Results from the Teacher Knowledge Survey

Annex D. Technical notes on analyses in this volume

Use of teacher and school weights

The statistics presented in this report were derived from data obtained through samples of schools, principals and teachers. Samples were collected following a stratified two-stage probability sampling design. This means that teachers (secondary sampling units) were randomly selected from the list of in-‑scope teachers for each of the randomly selected schools (first-stage or primary sampling units). For these statistics to be meaningful for a country, they needed to reflect the whole population from which they were drawn and not merely the sample used to collect them. Thus, survey weights must be used in order to obtain design-unbiased estimates of population or model parameters.

Final weights allow the production of country-level estimates from the observed sample data. The estimation weight indicates how many population units are represented by a sampled unit. The final weight is the combination of many factors reflecting the probabilities of selection at the various stages of sampling and the response obtained at each stage. Other factors may also come into play as dictated by special conditions to maintain the unbiasedness of the estimates (e.g. adjustment for teachers working in more than one school).

The statistics presented in this report that are based only on responses of principals were estimated using school weights (SCHWGT). Results based only on responses of teachers or on responses of teachers and principals (i.e. responses from school principals merged with teachers’ responses) were weighted by teacher weights (TCHWGT).

Use of scales

In this report, several scales are used, in particular in regression analyses. TALIS 2024 and TKS scales were constructed using the same international model parameters to be statistically equivalent across countries/territories and populations, facilitating scale score comparability across education systems. In general, scale scores created for TKS can be used in different types of analyses, including comparisons of country/territory means for each individual scale.

TKS scale scores are standardised to have a standard deviation of 2 across all education systems participating in TKS and where value 10 corresponds to the item mid-point value of the underlying items’ response scale. The only exceptions are the composite scales that combine different scales. These are standardised to have a standard deviation of 2 across all education systems participating in TKS and a mean of 10.

Analysing different scale scores based on the same items (e.g. a composite scale and its subscales) requires caution, as shared variance can influence the results. A detailed description of the construction and validation of TALIS 2024 and TKS scales can be found in Chapter 11 of the TALIS 2024 Technical Report (OECD, forthcoming[1]).

Exchange of information and ideas among teachers

The scale of exchange of information and ideas among teachers (T4EXINF) was constructed using teacher responses ("never", "once a year or less", "2-4 times a year", "5-10 times a year", "1-3 times a month", "once a week or more") about the following statements on how often they (TTG426/TKS18): "Exchange teaching materials with colleagues"; "Engage in discussions about the learning development of specific students"; "Work with other teachers in this school to ensure common standards in evaluations for assessing student progress".

Professional collaboration in lessons among teachers

The scale of exchange of information and ideas among teachers (T4COLES) was constructed using teacher responses ("never", "once a year or less", "2-4 times a year", "5-10 times a year", "1-3 times a month", "once a week or more") about the following statements on how often they (TTG426/TKS18): "Teach jointly as a team in the same class"; "Observe other teachers' classes and provide feedback"; "Engage in joint activities across different classes and age groups (e.g. projects)"; "Take part in collaborative professional learning".

Self‐efficacy in classroom management

The scale of self‐efficacy in classroom management (T4SECLS) was constructed using teacher responses (“not at all”, “to some extent”, “quite a bit”, “a lot”) about the extent to which they can do the following (TT4G27/TKS15): “Control disruptive behaviour in the classroom”; “Make my expectations about student behaviour clear”; “Get students to follow classroom rules”; “Calm a student who is disruptive or noisy”.

Self‐efficacy in instruction

The scale of self‐efficacy in instruction (T4SEINS) was constructed using teacher responses (“not at all”, “to some extent”, “quite a bit”, “a lot”) about the extent to which they can do the following (TT4G27/TKS15): “Craft good questions for students”; “Use a variety of assessment strategies”; “Provide an alternative explanation, for example when students are confused”; “Vary instructional strategies in my classroom”.

