fewer than 5,000 students per year, an entire age cohort is tested. Some countries used much larger samples than required to allow comparisons between regions. Test Each student takes a two-hour computer based test. Part of the test is multiple-choice and part involves fuller answers. There are six and a half hours of assessment material, but each student is not tested on all the parts. Following the cognitive test, participating students spend nearly one more hour answering a questionnaire on their background including learning habits, motivation, and family. School directors fill in a questionnaire describing school demographics, funding, etc. In 2012 the participants were, for the first time in the history of large-scale testing and assessments, offered a new type of problem, i.e. interactive (complex) problems requiring exploration of a novel virtual device. In selected countries, PISA started experimentation with computer adaptive testing. National add-ons Countries are allowed to combine PISA with complementary national tests. Germany does this in a very extensive way: On the day following the international test, students take a national test called PISA-E (E=Ergänzung=complement). Test items of PISA-E are closer to TIMSS than to PISA. While only about 5,000 German students participate in the international and the national test, another 45,000 take the national test only. This large sample is needed to allow an analysis by federal states. Following a clash about the interpretation of 2006 results, the OECD warned Germany that it might withdraw the right to use the "PISA" label for national tests. Data scaling From the beginning, PISA has been designed with one particular method of data analysis in mind. Since students work on different test booklets, raw scores must be 'scaled' to allow meaningful comparisons. Scores are thus scaled so that the OECD average in each domain (mathematics, reading and science) is 500 and the standard deviation is 100. This is true only for the initial PISA cycle when the scale was first introduced, though, subsequent cycles are linked to the previous cycles through IRT scale linking methods. This generation of proficiency estimates is done using a latent regression extension of the Rasch model, a model of item response theory (IRT), also known as conditioning model or population model. The proficiency estimates are provided in the form of so-called plausible values, which allow unbiased estimates of differences between groups. The latent regression, together with the use of a Gaussian prior probability distribution