Lindley's paradox

Have you ever played a game where you had to guess which cup a small ball was hidden under? Lindley's Paradox is when the cup with the ball seems to change even though you made the right choice.

It's like you guessed the right cup and saw the ball under it, but then your friend says, "No, no, no that's not the right one." However, you know you saw the ball under that cup.

Lindley's Paradox is a bit like that game. In statistics, we use something called hypothesis testing to see if there is enough evidence to say that something is true or not true.

However, sometimes the evidence can be very weak, and we might not have enough information to make a confident decision. But then, if we gather more data, the evidence can sometimes become even weaker than before!

This seems weird, right? How can more information make us less sure about something? It's like seeing the ball under the cup and someone telling you that you're wrong.

But in statistics, it's possible for random chance to cause fluctuations in the evidence we see. And sometimes, when we gather more data, these fluctuations can cancel each other out, making it harder for us to draw conclusions.

So, Lindley's Paradox is when the evidence for something becomes weaker as we collect more data, even though it seems like the data should make us more confident.