I have seen images of Nazis measuring noses in order to determine Jewishness. Did they have objective criteria to decide the result, or was this merely a pretence to make their own decisions? If they had objective criteria, did the figures survive?

So sorry, I have been busy and had to look some stuff up for this.

Anyways, here it goes:

The Nazi measured not only noses but primarily the skulls of Jews and Roma and Sinti. As far as I can tell, there were two major attempts to do this. One by the most important "race scientists" of the Third Reich, Erwin Baur, Eugen Fischer, and Fritz Lenz. In the mid-30s they measured the skulls of thousands of Roma and Sinti in Germany and published their results in 1936.

The other attempt took place in 1939 when the anthropological department of the Vienna Natural History Museum measured Polish Jewish POWs kept captive in Vienna by the thousands in the so called Stadiumsaktion (named so because they were kept in a football stadium in Vienna).

Additionally, there was the collection of Jewish skeletons of August Hirt with Rudolf Brandt and Wolfram Sievers who received dead Jews from the camps in order to measure their skulls during the war.

These pseudoscientific endeavors never lead to anything, which is why for defining Jews the Nazis reverted to ancestry as seen in the Nuremberg Laws and also why the Germanization commissions in Poland made rather erratic decisions when it came to determining who was a potential German and who was not.

The Bauer, Fischer, Lenz data can still be read today but I have no idea where the other stuff has gone to and if it survived the war (looking for it was what kept me from answering this here).