The deployment of large language models (LLMs) raises concerns regarding their cultural misalignment and potential ramifications on individuals and societies with diverse cultural backgrounds. While the discourse has focused mainly on political and social biases, our research proposes a Cultural Alignment Test (Hoftede's CAT) to quantify cultural alignment using Hofstede's cultural dimension framework, which offers an explanatory cross-cultural comparison through the latent variable analysis. We apply our approach to quantitatively evaluate LLMs, namely Llama 2, GPT-3.5, and GPT-4, against the cultural dimensions of regions like the United States, China, and Arab countries, using different prompting styles and exploring the effects of language-specific fine-tuning on the models' behavioural tendencies and cultural values. Our results quantify the cultural alignment of LLMs and reveal the difference between LLMs in explanatory cultural dimensions. Our study demonstrates that while all LLMs struggle to grasp cultural values, GPT-4 shows a unique capability to adapt to cultural nuances, particularly in Chinese settings. However, it faces challenges with American and Arab cultures. The research also highlights that fine-tuning LLama 2 models with different languages changes their responses to cultural questions, emphasizing the need for culturally diverse development in AI for worldwide acceptance and ethical use. For more details or to contribute to this research, visit our GitHub page https://github.com/reemim/Hofstedes_CAT/
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