Positive economics is objective and fact based, while normative economics is subjective and value based. Positive economic statements do not have to be correct, but they must be able to be tested and proved or disproved. Normative economic statements are opinion based, so they cannot be proved or disproved.
For example, the statement, "government
should provide basic healthcare to all citizens" is a normative economic
statement. There is no way to prove whether government "should"
provide healthcare; this statement is based on opinions about the role of
government in individuals' lives, the importance of healthcare and who should
pay for it.
The statement, "government-provided
healthcare increases public expenditures" is a positive economic statement,
because it can be proved or disproved by examining healthcare spending data in
countries like Canada and Britain where the government provides healthcare.