Humans quite frequently interact with conversational agents. The rapid advancement in generative language modeling through neural networks has helped advance the creation of intelligent conversational agents. Researchers typically evaluate the output of their models through crowdsourced judgments, but there are no established best practices for conducting such studies. Moreover, it is unclear if cognitive biases in decision-making are affecting crowdsourced workers' judgments when they undertake these tasks. To investigate, we conducted a between-subjects study with 77 crowdsourced workers to understand the role of cognitive biases, specifically anchoring bias, when humans are asked to evaluate the output of conversational agents. Our results provide insight into how best to evaluate conversational agents. We find increased consistency in ratings across two experimental conditions may be a result of anchoring bias. We also determine that external factors such as time and prior experience in similar tasks have effects on inter-rater consistency.