The quality of schools is not only determined by educational achievement. Non-cognitive characteristics, children's health, well-being, moral education are important. However, learning success is an essential component of school quality. The greatest successes here are the TIMSS and PISA projects, which are carried out in the format of a large study. Large-scale studies have made progress in discovering predictors that impact learning success. These are social and economic factors: urban-rural differences, gender differences, school type differences, family characteristics, etc. These are also educational factors - learning environment, educational curriculum, learning methods, etc. Psychological factors should also be mentioned: motivation, school self-concept. Unfortunately, the question of what role the school principal plays in ensuring good learning outcomes is still relatively poorly addressed. More has been done in areas such as evaluation research and school improvement studies. The limitation is that these are mostly local, sampling-based studies. Questionnaire methods based on subjective self-assessments are mostly used. Social desirability and confounding effects inevitably occur. There is a need to examine the impact of school leadership and principal's potential on students' learning achievements. This is about the total census data from state statistics. Learning outcomes are multi-causal in nature, so it is not worth hypothetically expecting that the principal's factor will be crucial. It's probably relatively small, but it's still there. How does the phenomenon occur? What statistical regularities occur here? There is currently no information on this. This research and report is dedicated to partially clarifying this question. School leadership can be conceptualized in different ways: through the career model, personality traits and leadership style, etc. The big data from state statistics handed over to the research team was characterized by a limited number of variables describing the position of the director. The study is limited a few aspects. 1. Can older school leaders of pre-retirement and retirement age ensure good student learning outcomes and be as effective as younger school leaders? The issue is particularly relevant in the major debate over raising the retirement age for workers in the EU. Is it appropriate to introduce a limit of two consecutive terms of office for school principals, as happened in Lithuania? 2. Is it appropriate to give official ranks to public school principals? Does a degree guarantee better educational achievement of students whose schools are led by such respected “elite” principals with higher prestige, symbolic capital and higher salary? Should such categories and ranks be seen only as a relic of the Prussian government system of the 18th-19th centuries? Should the director's performance be evaluated without regard to professional history and only based on actual results based on external audit? 3. Should an applicant who has previously been a good teacher representative and has experience in education become a principal? Is it appropriate to appoint a person with management experience in business or public sector as a director? The question is not only relevant to education and can hypothetically be transferred to other sectors. Who can be a good director of a museum, library, hospital: a specialist or a general manager? In Lithuania there has always been a rule that only a former educator with experience in education can lead a school. At the moment anyone with management experience and a university education can participate in the selection process to become a school director. The peculiarity of the study is that the answers to the questions were examined not on the basis of sampling studies, but on the basis of total census data, which ensures the objectivity, validity and universal generalizability of the discovered statistical regularities.

The study is based on total census data. This is data on the learning achievements of Lithuanian students, measured by standardised tests. Such centralised tests at national level are conducted in Lithuania by the National Agency for Education. The researchers received all anonymised data from the agency for the years 2015-2021. The total number of students tested is 248,000. The national tests are based on the example of TIMSS and PISA. In long tests, there are tasks on different topics and with different levels of difficulty. In terms of content, the tests covered the main subjects of maths, reading and writing in the lower grades, maths, state language (Lithuanian) and the main foreign language (English) in the upper grades. The mathematics test in 4th, 6th and 8th grade lasts up to 1 hour and includes 30-40 primary tasks. In the 10th grade, the test lasts up to 2 hours and comprises 30-40 tasks and in grade 12 lasts up to 3 hours and includes up to 25 tasks. The data originally collected for school administration is valid and also suitable for use in science. In the conclusion of the secondary and tertiary factorization, it became clear that the overall index of educational success can be derived from the estimates of various school subjects and defined as a dependent variable. The independent variable captures a specific career model of school headmasters. It comprises three primary main variables: 1) The age of the headmaster, 2) Was the supervisor a teacher before becoming a headteacher? What was the highest qualification category as a teacher at that time? In Lithuania, these are "teacher", "teacher-methodologist" and "teacher-expert". 3. Does the headmaster have a leadership category (official rank) or not? There are four possibilities in Lithuania: the director has / hasn’t categories I, II and III. The relative restriction of the hypothetical created career model was determined objectively and did not depend on the will of the researchers. The state Data provided to the researchers contained exactly this amount of information about the headmasters. When working with total census data, statistical tests and inferential statistics lose their usual significance, which are very characteristic of sampling studies. There is no sampling error and bias effects are unlikely. Cohen's effect of size was used to appropriately assess differences between compared group means. Differences of less than 0.20 standard deviation points were ignored and not interpreted.

The analysis of data revealed specific statistical regularities. 1. the older the headteachers, the more favourable the academic achievement of the pupils in these schools. 2. the higher the headteacher's leadership category, the more favourable the learning achievement of pupils. 3. the higher the teacher's career category before the headmaster held the position, the more favourable the learning achievement of the pupils in these schools. 4. the career model of head teachers, operationalised by the three variables mentioned above, has a systematic effect on the learning achievement of pupils. The sometimes-widespread expert opinion that the rotation of headmasters is necessary and the term limit (up to two consecutive terms of office) is controversial. The opinion that headteachers remain in their position for too long, the effectiveness of leadership decreases and the school begins to stagnate is controversial. Teachers who are established in the profession and have a good work record represent a good resource from which headteachers can be recruited. At least in public schools, it is appropriate to have a system of leadership categories. Such a system of symbolic and material promotion of leaders motivates the leaders and has a positive effect on the functionality of the school. The statistical regularities found give rise to discussions about the importance of raising the retirement age for employees, including public sector managers. Although statistical regularities were only found in the population of school headmasters, these can be hypothetically transferred to museums, libraries, etc. in relation to the population of managers. The position of head teacher should not be compared to the tenure of a politician or civil servant who is elected for two terms. It is a creative mission whose personal suitability should be confirmed on the basis of actual achievement, as determined by external audits, certification, with no time limit.

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