What is the relationship between effect size and noise? I understand that noise in measurement can affect the size of an observed effect. That noise can result in larger measurement error, which can reduce the size of the observed effect. However, I do not understand the mechanism. How can greater measurement error reduce the size of the observed effect? Can someone please explain this in a simple way that a non-statistician can understand?

An apt metaphor might be something like listening to a song on a car radio. You're driving around jamming to some great tunes (the signal) when suddenly there's a huge burst of static (the noise). You can still make out the song, but it's pretty indistinct and hard to tell it from the static. So even though the true effect size has not changed (it's the same song) the observed effect size (what you can make out) is a lot smaller because of the measurement error (the static).