Self‐efficacy in student engagement

The scale of self‐efficacy in student engagement (T4SEENG) was constructed using teacher responses (“not at all”, “to some extent”, “quite a bit”, “a lot”) about the extent to which they can do the following (TT4G27/TKS15): “Get students to believe they can do well in school work”; “Help students value learning”; “Motivate students who show low interest in school work”; “Help students think critically”.

Self‐efficacy (overall)

The scale of teacher self‐efficacy overall (T4SELF) is a composite scale score that was constructed as an average of the three subscales: self‐efficacy in student engagement (T4SEENG), self‐efficacy in instruction (T4SEINS) and self‐efficacy in classroom management (T4SECLS). Composite scale scores have a mean of 10 and a standard deviation of 2.

Clarity of instruction

The scale of clarity of instruction (T4CLAIN) was constructed using teacher responses (“never or almost never”, “occasionally”, “frequently”, “always”) about the frequency of performing the following actions in the target class (TT4G55/TKS24): “I present a summary of recently learned content”; “I set goals at the beginning of instruction”; “I explain what I expect the students to learn”; “I explain how new and old topics are related”.

Cognitive activation

The scale of cognitive activation (T4COGAC) was constructed using teacher responses (“never or almost never”, “occasionally”, “frequently”, “always”) about the frequency of performing the following actions in the target class (TT4G55/TKS24): “I present tasks for which there is no obvious solution”; “I give tasks that require students to think critically”; “I have students work in small groups to come up with a solution”; “I ask students to decide on own procedures for solving complex tasks”.

Classroom management

The scale of classroom management (T4CLASM) was constructed using teacher responses (“never or almost never”, “occasionally”, “frequently”, “always”) about the frequency of performing the following actions in the target class (TT4G51/TKS22): “I tell students to follow classroom rules”; “I tell students to listen to what I say”; “I calm students who are disruptive”; “When the lesson begins, I tell students to quiet down quickly”.

Adaptive learning

The scale of adaptive learning (T4ADLE) was constructed using teacher responses (“never or almost never”, “occasionally”, “frequently”, “always”) about the frequency of performing the following actions in the target class (TT4G55/TKS24): “I consider students’ prior knowledge and needs when planning a lesson”; “I point students to different materials for learning depending on their needs”; “I change my way of explaining when a student has difficulties understanding a topic or task”; “I adapt my teaching methods to students’ needs”; “I ask questions at various difficulty levels to check students’ understanding of the subject matter”.

Progression-based learning

The scale of progression-based learning (T4PBLE) was constructed using teacher responses (“never or almost never”, “occasionally”, “frequently”, “always”) about the frequency of performing the following actions in the target class (TT4G56/TKS25): “I let students review multiple examples”; “I select tasks for student practice that gradually increase in difficulty”; “I prepare students for difficulties that can occur while practicing”; “I let students practice similar tasks”.

Fulfilment of lesson aims

The scale of fulfilment of lesson aims (complexity of teaching) (T4FULFIL) was constructed using teacher responses (“not at all”, “to some extent”, “quite a bit”, “a lot”) about the extent to which the following aims were fulfilled in the past week (TT4G58/TKS26): “Presenting the content in a comprehensible way”; “Engaging students in work that challenges them”; “Providing students with feedback to support their learning”; “Offering students opportunities to practise what they learnt”; “Adapting teaching to meet the different needs of students”.

Workload stress

The scale of workload stress (T4WLOADT) was constructed using teacher responses (“not at all”, “to some extent”, “quite a bit”, “a lot”) about the extent to which the following situations are sources of stress at work (TT4G767/TKS16): “Having too much lesson preparation”; “Having too many lessons to teach”; “Having too much marking”; “Having too much administrative work to do”.

Higher values on the workload stress scale reflect greater perceived stress related to workload.

