To statistically test and evaluate the significance of asymmetric upward thickening and thinning trends and other cyclic patterns in turbidite successions, 28 bed-by-bed sections with a wide coverage in geological time, tectonic settings, facies characteristics, and depositional environments were measured and described. First, 286 sandstone packets were selected from the 28 turbidite sections through statistically based segmentation. Then, these packets were examined by three powerful correlation tests (Kendall's, Spearman's, and Pearson's correlation tests) and four tests for randomness. Only 34 (11.9%) of the sandstone packets pass tests designed to identify asymmetry at the 10% significance level. Monte Carlo simulation and calculation of cumulative binomial probabilities indicate that the number of asymmetric cycles identified in the original set of sandstone packets is indistinguishable from the number expected to result from random processes. Eighty-six sandstone packets from five sections were tested for upward coarsening and fining trends. Forty-two of these packets were from channel deposits and the rest from lobes and basin-plain deposits. Only 25 (29%) of the 86 packets coarsen or fine upward. However, 33-50% of packets from coarse-grained channel fills show asymmetric grain-size trends, mostly as upward-fining cycles (15 of the 42 tested packets from channel deposits). These upward-fining trends in channel deposits are interpreted as the result of channel filling or the stacking of onlapping deposits at a channel mouth. Results from this study strongly suggest that asymmetric bed-thickness cycles have essentially no statistical significance in turbidite successions, and therefore cannot provide a key criterion for identification of sub-environments in submarine fan systems. It follows that models for submarine fans based on the widely publicized hypothesis of common asymmetric cycles should be reconsidered. Instead, other criteria such as specific facies characteristics, large-scale geometry, and degree of sand-bed clustering may provide the best tools for discrimination of submarine fan sub-environments. In natural systems, the disordered vertical arrangement of thicker and thinner beds likely results from irregular variations in flow volumes, concentrations, and precise pathways of turbidity currents. Over the short time scales represented by tens of meters of section, most submarine fans are built by aggradation, not progradation, so that facies shifts are controlled mostly by channel switching and avulsion, and not by progressive basinward or landward advance or retreat of one sub-environment over another. Aggradation does not tend to generate asymmetric trends in bed thickness. The same arguments are believed to hold for grain-size trends in submarine-fan packets, except in the case of coarse-grained channel deposits, where upward fining is conspicuous.