Minimal Pair List Vowels 8 and 12, /ʊ/ versus /ə/ 1 pair

Since the schwa has to be unstressed while /ʊ/ is likely to be prominent, only a single pair was found in the dictionary:
backwoods backwards
The density figure is too small to be worth calculating.
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John Higgins
John Higgins retired in 2000, having spent the bulk of his career as a British Council English Language Officer working in Thailand, Turkey, Egypt and Yugoslavia and the last fifteen years in lectureships at Bristol University and then running an M.Sc. programme at Stirling University. His main field was EFL, with a special interest in CALL (computer-assisted language learning) in which, together with Tim Johns of Birmingham, he was responsible for important developments in methods and materials.
His publications include A Guide to Language Laboratory Material Writing, Universitetesforlaget, 1969, Computers and Language Learning, Collins, 1984, Language Learners and Computers, Longman, 1988, and Computers in English Language Learning, Intellect Press, 1992, together with numerous papers, reviews and pieces of software. He maintains a web page on minimal pairs and homographs for teachers of English pronunciation skills.