Student behaviour stress

The scale of student behaviour stress (T4STBEH) was constructed using teacher responses (“not at all”, “to some extent”, “quite a bit”, “a lot”) about the extent to which the following situations are sources of stress at work (TT4G767/TKS16): “Being held responsible for students’ achievement”; “Maintaining classroom discipline”; “Being intimidated or verbally abused by students”.

Higher values on the student behaviour stress scale reflect greater perceived stress related to student behaviour.

Workplace well‐being and stress

The scale of workplace well‐being and stress (T4WELS) was constructed using teacher responses (“not at all”, “to some extent”, “quite a bit”, “a lot”) about the extent to which the following situations occur (TT4G76): “I experience stress in my work”; “My job leaves me time for my personal life”; “My job negatively impacts my mental health”; “My job negatively impacts my physical health”.

Higher values on the workplace well-being and stress scale reflect lower levels of well-being.

Joy of teaching

The scale of joy of teaching (T4JOYTCH) was constructed using teacher responses (“strongly disagree”, “disagree”, “agree”, “strongly agree”) about the following statements (TT4G80/TKS27): “I like the subject(s) that I teach”; “I often feel happy while I teach”; “I generally teach with enthusiasm”; “The interesting challenges of teaching give me satisfaction”.

Job satisfaction with the profession

The scale of job satisfaction with the profession (T4JSPROT) was constructed using teacher responses (“strongly disagree”, “disagree”, “agree”, “strongly agree”) about the following statements related to how they feel about their job (TT4G78): “The advantages of being a teacher clearly outweigh the disadvantages”; “If I could decide again, I would still choose to work as a teacher”; “I regret that I decided to become a teacher”; “All in all, I am satisfied with my job”.

Job satisfaction with the work environment

The scale of job satisfaction with the work environment (T4JSENVT) was constructed using teacher responses (“strongly disagree”, “disagree”, “agree”, “strongly agree”) about the following statements related to how they feel about their job (TT4G78): “I would like to change to another school if that were possible”; “I enjoy working at this school”; “I would recommend this school as a good place to work”.

Job satisfaction (overall)

The scale of job satisfaction overall (T4JOBSAT) is a composite scale score that was constructed as an average of the two subscales: job satisfaction with the profession (T4JSPROT) and job satisfaction with the work environment (T4JSENVT). Composite scale scores have a mean of 10 and a standard deviation of 2.

Opportunities to learn – classroom instruction

The scale of opportunities to learn – classroom instruction (T4OTLCI) was constructed using teacher responses (“not at all”, “to some extent”, “quite a bit”, “a lot”) about the extent to which their training or subsequent professional learning prepared them in various topics about classroom instruction (TK4G11/TKS11): “Lesson design”; “Long-term planning”; “Time management in the classroom”: “Student behaviour and classroom management”; “Collaborative learning”; “Adaptive teaching”; “Classroom discourse and dialog”; “Setting clear learning expectations”; “Student-centred approaches”; “Teaching clarity”.

Opportunities to learn – student learning

The scale of opportunities to learn – student learning (T4OTLSL) was constructed using teacher responses (“not at all”, “to some extent”, “quite a bit”, “a lot”) about the extent to which their training or subsequent professional learning prepared them in various topics about student learning (TK4G12/TKS12): “Educational theories of learning”; “Student individual differences”; “Identification of learning difficulties”; “Psychological theories of child development”; “Science of learning”; “Taxonomies of learning”; “Self-regulated learning”; “Affective-motivational impacts on learning”.

Opportunities to learn – assessment

The scale of opportunities to learn - assessment (T4OTLSAS) was constructed using teacher responses (“not at all”, “to some extent”, “quite a bit”, “a lot”) about the extent to which their training or subsequent professional learning prepared them in various topics about assessment (TK4G13/TKS13): “Different purposes for assessment”; “Standards used to assess students”; “Creating and using rubrics for assessment”; “Peer and/or self-assessment”; “Standardised tests; “Grades and grading”; “Providing effective feedback to students”; “Data literacy”; “Monitoring learning progress”.

