During the last decades the improvement of school effectiveness is emerging objective of education reform strategies all around the world. Increasing emphasis on academic performance gives new importance to investigating factors that contribute to student achieving.  While innovation is seen as one of the main sources of growth and improvement of productivity and effectiveness not only in the economy but also in education sector, the relationship between innovation and students’performance is not straightforward. The same innovative solution may work in one context but remain ineffective in another; it may influence performance differently on the shorter and the longer term or it may change during implementation. One of the reasons of the difficulties is found in the fact that innovation designates simultaneously a product or outcome and a process. It is different to explore how innovation activities influences educational performance, or/and how (bad or good) educational performance indicates stronger innovation activity of schools.

Researches on educational innovation can be classified by function into 2 groups: one sees innovation as a dependent variable, the other as an independent one. In the first case researchers try to understand the causes or motives of innovativeness, in the second case they want to understand how innovation influences performance. The two types of causal relations can be briefly characterized by these two questions: A) How school innovation is influenced by student's performance and the social-organizational features of the school? B) How student's performance is influenced by the innovation activity and social-organizational characteristics of the school?

Our present explorative analysis aims to contribute to researches on the direction and magnitude of the cause-and-effect relationships between educational innovation and school effectiveness. It is based on linked data of survey of education sector’s innovation in Hungary, 2016 with long-term data of National Assessment of Basic Competencies, Hungary. While our analysis is based on data of a single country, the added value of national-level data construction allows us to conduct deeper analysis focusing on a more universal research question concerning the general mechanism of causal relationship between educational innovation and school effectiveness.

Our hypothesis is that based on a static linear causal models, no significant linear relationship can be disclosed between the school's innovation activity and the students’ performance in either of the causal directions. At the same time, some significant, non-linear relationship can be found between the long-term change in the school's performance and innovation activity: descending performance indicators can generate intense innovation activity, while intensive, long-term innovation activity typically accompanies sustained high performance indicators.

Present analysis is based on linked data of a primary school subsample of Educational Innovation Survey in Hungary, with school level time series data of National Assessment of Basic Competencies, Hungary from 2008 to 2016. The National ABC is a standard-based assessment designed similarly to the OECD PISA survey. It measures reading and mathematical competences of every student in Grade 6, 8 and 10. Since 2008 test scores are standardized on the base of 6th grades test results in 2008. Besides individual level data, the Educational Authority produces school-level aggregated data of students’ performance and background information of schools. It also involves background characteristics of schools, based on a background questionnaire. Educational Innovation Survey was conducted in 2016 among the heads of the educational units (organizations), with the questions concerning innovation activities and innovation-related features of institutions. Surveyed schools have the same institution ID as the National ABC, making it possible to link them. For present analyses, full 2016 year school level National ABC data of 8th grade students (including mean scores of their students’ scores on maths and reading, as well as data of institutional background questionnaire) were linked with their 8th grade students’ school-level mean scores from 2008 to 2015, and with the innovation survey data. 2014 year school level mean scores of 6th grade students (practically the students who were at 8th grade in 2016) were also involved to the merged data base. The full merged data base contains data of 1051 schools. General innovation activity of school were measured by composite innovation indicator that was calculated by sum of standardized scores of several innovation-related survey variable. For testing different direction and magnitude of possible linear relationship, OLS regression model-series were applied either with the dependent variable of composite innovation indicator; or with the school level mean of 8th grade test scores in 2016; or with the difference of school level mean of 8th grade test scores in 2016 and 6th grade test scores in 2014. For the models the proper school-level explanatory variable were involved as we mentioned above. For testing correlation between changes in schools’ performance and innovation activity; K-mean clusters of schools were modeled, based on above mentioned static characteristics of schools as well as indicator of changes in school performance over time, based on school level performance data between 2008 and 2016.

Result of OLS regression model-series reveal no significant linear relationship between the school's innovation activity and the students’ performance in either of the causal directions. At the same time, cluster analysis based on changes in school performance over time and indicator of school innovation activities reveal types of non-linear relationship between the long-term trends in the school's performance and innovation activity. In some schools descending performance indicators generated intense bottom-up innovation activity while in other schools it does not. The difference of these two group of schools is rooted to the characteristics of school leadership. Intensive bottom-up innovation activity typically accompanies sustained high performance indicators; while there is no significant relationship between magnitude of school innovation and performance in the schools where the mean of students’ test scores is around the average over time. These results reflect the non-linear, long term, dynamic nature of causal relationship between innovation and school effectiveness.

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