A method for determining the presence or absence of a chromosome aneuploidy for a sample comprising: (a) filtering, according to a read density distribution, portions of a reference genome, thereby providing a read density profile for a test sample comprising read densities of filtered portions, wherein: (i) the read densities comprise quantitative measures of counts of sequence reads mapped to the portions of the reference genome, wherein the sequence reads are reads of circulating cell-free nucleic acid from a test sample from a pregnant female, and (ii) the read density distribution is a distribution of average, mean, or median read densities, and is determined for read densities of portions for multiple samples; (b) adjusting the read density profile for the test sample by 1) subtracting a trained median value from test sample read densities and 2) removing components of the test sample read densities that correlate with one or more principal components from the profile, which principal components (i) are obtained from a training set of known euploid samples by a principal component analysis, and (ii) represent one or more biases in a read density profile, thereby providing an adjusted read density profile comprising adjusted read densities, wherein a plurality of biases is removed from the adjusted read density profile; (c) comparing the adjusted read density profile to a reference profile comprising read densities obtained from one or more reference samples, thereby providing a comparison; and (d) determining the presence or absence of a chromosome aneuploidy for the test sample according to the comparison, wherein one or more or all processing methods are performed by a processor, a micro-processor, a computer, in conjunction with memory and/or by a microprocessor controlled apparatus. (a) filtering, according to a read density distribution, portions of a reference genome, thereby providing a read density profile for a test sample comprising read densities of filtered portions, wherein: (i) the read densities comprise quantitative measures of counts of sequence reads mapped to the portions of the reference genome, wherein the sequence reads are reads of circulating cell-free nucleic acid from a test sample from a pregnant female, and (ii) the read density distribution is a distribution of average, mean, or median read densities, and is determined for read densities of portions for multiple samples; (i) the read densities comprise quantitative measures of counts of sequence reads mapped to the portions of the reference genome, wherein the sequence reads are reads of circulating cell-free nucleic acid from a test sample from a pregnant female, and (ii) the read density distribution is a distribution of average, mean, or median read densities, and is determined for read densities of portions for multiple samples; (b) adjusting the read density profile for the test sample by 1) subtracting a trained median value from test sample read densities and 2) removing components of the test sample read densities that correlate with one or more principal components from the profile, which principal components (i) are obtained from a training set of known euploid samples by a principal component analysis, and (ii) represent one or more biases in a read density profile, thereby providing an adjusted read density profile comprising adjusted read densities, wherein a plurality of biases is removed from the adjusted read density profile; (c) comparing the adjusted read density profile to a reference profile comprising read densities obtained from one or more reference samples, thereby providing a comparison; and (d) determining the presence or absence of a chromosome aneuploidy for the test sample according to the comparison, wherein one or more or all processing methods are performed by a processor, a micro-processor, a computer, in conjunction with memory and/or by a microprocessor controlled apparatus.