There is a confidence crisis in many scientific disciplines, in particular disciplines researching human behavior, as many effects of original experiments have not been replicated successfully in large-scale replication studies. While human-robot interaction (HRI) is an interdisciplinary research field, the study of human behavior, cognition and emotion in HRI plays also a vital part. Are HRI user studies facing the same problems as other fields and if so, what can be done to overcome them? In this article, we first give a short overview of the replicability crisis in behavioral sciences and its causes. In a second step, we estimate the replicability of HRI user studies mainly 1) by structural comparison of HRI research processes and practices with those of other disciplines with replicability issues, 2) by systematically reviewing meta-analyses of HRI user studies to identify parameters that are known to affect replicability, and 3) by summarizing first replication studies in HRI as direct evidence. Our findings suggest that HRI user studies often exhibit the same problems that caused the replicability crisis in many behavioral sciences, such as small sample sizes, lack of theory, or missing information in reported data. In order to improve the stability of future HRI research, we propose some statistical, methodological and social reforms. This article aims to provide a basis for further discussion and a potential outline for improvements in the field.