Chapter 3. Primary School Skill Development: from First to Sixth Grade ity on a unidimensional continuum, which represents their skill level. This process includes calibration, where the difficulty of each item is statistically determined and the likelihood of a student answering an item correctly is calculated based on their estimated ability. The final skill score reflects a student’s position on this continuum, which provides a more precise measure of their skill.5 Therefore, these skill scores can be compared across grades. Consequently, we are able to investigate students’ skill development over time. The question arises whether these skill scores are a reliable measure of students’ skills. One specific skill score only provides limited information on students’ performance, and test results depend on other factors, which could make these skill scores noisy. Therefore, skill scores are a measure of students’ true skills and random error.6 Whilemeasurement error in the dependent variable causes inefficiency, measurement error in the independent variable may cause attenuation bias, resulting in lower bound estimates. We discuss this matter in Section 3.4.2, where we discuss the IV approach that we use to reduce the im5More information about the conversion of the raw test scores to the skill scores used in this chapter can be found in the scientific justification of the LVS on the website of Cito, which is the provider of the tests. This scientific justification, written in Dutch, can be found on https://cito.nl/onderwijs/primair-onderwijs/wetenschappelijkeverantwoording-en-beoordelingen/. 6This error may arise due to a variety of reasons. First, measurement error may arise due to a transitory shock in students’ performance. Students may have a good or bad day, and environmental circumstances may affect students’ performance. Second, the ways in which tests are taken may cause measurement error. Some students take the test on paper, whereas others take a digital test. While tests are comparable, some students may score better or worse taking the digital test (e.g., students with bad handwriting are ‘penalized’ for this in the spelling test on paper, or the adaptiveness of the digital test might motivate certain students). Third, test timing may affect skill scores. And fourth, other factors may influence the extent to which skill scores measure true ability. 50
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