A computer-implemented method for detecting the presence or absence of a fetal aneuploidy, comprising: (a) obtaining counts of nucleotide sequence reads mapped to reference genome sections, wherein the nucleotide sequence reads are obtained from a group of test samples each comprising circulating, cell-free nucleic acid from a pregnant female, wherein the test samples are sequenced under one or more common experimental conditions; (b) for each test sample, filtering genome sections based on one or more of redundant data, non-informative data, noisy data, genome sections with overrepresented sequences, and genome sections with underrepresented sequences; and/or calculating a measure of error for the counts of sequence reads mapped to some or all of the genome sections and removing the counts of sequence reads for certain genome sections according to a threshold of the measure of error, thereby providing filtered genome sections; (c) for each test sample, normalizing the counts for the filtered genome sections, or normalizing a derivative of the counts for the filtered genome sections, by adjusting the counts for experimental condition-induced variability, wherein the adjusting comprises subtracting expected counts from the counts for the genome sections, thereby generating a subtraction value, and dividing the subtraction value by an estimate of variability, which expected counts and estimate of variability are based on the experimental condition-induced variability of the counts for the filtered genome sections, thereby obtaining normalized counts for filtered genome sections; and (d) detecting the presence or absence of a fetal aneuploidy for each test sample based on the normalized counts for the filtered genome sections. (a) obtaining counts of nucleotide sequence reads mapped to reference genome sections, wherein the nucleotide sequence reads are obtained from a group of test samples each comprising circulating, cell-free nucleic acid from a pregnant female, wherein the test samples are sequenced under one or more common experimental conditions; (b) for each test sample, filtering genome sections based on one or more of redundant data, non-informative data, noisy data, genome sections with overrepresented sequences, and genome sections with underrepresented sequences; and/or calculating a measure of error for the counts of sequence reads mapped to some or all of the genome sections and removing the counts of sequence reads for certain genome sections according to a threshold of the measure of error, thereby providing filtered genome sections; (c) for each test sample, normalizing the counts for the filtered genome sections, or normalizing a derivative of the counts for the filtered genome sections, by adjusting the counts for experimental condition-induced variability, wherein the adjusting comprises subtracting expected counts from the counts for the genome sections, thereby generating a subtraction value, and dividing the subtraction value by an estimate of variability, which expected counts and estimate of variability are based on the experimental condition-induced variability of the counts for the filtered genome sections, thereby obtaining normalized counts for filtered genome sections; and (d) detecting the presence or absence of a fetal aneuploidy for each test sample based on the normalized counts for the filtered genome sections.