Opportunities to learn – additional pedagogical topics

The scale of opportunities to learn – additional pedagogical topics (T4OTLSAP) was constructed using teacher responses (“not at all”, “to some extent”, “quite a bit”, “a lot”) about the extent to which their training or subsequent professional learning prepared them in various topics about assessment (TK4G14/TKS14): “Teaching in a multicultural setting”; “Teaching in a multilingual setting”; “Teaching students from socio-economically disadvantaged homes”; “Methods for inclusion and inclusive pedagogies”; “Accommodating students with special education needs”; “Identifying and/or meeting the learning needs of gifted students”; “Teaching cross-disciplinary”; “Using <digital resources and tools> in instruction”; “Classroom climate”; “Students' social and emotional development”; “Identifying and intervening when students display emotional problems”.

International averages

This report includes eight arithmetic and one weighted average (for more detail about the country coverage of the international averages, see Table A D.1):

• OECD average-4: arithmetic average across the 4 OECD education systems with a data adjudication rating of “good”, “fair” or “poor” participating in TKS 2024. The report refers to the average teacher as equivalent shorthand for the average teacher “across the 4 OECD education systems participating in TKS”.

• TKS average-8: arithmetic average across the 8 TKS 2024 education systems with a data adjudication rating of “good”, “fair” or “poor”.

Table A D.1. Country coverage of international averages in TKS 2024

Country/territory	OECD average-4	TKS average-8
Chile	X	X
Croatia		X
Morocco		X
Poland	X	X
Portugal	X	X
Saudi Arabia		X
South Africa		X
United States	X	X

In this publication, the OECD average is generally used when the focus is on providing a global tendency for an indicator and comparing its values across education systems. In the case of some education systems, data may not be available for specific indicators, or specific categories may not apply. Therefore, readers should keep in mind that the term “OECD average” refers to the OECD education systems included in the respective comparisons. In cases where data are not available or do not apply to all sub-categories of a given population or indicator, the “OECD average” may be consistent within each column of a table but not necessarily across all columns of a table.

Standard errors and significance tests

The statistics in this report represent estimates based on samples of teachers and principals, rather than values that could be calculated if every teacher and principal in every country had answered every question. Consequently, it is important to measure the degree of uncertainty of the estimates. In TALIS, each estimate has an associated degree of uncertainty that is expressed through a standard error. The use of confidence intervals provides a way to make inferences about the population means and proportions in a manner that reflects the uncertainty associated with the sample estimates. From an observed sample statistic and assuming a normal distribution, it can be inferred that the corresponding population result would lie within the confidence interval in 95 out of 100 replications of the measurement on different samples drawn from the same population. The reported standard errors were computed with a balanced repeated replication (BRR) methodology.

Differences between sub-groups

Differences between sub-groups along teacher (e.g. female and male teachers) and school characteristics (e.g. schools with a high concentration of students from socio-economically disadvantaged homes and schools with a low concentration of students from socio-economically disadvantaged homes) were tested for statistical significance. All differences marked in bold in the data tables of this report are statistically significantly different from 0 at the 95% level.

In the case of differences between sub-groups, the standard error is calculated by taking into account that the two sub-samples are not independent. As a result, the expected value of the covariance might differ from 0, leading to smaller estimates of standard error as compared to estimates of standard error calculated for the difference between independent sub-samples.

Analysis using scores from the assessment of general pedagogical knowledge

Following standard practices in international large-scale assessments, IRT modelling was used to construct a scale of general pedagogical knowledge on the basis of teachers’ answers to assessment items. The scale was set in such a way that the average score across all TKS participating countries, giving the same weight to each country, equals 250 points, with a standard deviation of 50 points.

For each teacher, five plausible values were drawn a posterior distribution of scores, after conditioning on all available background information.

