The post hoc; ergo, propter hoc fallacy occurs when the cause/effect relationship is inaccurate or nonexistent. Basically, it incorrectly assumes that A is the cause of B. These can come in the form of (1) an inaccurate assumption of cause/effect, (2) a causal oversimplification where one assumes that one cause is responsible for an effect when, in fact, multiple causes are responsible, and (3) because of similar timing between two entities, one must have caused the other.
Example: Kelly has amazing handwriting. Kelly also wears high-heeled shoes. Because Kelly wears high-heeled shoes, she has calligraphy-like handwriting.
Obviously.
Example: I didn't get any sleep last night because the train came by several times, blasting its horn.
Actually, the train always comes by several times each night and toots its horn. I always sleep right through it. I got no sleep last night because I drank a cup of coffee before going to bed, and the caffeine kept me awake.
Example: Obviously, the methane escaping from the rear ends of cows is responsible for climate change.
(Climate change has many causes, some of them natural, some of them human-made. Burning of fossil fuels, aerosol sprays, and methane from cows are just a few of the many causes.)
Example: The tree in my front yard was toilet-papered on Saturday; therefore, the city chopped it down the following Monday.
They did chop it down that Monday, but the timing of these two events was just a coincidence. The tree was chopped down because it had a big crack in it and had been marked for removal well before being TPd. That just happened to be the day the City of Baraboo sent out a crew to cut it down.
Example: "We never had any nuclear weapons before women got the right to vote; therefore, women are responsible for the development of nuclear weapons."
This actually isn't a logical fallacy. Women are to blame.
;)
(Adapted from: http://www.brainpickings.org/index.php/2014/01/03/baloney-detection-kit-carl-sagan/)