What you want is not to detect if stdin is a pipe, but if stdin/stdout is a terminal.
The OP wasn't wrong in exactly the way this comment implies: he didn't just ask how to detect whether stdin is a pipe. The OP actaully asked how to detect whether it is a terminal or a pipe. The only mistake he made, then, was in assuming those were the only two possible alternatives, when in fact there is (apparently) a 3rd one: that stdin is redirected from a file (not sure why the OS would need to treat that any differently from a pipe/stream but apparently it does).
This omission is answered/corrected more clearly here:
stdin can be a pipe or redirected from a file. Better to check if it is interactive than to check if it is not.