Plausible values allow to compute standard errors that correctly reflect the imputation variance, accounting for both sampling and measurement error. All statistics, including regression coefficients, based on GPK use all five plausible values, and the associated standard errors account for both the sampling and the imputation variance (OECD, forthcoming[1]).

For ease of interpretation, when GPK scores are used as regressors in a regression analysis, they are standardised to have a mean of zero and a standard deviation of one across all participating countries. In this way, the resulting coefficient can be directly interpreted as the expected change in the dependent variable associated with a one-standard deviation change in GPK.

Pearson correlation coefficient

In this report, Pearson correlation coefficients are used to quantify relationships between system-level statistics. Correlation coefficients measure the strength and direction of the statistical association between two variables. They vary between -1 and 1; values around 0 indicate a weak association, while the extreme values indicate the strongest possible negative or positive association. The Pearson correlation coefficient (indicated by the letter r) measures the strength and direction of the linear relationship between two variables.

Statistics based on regressions

Regression analysis was conducted to explore the relationships between different variables. Multiple linear regression was used in those cases where the dependent (or outcome) variable was considered continuous. Binary logistic regression was employed when the dependent (or outcome) variable was a binary categorical variable. Regression analyses were carried out for each country separately. Similarly to other statistics presented in this report, the OECD and TKS averages refer to the arithmetic mean of country-level estimates.

Control variables included in a regression model are selected based on theoretical reasoning:

• Controls for teacher characteristics: teacher’s gender, age and years of teaching experience.

• Controls for target class characteristics: class size, class intake of students who have difficulties understanding the language(s) of instruction, class intake of low achieving students, and class intake of students with special education needs.

• Controls for school characteristics: school location, school governance type, school intake of students from socio-economically disadvantaged homes, school intake of students who have difficulties understanding the language(s) of instruction, and school intake of students with special education needs

In the case of regression models based on multiple linear regression, the explanatory power of the regression models is also highlighted by reporting the R-squared (R²), which represents the proportion of the observed variation in the dependent (or outcome) variable that can be explained by the independent (or explanatory) variables.

In order to ensure the robustness of the regression models, control variables were introduced into the models in steps. This approach also required that the models at each step be based on the same sample. The restricted sample used for the different versions of the same model corresponded to the sample of the most extended (i.e. with the maximum number of independent variables) version of the model. Thus, the restricted sample of each regression model excluded those observations where all independent variables had missing values.

Regression analyses presented in this report handle missing data by listwise deletion. In the result tables, regression models that are based on 25% to 50% of the full sample are highlighted with a † next to the country/territory label. Analyses based on less than 25% of the full sample are excluded from the report.

Restrictive models that include many independent variables and are based on small samples can lead to limited variability in some independent variables. This, in turn, may cause the corresponding coefficients to appear either very small or very large. In this report, such independent variables are treated as constants and therefore excluded from the regression model. These suppressed variables are marked with the missing value symbol “m” in the results tables. Please note that this approach – suppressing independent variables with little or no variability – is not applied to control variables.

Multiple linear regression analysis

Multiple linear regression analysis provides insights into how the value of the continuous dependent (or outcome) variable changes when any one of the independent (or explanatory) variables varies while all other independent variables are held constant. Everything else held constant, on average, a one-unit increase in the independent variable ($X_i$) is associated with an increase in the dependent variable ($\text{Y}$) by the units represented by the regression coefficient (${\beta }_i$):

$\text{Y = }{\beta }_0+{\beta }_1{X}_1+ \text{…} +{\beta }_i{X}_i+\epsilon$

When interpreting multiple regression coefficients, it is important to keep in mind that each coefficient is influenced by the other independent variables in a regression model. The influence depends on the extent to which independent variables are correlated. Therefore, each regression coefficient does not capture the total effect of independent variables on dependent variables. Rather, each coefficient represents the additional effect of adding that variable to the model, if the effects of all other variables in the model are already accounted for. It is also important to note that, due to the cross-sectional nature of TALIS data, no causal conclusions can be drawn.

