Image Quality of MRI brain scans is strongly influenced by within scanner head movements and the resulting image artifacts alter derived measures like brain volume and cortical thickness. Automated image quality assessment is key to controlling for confounding effects of poor image quality. In this study, we systematically test for the influence of image quality on univariate statistics and machine learning classification. We analyzed group effects of sex/gender on local brain volume and made predictions of sex/gender using logistic regression, while correcting for brain size. From three large publicly available datasets, two age and sex-balanced samples were derived to test the generalizability of the effect for pooled sample sizes of n=760 and n=1094. Results of the Bonferroni corrected t-tests over 3747 gray matter features showed a strong influence of low-quality data on the ability to find significant sex/gender differences for the smaller sample. Increasing sample size and more so image quality showed a stark increase in detecting significant effects in univariate group comparisons. For the classification of sex/gender using logistic regression, both increasing sample size and image quality had a marginal effect on the Area under the Receiver Operating Characteristic Curve for most datasets and subsamples. Our results suggest a more stringent quality control for univariate approaches than for multivariate classification with a leaning towards higher quality for classical group statistics and bigger sample sizes for machine learning applications in neuroimaging.