One paper I’ve always admired is Gerd Fraenkel’s ‘Mutual Intelligibility Between Turkish of Turkey and Azerbaijani’ in American Studies in Altaic Linguistics ed. Nicholas Poppe (Bloomington: Indiana University, 1962). After writing in an earlier work that these two languages
are about as mutually intelligible as Danish and Norwegian, Fraenkel decided to validate this assertion with hard figures. He prepared 75 sentences in English of increasing complexity, had them translated into Turkish and Azerbaijani by native speakers, and then played them back to a set of testees. Each listener had to select which one of four figures presented to him the sentence was related to. The results were that each group understood no less than 33% of the material and no more than 65%.
The author notes some complications inherent here. Not all of the subjects were equally motivated. Even people who were keen and alert at the beginning of the test had flagging interest. Finding Azeris who had not been exposed to Turkish was also difficult. Still, I admire the effort to reach a number instead of always comparing the languages in question to some other two languages. When the mutual intelligibility of Hill Mari and Meadow Mari, for example, is claimed to be
less than the languages formerly called Serbo-Croatian, that doesn’t really clarify the issue for many readers. I think a study like this would be useful for many of the peoples I have worked with.