An analysis of the Rietveld profile refinement method used in the interpretation of neutron or X-ray powder diffraction patterns has been carried out. It is shown that the values obtained for the structural parameters are not exactly the same as those obtained from an integrated intensity refinement of the same data and that the standard deviations of the parameters are determined incorrectly. Whilst the differences in the values of the parameters may not be statistically significant, the fact that their standard deviations are estimated incorrectly severely limits their usefulness. These conclusions are confirmed by refinement of a number of data sets using both methods and in most of these cases the standard deviations are found to be underestimated by the profile refinement method by a factor of at least two. Discussions based on the results of profile refinement must therefore be reconsidered and the relative value of powder diffraction techniques must be reviewed.