In the PHB there is a section on typical difficulty classes:
Just looking at the numbers, I would say that an average person failing at an easy task 50% of the time is somewhat strange, so have always assumed that these scores are taking proficiency into account.
As a result when people suggest making an Intelligence check, rather than Intelligence (Arcana) I don't like that because it makes the check statistically harder. IE: I assumed this table was meant to account for proficiency and skill use, rather than just raw ability scores.
However it has recently been suggested to me that these are the default DC's for the untrained, so what is actually happening is that proficiency makes the task easier.
When looking to set a DC for a check, if I was going to not include proficiency, would I still use the same table, or should I adjust the value down to account for my DM decision not to allow a skill proficiency?