The four levels are called: stream-enterer, once-returner, non-returner and fully Enlightened. According to the teachings the stream-enterer has totally let go of doubt, attachment to rights and rituals, and has insight into the non-personal quality of things - Anatta. So, if a person becomes a stream-enterer than doubt no longer arises. In a once-returner, sense desire and aversion has become very subtle. In a non-returner it's completely eliminated but there is still restlessness and some worry based on the sense of I and me. This is totally eliminated when one is a fully Enlightened being.