For anyone whose number is close to the correct answer, and who chooses a number in the vicinity as his/her own answer, the information whether that answer was picked because of anchoring effects or because of being an expert in dendrology is lost.

The sample size is probably large enough to still have reasonable predictive power without these cases, but the problem could have been circumvented by e.g. providing biased numbers, both too low and too high.

Any statistical trickery can only lead to a prediction about how likely people in the above scenario are to choose their answer based on anchoring versus based on knowledge, but that is using information from the other samples to speculate about the causal factors of our special cases, our special cases from above wouldn't have added any information gain.

Saying "From the data, I can speculate that person A who chose a number close to the correct result and close to his random number did so because of anchoring / knowing the answer" doesn't add to the strength of your result, it's like saying that "Hypothetically, if a person A chose a number close to the correct result and close to his random number, I would expect that he would do so for reason X".