Final answer:
The psychological principle is stereotype threat, where negative stereotypes about a social group negatively affect performance. In this case, women's performance in online chess is impacted by the belief that men are generally better at chess.
Step-by-step explanation:
The psychological principle that helps explain why women tend to perform more poorly when they believe their online chess opponent is male is the stereotype threat. Stereotype threat refers to the phenomenon where individuals are aware of negative stereotypes about their social group and it negatively affects their performance in a specific domain.
In the context of women playing online chess, the stereotype threat arises from the belief that men are generally better at chess than women. This belief can create anxiety and self-doubt in women, leading to poorer performance. It is important to note that this is not a reflection of women's actual abilities, but rather the psychological impact of societal stereotypes.