This research seeks to obviate the need for creating QA datasets and grading (chatbot) LLM responses when comparing LLMs' knowledge in specific topic domains. This is done in an entirely end-user centric way without need for access to any inner workings of the LLM, so long as it can be prompted and given a random seed to create different generations to the same prompt. The paper does this by, for a given topic domain, defining the "response dispersion" of an LLM by repeatedly asking an LLM the same opinion question about that topic domain. Namely, the response dispersion is the count of singular values needed to explain 95% of the variance in the embedding matrix of the LLM's responses. It is found that the response dispersion is inversely correlated with accuracy on relevant QA evaluations (average spearman rank correlation stronger than -.59). A use-case analysis shows that when comparing two different LLMs on the same topic domain, comparing their response dispersion is a suitable replacement for comparing their QA accuracy between 74% and 89% of the time, the range depending on certain reasonable accuracy-difference tolerances that may be acceptable to an end-user in exchange for the labor being saved using response dispersion instead of QA accuracy for comparison. Two response embeddings are studied for creating the embedding matrix in this study, one is from OpenAI's APIs and one is a novel embedding, here named reference sentence similarity embeddings, that can be computed locally and performs very nearly as well in calculating response dispersion. Also in this research, a pre-existing dataset called the IRC-Wiki Trivia dataset, originally developed for trivia games, has been re-purposed, curated, and the curation, called IRC-WikiTriviaQA, is made available for the purpose of this research.