Crowd motions usually play a basic role of analyzing and understanding abnormal events. However, only using these visible features cannot fully describe the scenarios because the influence caused by an abnormal event is not considered from the social psychological point of view. Although the invisible influences cannot be directly observed through the video, they objectively exist and have precise definitions and specific analytical methods in sociology and psychology. Therefore, a mid-level representation named global event influence (GEI) for global anomaly detection in dense crowds is introduced. The proposed GEI integrates the crowd motions and social psychology attributes to improve the description of crowds. For this, low-level motion features are abstracted as crowd attributes of scale, velocity, and disorder. Then, the detailed definitions and mathematical expressions of GEI are presented through calculating the convolution of rise factor and decay factor. Based on GEI, a model for global anomaly detection is proposed. Compared with most previous methods, our proposed model is robust to detect not only the occurrence of anomalous events but also elimination time of the event influence. Accordingly, strategies for event occurrence detection and influence elimination detection are proposed, respectively. In addition, a dataset of dense crowds is introduced and used for evaluation. The experimental comparison on benchmark datasets shows that the performance of our GEI model has not only the competitive accuracy of event occurrence detection but also the claimed effectiveness of influence elimination, which is more advanced than others.