Unauthorized Users Can Post

I just installed WP. In the Options/General section, I did NOT select the option to let any registered users write posts. However, it so happens that my users CAN write posts. I definitely do not want this. How do I fix the situation so that readers have no authority to do that? Is this a known issue? It may have been asked before, I just haven’t found the answer. Does this have anything to do with the view level I assign to a user? My understanding is that setting a user’s level of reading does not give them writing authority. Please help! Thanks.