Why do psychology researchers frequently misplace commas, in relationship to coordinating conjunctions? [closed]

None of the real-world examples you give are grammatically incorrect. For instance, the first example you give is:

One of the most notorious examples of a crime that wasn't is the case of O.J. Simpson and the 1994 murder of his wife Nicole Brown Simpson and her friend Ronald Goldman. O.J. Simpson was charged and tried for the crime and, after a year-long highly publicized (and televised) trial, received a verdict of "not guilty."

Presumably, you are referring to the comma before "after a year-long ...". This is quite different from the example you give of "I hit my brother with a stick, and he cried." In "I hit my brother with a stick, and he cried.", "and" is coordinating between "I hit my brother with a stick" and "he cried". In the example you give, however, "and" is coordinating between "O.J. Simpson was charged and tried for the crime" and "[O.J. Simpson] received a verdict of 'not guilty'". The phrase "after a year-long highly publicized (and televised trial)" is an adverbial phrase modifying the verb "received". So unlike your example of "I hit my brother with a stick, and he cried", what follows "and" is not the clause being coordinated, but an adverbial phrase that is modifying the verb in the coordinated clause. By setting this phrase off with comma, the writer is basically saying "hey, I know I just wrote a coordinating conjunction, and so you'll be expecting the clause that's being coordinated, but I'm just letting you know that the next phrase you read isn't going to be that clause". Furthermore, this is an introductory adverb, and those should be followed by a comma. For instance, if you say "Last Tuesday, I ate a bagel", there's a comma after "Last Tuesday" because it's an adverbial phrase placed before the verb it modifies. If it were instead "I ate a bagel last Tuesday", a comma would not be appropriate. This is discussed in the second rule in the owl.purdue.edu link you provided.

The page also says in rule 3 "Use a pair of commas in the middle of a sentence to set off clauses, phrases, and words that are not essential to the meaning of the sentence." The phrase "after a year-long highly publicized (and televised) trial" is not essential to the meaning of the sentence.