Given this sounds like a particularly spectacular failure in the hiring process I'd suggest that the only reasonable course of action would be to have a conversation with the new employee and see if a suitable plan can be worked out between them and the company.
Explain that you don't think they are going to work out in the position they have been hired to do and talk about the possibility of moving them to a Data Analysis role (if such a position is available - don't go around putting that sort of offer on the table without knowing that it exists!). If at all possible I strongly recommend avoiding using the word "demotion", it has significant negative connotations and is unlikely to result in any productive dialogue. Instead talk about it as a "move" or a "transfer", if it offers less money then the PM role then obviously you need to mention that but do so sympathetically.
There's the very real possibility that the employee doesn't want a Data Analysis role (they did after all apply for a PM role) and if they don't then you can talk about the fact that they will have to leave.
The key thing here is to involve them in the process, don't just dictate to them "you're a crap PM, so you're a Data Analyst now and here's your reduced paycheck" that sort of thing. Because doing so will likely result in a hugely demotivated and possibly disgruntled employee and that serves nobody.