A laser Doppler Anemometer (LDA) is used to make Reynolds stress measurements in a fully developed, turbulent pipe flow. Traverses are made to measure shear stress, normal stresses, and the correlation coefficient. To assess the accuracy of this system, these measurements are compared with results from other published investigations. The differences between the published reports are discussed to emphasize how much turbulence measurements can vary, even in a well-studied flow. Descriptions are included about LDA theory and turbulence measurement techniques. The techniques discussed include the selection of proper sampling rate, the reduction of statistical bias, the choice of amplification, and optimization practices.