Words like so, no, vocabulary, and don’t all contain the long o sound inside them. But I regularly hear native English speakers pronouncing the [oʊ] sound in these words (and some others containing this same vowel sound) as if it were “cut in half.” They seem to pronounce only “half of the vowel.” So, to me, most of the time the long o sounds more like [o] or maybe [ə] in the words I’ve mentioned above.
Is this an example of vowel reduction, or is it just my impression?
One thing you need to understand is that the things you may have been taught “are” diphthongs are not necessarily such under all possible circumstances. And while some of this is the normal reduction in unstressed syllables, some of it is not — because they were never diphthongs to begin with for those speakers.
In the case of vocabulary, since that’s in an unstressed syllable, it is subject to reduction to [ɵ] or [ə]. The [ɵ] sound might be the one that you are hearing which is halfway between [o] and [ə]: a neutral vowel like a schwa, but rounded like an o.
For so and no, those are usually diphthongs when at the end of an utterance or stressed, but they may be monophthongs in other places, whether [o], [ɵ], or [ə].
In the case of don’t, you have the nt-reduction happening too, so that’s often just [dõʔ] with a slightly nasalized [õ] replacing the n by coloring the earlier [o] through regressive assimilation, and a brief glottal stop where the t used to be.
In North America (and also Scotland, amongst other places), the off-glides in both /eɪ/ and /oʊ/ are known to be realized as monophthongs in many speakers and environments: just [e] and [o] alone suffice. That’s what makes it a “long e” or “long o” to them, not whether it has a glide.
This is not a matter of “not pronouncing half the sound”, because for native speakers, these are not diphthongs in their minds. If and when they become such, it is nothing but a phonetic allophone, and so you won’t be able to find a minimal pair between the glide and non-glide version.
Indeed, this is what schoolchildren are taught; they are not taught about a diphthong, although some teachers may admit to it if prodded about words where the vowel comes at the end without a final consonant, as in bay or snow where there isn’t a consonant rather than like in bare and spoke whether there is. You will quite often find the latter pair without a glide in them at all in North America. This is not lazy pronunciation; it is normal.
These phonetic effects where the “long” vowel may or may not become a falling diphthong with an off-glide may be too subtle to be useful for non-native speakers trying to learn English. Certainly our schoolchildren are not taught them.
The “long o” of phonemic /o/ contrasts with the “short o” of phonemic /ɔ/, not with the diphthong [oʊ], which is only an allophone. Similarly, the “long e” of phonemic /e/ contrasts with the “short e” of phonemic /ɛ/, not with they diphthong [eɪ], which again is still only an allophone.
It may be more useful for such learners to instead concentrate on phonemics, with the understanding that diphthongization is a phonologic effect that occurs universally in particular environments, and that this particular diphthongization is almost never phonemic in English.
Do you mean that the glide part of the diphthong can be lost when the vowel does not have primary stress? If so, yes, I also hear this. Similarly the long e: diphthong can lose its off-glide in the first syllable of words like "maintain" and the second syllable of words like "female".
With vocabulary it's easy -- a legit pronunciation with a diphthong reduced to ə is pretty common.
But even the rest of the words you listed have weak pronunciation forms (with a possible exception of don't):
(Source: Longman Pronunciation Dictionary)
