FANBOYS — for, and, nor, but, or, yet, so — can join two complete sentences with a comma. Without one of those words, the comma is a splice. The wider comma list is in ACT comma rules.
Both sides have to be sentences
The bus was late, so we started without him. Each side could stand alone, and so is a FANBOYS word, so the comma is right. The bus was late, we started without him is wrong. She wrote the essay and revised it needs no comma, because the second half has no subject of its own.
What makes a clause independent is in independent and dependent clauses.
However is not on the list
However, therefore, and moreover are not FANBOYS. They take a semicolon, not a comma. That contrast is in conjunctive adverbs. Punctuation overall is in ACT punctuation rules.
The bottom line
Comma plus for, and, nor, but, or, yet, or so, and only when both sides are full sentences.
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