We report the results of direct measurements of velocity profiles in a microchannel with hydrophobic and hydrophilic walls, using a new high-precision method of double-focus spatial fluorescence cross correlation under a confocal microscope. In the vicinity of both walls the measured velocity profiles do not go to zero by supplying a plateau of constant velocity. This apparent slip is proven to be due to a Taylor dispersion, an augmentation by shear diffusion of nanotracers in the direction of flow. Comparing the velocity profiles near the hydrophobic and hydrophilic walls for various conditions shows that there is a true slip length due to hydrophobicity. This length, of the order of several tens of nanometers, is independent of the electrolyte concentration and shear rate.