In an effort to better understand the behavior of large language models (LLM), researchers recently turned to conducting psychological assessments on them. Several studies diagnose various psychological concepts in LLMs, such as psychopathological symptoms, personality traits, and intellectual functioning, aiming to unravel their black-box characteristics. But can we safely assess LLMs with tests that were originally designed for humans? The psychology domain looks back on decades of developing standards of appropriate testing procedures to ensure reliable and valid measures. We argue that analogous standardization processes are required for LLM assessments, given their differential functioning as compared to humans. In this paper, we propose seven requirements necessary for testing LLMs. Based on these, we critically reflect a sample of 25 recent machine psychology studies. Our analysis reveals (1) the lack of appropriate methods to assess test reliability and construct validity, (2) the unknown strength of construct-irrelevant influences, such as the contamination of pre-training corpora with test material, and (3) the pervasive issue of non-reproducibility of many studies. The results underscore the lack of a general methodology for the implementation of psychological assessments of LLMs and the need to redefine psychological constructs specifically for large language models rather than adopting them from human psychology.