Contemporary learning models for computer vision are typically trained on very large (benchmark) datasets with millions of samples. These may, however, contain biases, artifacts, or errors that have gone unnoticed and are exploitable by the model. In the worst case, the trained model does not learn a valid and generalizable strategy to solve the problem it was trained for, and becomes a 'Clever-Hans' (CH) predictor that bases its decisions on spurious correlations in the training data, potentially yielding an unrepresentative or unfair, and possibly even hazardous predictor. In this paper, we contribute by providing a comprehensive analysis framework based on a scalable statistical analysis of attributions from explanation methods for large data corpora. Based on a recent technique - Spectral Relevance Analysis - we propose the following technical contributions and resulting findings: (a) a scalable quantification of artifactual and poisoned classes where the machine learning models under study exhibit CH behavior, (b) several approaches denoted as Class Artifact Compensation (ClArC), which are able to effectively and significantly reduce a model's CH behavior. I.e., we are able to un-Hans models trained on (poisoned) datasets, such as the popular ImageNet data corpus. We demonstrate that ClArC, defined in a simple theoretical framework, may be implemented as part of a Neural Network's training or fine-tuning process, or in a post-hoc manner by injecting additional layers, preventing any further propagation of undesired CH features, into the network architecture. Using our proposed methods, we provide qualitative and quantitative analyses of the biases and artifacts in various datasets. We demonstrate that these insights can give rise to improved, more representative and fairer models operating on implicitly cleaned data corpora.