Human evaluation has been widely accepted as the standard for evaluating chat-oriented dialogue systems. However, there is a significant variation in previous work regarding who gets recruited as evaluators. Evaluator groups such as domain experts, university students, and professional annotators have been used to assess and compare dialogue systems, although it is unclear to what extent the choice of an evaluator group can affect results. This paper analyzes the evaluator group impact on dialogue system evaluation by testing 4 state-of-the-art dialogue systems using 4 distinct evaluator groups. Our analysis reveals a robustness towards evaluator groups for Likert evaluations that is not seen for Pairwise, with only minor differences observed when changing evaluator groups. Furthermore, two notable limitations to this robustness are observed, which reveal discrepancies between evaluators with different levels of chatbot expertise and indicate that evaluator objectivity is beneficial for certain dialogue metrics.