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Does anyone disagree?
I disagree with "precisely". Obviously the distribution skews to "University" for older people and "Uni" for younger people, but at the crossover there will be a 50/50 split. Becasue there is no hard cut off, you could only say that the probability that somebody falls into the older or younger demographic can be predicted with a success rate of over 50% if you know whether they say Uni or University.
I also don't know whether that crossover is at "born in year x" or whether it's really at "born x years ago" where x changes by more or less than 1 for each year that passes. Is "Uni" infecting older people as its prevalence grows in the general population, or do people start to switch back to "University" as they mature?
What you are developing is not a theory, it's a hypothesis. You now need some proper observational data to test it, and if you want to test it properly you need a longitudinal study.
I am developing a theory that use of the word 'university'† rather than 'uni' precisely determines if someone was born before 1977. Does anyone disagree?
† or 'college' for Oxbridge, Durham etc