Regression coefficients in bold in the data tables are statistically significantly different from 0 at the 95% confidence level.

Binary logistic regression analysis

Binary logistic regression analysis enables the estimation of the relationship between one or more independent (or explanatory) variables and the dependent (or outcome) variable with two categories. The regression coefficient ($\beta$) of a logistic regression is the estimated increase in the log odds of the outcome per unit increase in the value of the predictor variable.

More formally, let $\text{Y}$ be the binary outcome variable indicating no/yes with 0/1, and $p$ be the probability of $\text{Y}$ to be 1, so that $p=prob\left(Y=1\right)$. Let $X_1 , \dots X_k$ be a set of explanatory variables. Then, the logistic regression of $\text{Y}$ on $X_1 , \dots X_k$estimates parameter values for ${\beta }_0, {\beta }_1, \dots {\beta }_k$ via the maximum likelihood method of the following equation:

$Logit\left(p\right)= \log \left(p/\left(1-p\right)\right)= {\beta }_0+{\beta }_1{X}_1+ \text{…} +{\beta }_k{X}_k$

Additionally, the exponential function of the regression coefficient $\left(exp\left(\beta \right)\right)$ is obtained, which is the odds ratio ($OR$) associated with a one-unit increase in the explanatory variable. Then, in terms of probabilities, the equation above is translated into the following:

$p= exp\left({\beta }_0+{\beta }_1{X}_1+ \text{…} +{\beta }_k{X}_k/1+exp\left({\beta }_0+{\beta }_1{X}_1+ \text{…} +{\beta }_k{X}_k\right)\right)$

The transformation of log odds ($\beta$) into odds ratios$\left(exp\left(\beta \right);OR\right)$ makes the data more interpretable in terms of probability. The odds ratio ($OR$) is a measure of the relative likelihood of a particular outcome when a specific condition is present (the antecedent) compared to when it is not. The odds ratio for observing the outcome when an antecedent is present is:

$OR=\frac{\left(p_1/(1-p_1)\right)}{\left(p_2/(1-p_2)\right)}$

where $p_1/(1-p_1)$ represents the “odds” of observing the outcome when the antecedent is present, and $p_2/(1-p_2)$ represents the “odds” of observing the outcome when the antecedent is not present. The reader should note here that odds are not probabilities, but relative probabilities, i.e. the ratio between the probability of an event occurring over the probability of the event not occurring. This distinction matters especially when the probability of the outcome is high. When the probability of the outcome is low, $p/(1-p)\approx p$.

An odds ratio below one indicates that the odds of the outcome decrease when the value of the explanatory variable increases by 1; an odds ratio above 1 indicates that the odds of the outcome increase when the value of the explanatory variable increases by 1; and an odds ratio equal to 1 indicates that the odds of the outcome are not related to changes in the explanatory variable.

For instance, if the association between being a female teacher and working part-time is being analysed, the following odds ratios would be interpreted as:

• 0.2: Female teachers have 80% lower odds of working part-time than male teachers.

• 0.5: Female teachers have half the odds of working part-time than male teachers.

• 0.9: Female teachers have 10% lower odds of working part-time than male teachers.

• 1: Female and male teachers have equal odds of working part-time than male teachers.

• 1.1: Female teachers have 10% higher odds of working part-time than male teachers.

• 2: Female teachers have twice the odds of working part-time than male teachers.

• 5: Female teachers have five times the odds of working part-time than male teachers.

A bold character indicates that the odds ratios are statistically significantly different from 1 at the 95% confidence level. To compute statistical significance around the value of 1 (the null hypothesis), the odds-ratio statistic is assumed to follow a log-normal distribution, rather than a normal distribution, under the null hypothesis.

