book about her experiences. Comparisons between Gymnasium and Gesamtschule (comprehensive school) German Gymnasiums are schools which aim to prepare students for college education. These schools are selective, and tough grading is a traditional element of the teaching. The culture of these works against students of average academic ability who barely qualify for a Gymnasium place, and who may then find themselves on the bottom of their class; these same students would have achieved better grades for the same effort if they had attended a non-selective comprehensive school (Gesamtschule). A study revealed that a sample of Gymnasium high school seniors of average mathematical ability who chose to attend advanced college-preparatory math classes at their school ("Leistungskurs") found themselves in the very bottom of their class and had an average grade of 5 (i.e. failed the class). Comprehensive school students of equal mathematical ability found themselves in the upper half of the equivalent course in their school and obtained an average grade of 3+. It was found that students who graduated from a Gesamtschule tend to do worse in college than their grades in high school classes would predict - and vice versa for Gymnasium students. Predictive ability Often the German grades are treated like an interval scale to calculate means and deviations for comparisons. Even though it lacks any psychometric standardization, the grading system is often compared to normally distributed norm-referenced assessments. Using an expected value of 3 and a standard deviation of 1, transformations into other statistical measures like Percentiles, T, Stanine etc. or (like in the PISA studies) an IQ scale are then possible. This transformation is problematic both for high school grades and for university grades: At high school level, schooling in most of Germany is selective—thus for instance a Gymnasium student who is underperforming compared to his classmates may still be close to or above average when compared to his entire age group. At university level, the distribution is highly non-normal and idiosyncratic to the subject. Substantially more German students fail exams in university than in other countries (usually about 20–40%, often even more). Grades awarded vary widely between fields of study and between universities. (In law degrees, for instance, only 10–15% of candidates are awarded a grade better than "befriedigend".) This might be one reason for the low graduation rates at university in international comparisons, as well as for the small number of people who obtain