For more than a decade, evidence has been accumulating that certain modification of the geometry of the bounding surface of turbulent shear flows can passively reduce viscous drag. An effective and relatively easy to manufacture modification is a surface of grooves, known as riblets, aligned with the mean flow direction. Although such riblets considerably increase the wetted surface to planform area ratio, they have shown significant net reductions in viscous drag when compared to a similar flow over a flat plate. Both Bacher and Smith and Hooshmand show little change in the skewness and flatness values of streamwise fluctuations over the riblet surfaces. However, these measurements were not made very close to the riblet surface. The new results reported in this paper reveal in detail how much these streamwise fluctuation statistical characteristics are altered by riblets near their bounding surface.