Single women in Puritan society had a very low social status and did not have much influence in society, but they were seen as very innocent, pure and credible people, since they were not married and had not been "corrupted". This is because, single women, in Puritan society, were considered children and therefore shared the same innocence, until they entered adulthood, where they would get married and leave the status of a child and, consequently, the status of incocence. Women prostitutes were also not considered innocent and did not deserve to be heard because of their sinful nature.
In "The crucible" the girls who started the accusations, mainly Abigail, were single and that's why nobody believed they were lying. Abigail used her reputation as an "innocent" to accuse all the people she believed should get out of her way, as no one knew she was Proctor's lover, her words were easily accepted by everyone.