Correlation-Causation Gag

"My bear went off!"

—Radar, M*A*S*H, after pointing a teddy bear at the colonel at the same time someone shoots himself in the foot

Essentially, this trope is where a character doing something minor seemingly causes some major effect, although it's obvious that's actually not the case. If the character is an animal, young, or just plain stupid, they might think that they actually caused whatever the effect was. Take, for example:

Alice and Bob are playing around in the woods, Flynning with some sticks. But when their sticks clash, they hear a massive explosion! Did the clashing of two seemingly normal sticks sound off such a massive bang?

Of course it didn't, but the gag is that it seemed like it did. What actually happened was dynamite detonating about half a mile away to open a mine, or a warship firing its guns in the distance, or something similar; they just heard the explosion at the same time their sticks hit.

The name comes from the logical fallacy of Correlation vs. Causation (two things happening in succession or together does not imply that one caused the other). This is where the humor or irony in this trope comes from.

Often Played for Laughs (or at least irony). Framed for Heroism is a specific subtrope. It can, however, be Played for Drama, as it can be used to reveal something ominous (like an invasion or gunfire). If a minor act truly does have a catastrophic effect, that is Unwitting Instigator of Doom.

Examples of Correlation-Causation Gags include:

Advertising

In the "Darth Vader Kid" Super Bowl commercial, a boy tries to use The Force to manipulate everyday objects around the home, but is continually disappointed. He then tries to use it on his dad's Volkswagen, and his dad starts the engine remotely, making him think he has succeeded.

Anime and Manga

In Fullmetal Alchemist: The Sacred Star of Milos, near the beginning, Alphonse sets off a party popper, and at the same time there is an explosion outside causing all the glass in the windows behind him to shatter. He cries out "That wasn't me!"

Film

In The Dark Knight, two boys are mime-shooting imaginary guns at cars on the street. Suddenly, there's an explosion where they were aiming, making it seem as though they caused it.
In The Lion King, Simba roars, trying to scare off the hyenas attacking him and Nala, but as a small cub he can only manage a small growl-ish thing. The hyenas taunt him about it, goading him to try again, but this time Mufasa roars at the exact same time Simba does.
- Invoked darkly again in the stampede scene; Simba is practicing his roar (nudged on by Scar), and when he manages a particularly loud one, the wildebeest begin the stampede...which the hyenas had started on a cliff above by attacking them. Scar uses this to his advantage in making Simba think he killed his father.
In Indiana Jones and the Last Crusade, there's a scene where Indy is trying to break into a secret passage in a library, causing loud thumps to echo through the library—coincidentally in time with the librarian stamping a pile of books. At one point, the librarian stops and looks at the stamp with a puzzled expression.
In Mallrats, Silent Bob tries to use the force to retrieve a fallen VHS. Someone bumps the support it had fallen on, knocking it up into Bob's hand. This later triggers his only line in the movie, where he quotes Yoda.
In Space Jam, Wayne Knight's character takes a photograph of Michael Jordan just as the latter is sucked down a golf hole. After a second, Bill Murray demands to know what kind of camera that is, and that it not be pointed at him.
In The Adventures of Ichabod and Mr. Toad, Brom Bones has a dog howl just as Ichabod is giving a singing lesson, causing him to think he produced the sound himself.

Literature

In Good Omens, the witch-finder Shadwell mistakes Aziraphale for a demon and points an accusing finger at him at the exact moment Aziraphale's mortal body is destroyed from the backlash of scuffing a pentagram. Shadwell spends the rest of the novel believing he has the power to banish demons with his finger.

Live Action TV

In the Season 4 Mash episode "The Gun", Radar is blamed for the loss of a colonel's personal revolver (actually stolen by Frank Burns). Radar eventually gets drunk and confronts the colonel with a teddy bear; at the same time Frank tries to return the gun...and shoots himself in the foot.
In an episode of Star Trek: The Next Generation a child who was the lone survivor of a destroyed starship thinks he caused it because he accidentally hit a computer console when he was thrown off-balance just before everything blew up.
In one episode of The Fresh Prince of Bel-Air, Uncle Phil runs for a judge position against a former mentor of his, who is rather nasty in his campaign. When the former mentor wins, Phil insists that they go to his party anyway. At the party, Will derides his uncle's opponent, culminating in a, "You can drop dead for all I care!" He does.
In the episode of Jeeves and Wooster where Bertie goes to stay in Devon, there's a scene where somebody blows a car horn several times to attract his attention, each time just as he's blowing a note in the trombone he's learning to play, with the result that the trombone apparently makes a noise even Bertie can tell trombones shouldn't make.
In Alice, Charlie gets in one last shot from his crossbow, and then the Hearts Casino explodes. He triumphantly whispers, "Bullseye!" before passing out. Cut to the arrow landing uselessly in the middle of a field.

Video Games

In the World of Warcraft Goblin starting zone, there's a game going on of a sport similar to soccer, but played by woodcutting robots of death with a bomb for a ball. The player character takes part in such a game, but kicks the bombball through the goalposts so hard it flies into a nearby volcano, which then erupts, starting the titular Cataclysm event.

Western Animation

In Avatar: The Last Airbender, Momo is playing with some pebbles. He drops one on a rock, but at the exact moment the pebble hits the rock, a nearby Earthbender chucks a rock at a wall, making it seem as if Momo's pebble caused the bang. Made hilarious when it happens twice.

Other

In one of Jeff Dunham's routines, Walter tells a story about how he told his grandson to pull Grandpa's finger. When the boy did, an earthquake went off.

Walter: Little snot will clean his room when told.

Subverted in a Russian Humour story about a warship. A torpedo is fired in the ship's direction, and the captain wants the bosun to prevent crew panic. The bosun comes to the deck and yells: "Let's bet that I can sink our ship with a fart!" and promptly farts. An explosion, fire, everybody jumps into the water. The captain angrily yells: "You're an idiot, bosun, and your jokes are stupid! The torpedo missed!".