Illusory correlation is a psychological concept that refers to the phenomenon when people believe they see a relationship between two things when no such relationship actually exists.
Imagine you're watching a sports game on TV and you notice that your team tends to win more often when you're wearing your lucky shirt. You start to believe that your wearing the shirt somehow influences the outcome of the game. That's an example of an illusory correlation. You're perceiving a relationship between your shirt and the game results, but in reality, your shirt has no impact on how the game turns out.
We often fall into the trap of illusory correlation because our brains are wired to recognize patterns and make connections. This can lead us to see patterns that don't actually exist, especially when we're only paying attention to information that confirms our beliefs and ignoring information that contradicts them.
So, illusory correlation is when we mistakenly believe two things are related when they're not, often because we're paying more attention to certain pieces of information and not enough to others.