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Common knowledge (CK) is a phenomenon where a group of individuals each knows some collection of information, and, in essence, everyone knows that everyone knows the information. There are many applications involving CK, including business decision making, protests and rebellions, and online advertising. CK can lead to contagion and collective action but in ways that are fundamentally different from classic (e.g., Granovetter) threshold models used in the social sciences. Researchers developed CK models to enable the computation of contagion in networked populations. But these models have largely not been investigated using experiments with human subjects. In this work, we conduct a successive analysis of online CK experiments. We devise a flexible and interpretable statistical method to investigate the effects of significant factors, such as network structure and communication type. Among our findings, we demonstrate a phase change in group payout in the games that is caused by prohibiting player communication.