Statistics based on multilevel models

In this volume, variance components (between- and within-school variation) and the share of variation between schools (Table MCOB.UND.VARSEG) are estimated using multilevel models. Multilevel models are generally specified as two-level regression models (teacher and school levels), with normally distributed residuals, and estimated with maximum likelihood estimation. Models were estimated using the Stata (version 19) “mixed” module, accounting for teachers and schools weights.

The total variation in teachers’ general pedagogical knowledge is calculated directly from the distribution of teachers’ scores as the square of the standard deviation for all teachers, using only final teacher weights. Due to the unbalanced, clustered nature of the data, the sum of the between- and within-school variation components, as an estimate from a sample, does not necessarily add up to the total.

The share of variation between schools equals the intraclass correlation coefficient (ICC):

$ICC=\frac{{\sigma }_B^2}{{\sigma }_B^2+{\sigma }_W^2}$

where ${\sigma }_B^2$ and ${\sigma }_W^2$ represent, respectively, the between- and within-variance component.

For statistics based on multilevel models (such as the estimates of variance components) the standard errors are not estimated with the usual replication method, which accounts for stratification and sampling rates from finite populations. Instead, standard errors are “model-based”: their computation assumes that schools, and teachers within schools, are sampled at random (with sampling probabilities reflected in school and student weights) from a theoretical, infinite population of schools and students, which complies with the model’s parametric assumptions. The standard error for the estimated ICC is calculated by deriving an approximate distribution for it from the (model-based) standard errors for the variance components, using the delta method.

The dissimilarity index

The dissimilarity index, which is commonly used as a measure of segregation, captures departure from evenness in the allocation of teachers with different characteristics (in the context of this volume, teachers with different levels of general pedagogical knowledge) to schools. If teachers were randomly allocated to schools, one would expect an even allocation, where the share of teachers with high GPK in each school would equal the share of high GPK teachers in the population. When the population is divided in two mutually exclusive groups $a$ and $b$ (for example, teachers being or not in the top quarter of the national distribution of GPK), the dissimilarity index can be written as:

$D=\frac{1}{2}\sum _{j=1}^J\left|\frac{n_j^a}{N^a}-\frac{n_j^b}{N^b}\right|$,

Where $n_j^a$ and $n_j^b$ stand for the number of teachers of type $a$ and $b$ in school $j$ and $N^a$and $N^b$ denote the number of teachers of the two groups in the population.

The dissimilarity index can take values between 0 (when the allocation of teachers in schools perfectly resembles the teacher population of the country) and 1 (when teachers with a certain characteristic are concentrated in a single school). A high dissimilarity index is an indication of teachers with a certain characteristic being highly concentrated in certain schools. Figure A D.1 shows an example in which teachers may be Type A or Type B. They are distributed across six schools, each with a capacity of six teachers. Complete clustering is observed when all the Type A teachers are in one and only one school. No clustering corresponds to a situation where all schools are equally composed of one Type A teacher and five Type B teachers.

Figure A D.1. Illustrative example: complete vs. no clustering of teachers

Source: (OECD, 2022[2])

The dissimilarity index can be interpreted as the sum of the share of teachers of the two mutually exclusive groups who have to be reallocated in order to obtain an identical distribution across all schools. This is best clarified with a concrete example. Consider the same number of schools and of type A and type B teachers as depicted in Figure A D.1, but a different, intermediate situation in which the six type A teachers would be only present in two schools (for example three in the first school and three in the second school). To restore evenness, four type A teachers (ie. $2/3$ of all type A teachers) would need to move to a different school. To preserve school size constant, four type B teachers (ie. $4/30$ of all type B teachers) would also need to change schools, to replace the type A teachers. In this situation, the dissimilarity index would then equal $\frac{4}{30}+\frac{2}{3}=\frac{24}{30}=\frac{4}{5}=0.8$.

