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ChatGPT is a powerful large language model (LLM) that covers knowledge resources such as Wikipedia and supports natural language question answering using its own knowledge. Therefore, there is growing interest in exploring whether ChatGPT can replace traditional knowledge-based question answering (KBQA) models. Although there have been some works analyzing the question answering performance of ChatGPT, there is still a lack of large-scale, comprehensive testing of various types of complex questions to analyze the limitations of the model. In this paper, we present a framework that follows the black-box testing specifications of CheckList proposed by Ribeiro et. al. We evaluate ChatGPT and its family of LLMs on eight real-world KB-based complex question answering datasets, which include six English datasets and two multilingual datasets. The total number of test cases is approximately 190,000. In addition to the GPT family of LLMs, we also evaluate the well-known FLAN-T5 to identify commonalities between the GPT family and other LLMs. The dataset and code are available at https://github.com/tan92hl/Complex-Question-Answering-Evaluation-of-GPT-family.git