An analysis of polarimetric measurements in the presence of noise is presented with emphasis on rotating polarizer polarimeters. A method is presented for estimating the error bars associated with a polarization measurement of an object whose intensity is rapidily fluctuating in a noisy manner. The method requires knowledge of the power spectral density of the intensity fluctuation, and uses this information combined with the sequence of polarizing element settings and measurement times to determine the error bar estimate. The rotating polarizer polarimeter is used as an example of this technique. A relationship is established between the power spectrum of the source intensity fluctuations and the error bars associated with measurements of the stokes vector elements. The impulse response and transfer function of a polarimetric measurement and data reduction sequence are introduced.