Born Patricia McKenna in Boston, Massachusetts, she grew up in Hanover, New Hampshire, where her father was a resident psychiatrist at Dartmouth College.
She also studied under W. H. Auden at Young Men's Hebrew Association of New York City in 1955.
She divorced in 1968, the same year that while an artist in residence at the MacDowell Colony in Peterborough, New Hampshire, she met Leonard Wallace Robinson.
Goedicke and Robinson returned to the United States in 1981, and she became professor at the University of Montana, where she taught until her retirement in 2003.
Goedicke died of pneumonia and a complication of lung cancer, at St. Patrick Hospital and Health Sciences Center in Missoula, Montana.