What is the test for a princess according to Hans Christian Anderson's fairy tale?

In "The Princess and the Pea" a test of letting a woman sleep overnight on top of a pile of mattresses, after a single dried pea had been placed under the lowest mattress, was done. She complained in the morning that she had not sleep well as there was something hard in the bed. So proving that she must actually be a princess, royal, and suitable for the prince to marry.