scores of the five items and take the average to obtain the disciplinary atmosphere index. The index ranges from 1 score to 4 scores. The higher the score is, the better the disciplinary atmosphere of the student’s class is. The Cronbach’s alpha coefficient of the 5 items is 0.894, which has high internal consistency reliability. Then, the scores of each student in each school are summed and averaged to synthesize the school-level disciplinary atmosphere.
- 11.
Competitive/Cooperative atmosphere among students: it is aggregated from the mean value of the competitive/cooperative atmosphere among students perceived by students in the student questionnaire. The measurement of the two variables in the student questionnaire consists of four items for the question “Think about your school: how true are the following statements?”:
“Students seem to value competition/cooperation”,
“It seems that students are competing/cooperating with each other”,
“Students seem to share the feeling that competing/cooperating with each other is important”,
“Students feel that they are being compared with others”/“Students feel that they are encouraged to cooperate with others”.
The answer is “Not at all true” for 1 score, “Slightly true” for 2 scores, “Very true” for 3 scores, and “Extremely true” for 4 scores. The index ranges from 1 to 4 scores. The higher the score is, the higher the perceived level of competitive/cooperative atmosphere is. The Cronbach’s alpha coefficient between the 4 items of competition is 0.813 and of cooperation is 0.934, which have high internal consistency reliability. Then, the scores of each student in each school are added and averaged to synthesize the index of competitive/cooperative atmosphere among students at the school level.