What do you call a belief that is established without being based on facts?

The term that defines a belief established without being based on facts is "myth." A myth typically arises from cultural narratives, tradition, or social beliefs rather than empirical evidence or scientific validation. Myths often serve to explain phenomena in ways that resonate with a community's worldview, but they do not hold up under scrutiny when examined through factual or experimental lenses.

In contrast, a theory is an explanation developed based on evidence and tested through observation and experimentation. A fact is an objective statement that can be proven true or false. A hypothesis is a proposed explanation made as a starting point for further investigation, which is typically testable and based on existing knowledge. These definitions highlight why the concept of a myth, rooted in unfounded belief rather than validated evidence, stands out as the correct answer in this context.