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I am currently working with the Brandsma data of the mice package in R for teaching purposes.

The dataset is from Snijders&Bosker(2012), or rather Brandsma&Knuver(1989) and Knuver&Brandsma(1993), containing data from 4106 pupils attending 216 schools in the Netherlands:

  • Snijders, T. A. & Bosker, R. J. (2011). Multilevel analysis: An
    introduction to basic and ad-vanced multilevel modeling. Sage.

  • Brandsma, H. P., & Knuver, J. W. M. (1989). Effects of school and classroom characteristics on pupil progress in language and arithmetic. International Journal of Educational Research, 13(7), 777-788.

  • Knuver, A. W., & Brandsma, H. P. (1993). Cognitive and affective
    outcomes in school effec-tiveness research. School effectiveness and school improvement, 4(3), 189-204.

There are several variables that are giving test results at the beginning and at the end of the observation period (lpr, apr, lpo and apo).

However, I do not quite understand what the theoretical range of these test scores is and I do not find any explanation on this in the according references.

I have read so far that in the Netherlands scores can range from 1 to 10 with 1 being the lowest, 10 the highest and 4 unsatisfactory (not passed). However, the distribution of the variables looks like this:

Distribution of test scores

So I am currently understanding the values as percentage, e.g. if the student got a 5.5 the grade will be 55%.

If this is true, most or even all of the students have failed the according test.

Could anyone who knows a bit more about the Dutch grading system or the Brandsma data or who has a better understanding of how the data might have been collected/manipulated explain how it ends up with this distribution?

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In the end I assumed that the test results each have their own maximum number of points and that lpr, apr, lpo and apo give the number of points each student achieved. As far as I understand, we don't know how many points they could have achieved in theory.

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