The transistor's emitter has to be on the same 0V as the Arduino, otherwise the voltage on the Arduino output to the base, which is 5v as far as Arduino is concerned, has no meaning to the transistor. It would be like taking a 5V battery and putting the + on the base but not connecting the other side of the battery. Or trying to hear one hand clapping. Waaaay too Zenny for me.
Look at my schematic a few posts earlier.