IntroductionFinnish companies are legally required to insure their employees against occupational accidents. Insurance companies are then required to submit information about occupational accidents to the Finnish Workers’ Compensation Center (TVK), which then publishes occupational accident statistics in Finland together with Statistics Finland. Our objective is to detect silent signals, by which we mean patterns in the data such as increased occupational accident frequencies for which there is initially only weak evidence, making their detection challenging. Detecting such patterns as early as possible is important, since there is often a cost associated with both reacting and not reacting: not reacting when an increased accident frequency is noted may lead to further accidents that could have been prevented. Method: In this work we use methods that allow us to detect silent signals in data sets and apply these methods in the analysis of real-world data sets related to important societal questions such as occupational accidents (using the national occupational accidents database). Results: The traditional approach to determining whether an effect is random is statistical significance testing. Here we formulate the described exploration workflow of contingency tables into a principled statistical testing framework that allows the user to query the significance of high accident frequencies. Conclusions: Our results show that we can use our iterative workflow to explore contingency tables and provide statistical guarantees for the observed frequencies. Practical Applications: Our method is useful in finding useful information from contingency tables constructed from accident databases, with statistical guarantees, even when we do not have a clear a priori hypothesis to test.