In case the share of type A and type B teachers in the overall population are known, it is possible to easily derive from the dissimilarity index the percentage of all teachers that need to change school to restore evenness. Let $M_a^{}$ and $M_b^{}$ denote the number of teachers of groups $a$ and $b$ who need to move to restore evenness. Since school size must be preserved, teachers will always need to swap, therefore $M^a=M^b=M$. The dissimilarity index can then be written as and letting $p=N^a/\left(N^a+N^b\right)$ denote the share of group $a$ in the population, the dissimilarity index can be rewritten as:

$D=\frac{M}{N^a}+\frac{M}{N^b}=M\frac{N^a+N^b}{N^a{N}^b}$

The share $S$ of the total teacher population that needs to move can be then expressed as a function of $D$ and $p=\frac{N^a}{N^a+N^b}$ the share of teachers of type $a$ in the population:

$S=\frac{2M}{N^a+N^b}=2D\frac{N^a{N}^b}{{\left(N^a+N^b\right)}^2}=2Dp(1-p)$

In the example made above, $p=\frac{6}{36}=\frac{1}{6}$. Knowing that $D=0.8$, it is then possible to derive $S=2\times \frac{4}{5}\times \frac{1}{6}\times \frac{5}{6}=\frac{8}{36}$.

In the analysis presented in Chapter 1 of this report, the dissimilarity index is computed focusing on teachers in either the top or the bottom quarter of the national distribution of GPK. As a result, in all countries $p=0.25$, and $S=2Dp\left(1-p\right)=0.375\times D$.

It should be noted that the interpretation of the dissimilarity index can become more difficult when the share of one group is very small. When there are more schools than actual teachers with a certain characteristic, the value of the dissimilarity index will be larger than zero, even if those teachers are randomly allocated across schools (OECD, 2019[3]; OECD, 2022[2]). This situation should not apply to the analysis presented in this report, as by construction the analysis focus on a relatively large group, composed of 25% of the overall teacher population.

The value of the dissimilarity index is also affected by the size of the units (i.e. schools) across which the distribution of individuals is analysed. Notably, if the units’ sizes are small, then the dissimilarity index tends to overestimate the level of deviations from randomness (also known as small-unit bias) (Carrington and Troske, 1997[4]; D’Haultfœuille and Rathelot, 2017[5]). For example, the smaller the schools in terms of the number of teachers teaching in the school, the more likely it is to observe a deviation from the random allocation of teachers with certain characteristics.

References

[4] Carrington, W. and K. Troske (1997), “On measuring segregation in samples with small units”, Journal of Business & Economic Statistics, Vol. 15/4, p. 402, https://doi.org/10.2307/1392486.

[7] D’Haultfœuille, X., L. Girard and R. Rathelot (2021), “segregsmall: A command to estimate segregation in the presence of small units”, The Stata Journal, Vol. 21/1, pp. 152-179, https://doi.org/10.1177/1536867X211000018.

[5] D’Haultfœuille, X. and R. Rathelot (2017), “Measuring segregation on small units: A partial identification analysis”, Quantitative Economics: Journal of the Econometric Society, Vol. 8/1, pp. 39-73, https://doi.org/10.3982/QE501.

[2] OECD (2022), Mending the Education Divide: Getting Strong Teachers to the Schools That Need Them Most, TALIS, OECD Publishing, Paris, https://doi.org/10.1787/92b75874-en.

[3] OECD (2019), Balancing School Choice and Equity: An International Perspective Based on Pisa, PISA, OECD Publishing, Paris, https://doi.org/10.1787/2592c974-en.

[1] OECD (forthcoming), TALIS 2024 Technical Report, TALIS, OECD Publishing, Paris.

[6] UNESCO-UIS (2012), International Standard Classification of Education: ISCED 2011, UNESCO Institute for Statistics, Montreal, http://uis.unesco.org/sites/default/files/documents/international-standard-classification-of-education-isced-2011-en.pdf.