Does your TV support 480p, i.e: progressive scan? Ours has a component input, but does not support 480p. If your TV only supports 480i, which is the case of most NTSC televisions, then a component cable does next to nothing for you.
I did notice some improvement when I purchased an S-Video cable adapter for my Game Cube. Is there any noticable improvement on a standard def TV when going from RCA -> S-Video -> Component?
There are too many factors to say exactly. My guess at least is that it will be different at least in some small way. Even if the difference were as big as it could possibly be, I don't think that's enough to make a significant difference worth spending any money on. My bet is that if you took screenshots in all three scenarios that you will find some differences. However, if you were to take a properly conducted double-blind test, you wouldn't be able to tell the difference at all. In other words, any differences you notice will be more psychological than technological.
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I did notice some improvement when I purchased an S-Video cable adapter for my Game Cube. Is there any noticable improvement on a standard def TV when going from RCA -> S-Video -> Component?