What's the relationship between screen brightness and battery life?

My guess is that the brighter the screen, the shorter the battery life because it uses more power. But I think there are more factors influence it.

I think it's various for different technology. For exampel for LED screen, it uses backlight at lot so a brighter screen may impact battery life a lot. But for e-ink display, it's a different story. However I'm not sure if the grayscale on e-ink display can be treated as brightness though.