1. A method of driving an organic light emitting diode display device having first to third sub-pixels and a white sub-pixel, comprising: judging a gray level of an image data for the first to third sub-pixels as a group, the gray level representing a brightness of a white portion of the image data; classifying the gray level of the image data into one of a low gray level group, a middle gray level group and a high gray level group according to the brightness of the gray level of the image data, wherein each of the low gray level group, middle gray level group, and high gray level group includes a brightness range, the brightness range of the middle gray level group is above the brightness range of the low gray level group, and the brightness range of the high gray level group is above the brightness range of the middle gray level group and includes a highest gray level brightness; displaying an image using the first to third sub-pixels but not the white sub-pixel when the gray level of the image data is classified into the low gray level group; displaying the image using the first to third sub-pixels and the white sub-pixel when the gray level of the image data is classified into one of the middle and high gray level groups; generating a first data voltage applied to the white sub-pixel to be smaller than second data voltages applied to the first to third sub-pixels for any gray level when the gray level of the image data is classified into the middle gray level group; and generating the first data voltage applied to the white sub-pixel to be equal to the second data voltages applied to the first to third sub-pixels for any gray level when the gray level of the image data is classified into the high gray level group.