An investication into the measurement invariance according to OECD countries of TIMSS 2015 eight grade math achievement test

In this study by using TIMSS 2015 data, the mathematical achievement of the eighth grade students who participated in the mathematics achievement test is analysed. It is tried to determined what kind of invariance is the best provided if this success is different in terms of countries, whether it provides invariance or not. Considering common and different aspects in the studies conducted previously in this field, the recommendations for the practitioner and the research are mentioned in important points. In first step, among cognitive test booklets implemented in TIMSS 2015, booklet 11 which was used commonly by all countries was selected for this correlational survey study and the study was conducted using dataset belonging to 301.472 students that took booklet 11 in the countries that attend TIMSS. Test statistics, normality tests and reliability coefficients were examined for the eighth grade mathematic achievement test scores of the countries and it was concluded that the measures of central tendency and distribution were similar. For simplicity, it is possible to say that the data set has a close distribution to normal. The reliability coefficients and internal consistency of test items were generally good. In the following stage, OECD countries were selected and 7.223 students attending the eighth grade in these countries were subjected to confirmatory factor analysis and the measurement models were validated for all groups. The χ2 / sd ratio was found to be quite good. When considered to the compliance indices, it is seen that CFI datas are compatible with the patterns in all countries. It is determined GFI datas are delivering compatible results in Hong Kong, Swedish, Italy, Japan, Korea and Turkey , for the other countries it extremely shows the compatible results, SRMR datas are closed to harmony in Hong Kong, Swedish, Italy, and for the rest of the other countries it is estimated that they show the best compatible. When compatible index evaluated in general, it is decided that evaluation models of all countries are verified for all groups. Then, for all groups, covariance matrices were tested for equality. The other step is testing of measurement invariance. Considering the results of the covariance matrices equality test for the mathematics achievement test scores of OECD member countries, it can be stated that the fit indexes are in good agreement. H0 (there is no significant difference between the more restricted model and the less restricted model) and H1 (there is a significant difference between the more restricted model and the less restricted model) hypotheses are established, and the measurement invariance is tested by multi-group confirmatory factor analysis. It can be said that the values of the fit indices for the structural invariance are acceptable and the model is confirmed. Then, H0 has been rejected because of a significant difference between the models based on the nested model based on Model 2, Model 3 and Model 4, which were established as an alternative to Model 1, respectively the configural (structural) invariance (Model 1) and the weak factorial invariance (Model 2), configural (structural) invariance (Model 1) and strong factor invariance (Model 3), weak factorial invariance (Model 2) and strong factorial invariance (Model 3). (H1 was accepted.) H0 was accepted because of a significant difference between the configural (structural) invariance (Model 1) and the strict factorial invariance (Model 4), the strong factorial invariance (Model 3) and the strict factorial invariance (Model 4) (H1 was rejected). As a result, the results of the study showed that the measurement invariance was not achieved for OECD member countries, and the best model for measurement invariance was the strong factorial invariance model. In the literature, some research results reported that the measurement invariance between different countries was ensured in large scale studies. On the contrary, some research results reported that the measurement invariance could not be achieved in the measurement tools used among individuals with different languages and different cultures. In the context of these results, the necessity of the presence of people from different cultures and nationalities in the article writing because each country has its own unique experience, historical, cultural values and traditions. From the preparation of the exam question, to the implementation of the exam and even to the examination and analysis of the exam result, the decision-makers and politicians in the education should not be too confident in the group fixtures because they have very important functions in these exams. The interpretation of the measurement invariance according to the measured characteristics and the type of application, and the efforts to be meticulously performed, create suggestions for the practitioner. Including different countries and demographic variables in future studies as suggestions for research, analysis of different booklet types and success areas, determining which method can be more effective by testing the measurement invariance with different methods, In order to make the interpretations made before different comparisons between different groups such as language, gender and culture, to be more meaningful and healthy, it is very important to carry out the measurement invariance of the measurement tool with great care. When all the results are evaluated, the comparability of the results obtained from the results of mathematics achievement in the TIMSS 2015 application against the participants with different countries, languages, genders and cultures, and the comments made accordingly, cannot be ensured by the measurement invariance is becoming. However, measurement of the results of large-scale exam applications can not be achieved in measuring the results, especially when making comparisons between countries and must be taken into consideration diligently.