Fig. 1

Multinomial Processing Tree Model. Combined multinomial processing tree model for the direct questioning group (upper tree) and for the two indirect questioning groups for the Extended Crosswise Model (two lower trees) adapted for the present question. The response options for the participants in the survey are depicted in the squares on the right. Parameter π _• represents the prevalence estimate for personal hygiene behaviour (thorough hand washing) during the COVID-19 pandemic (carriers of the sensitive attribute). Parameter p_May-July is the known prevalence of the answer to the non-sensitive question (the likelihood of the participant’s mother having been born in May, June or July), also referred to as the randomisation probability