Could a Massage Therapist or Electrologist satisfy the federal requirements to be compensated as an independent agent by a retail salon in Indiana?

If they don't have you on payroll, don't determine your hours, don't directly supervise you then you could be considered and independent contractor.

Here is information directly from the IRS regarding employee vs. independent contractor
http://www.irs.gov/businesses/small/article/0,,id=99921,00.html