Are you speaking of sentences found in published literature? I’ve seen it done for effect now and then—for instance, to indicate in dialogue that a character is speaking an unfamiliar name or word, something like this: “In Amrika they call this noodle mah-kah-ro-nee.” But more than a little of this sort of thing would grow annoying very quickly, so I’m glad to say I don’t see much of it.
Or are you just looking for any kind of made-up example? Informal “phonetic” spelling depends, of course, on shared conventions for the spelling you do use. In the example you gave, we know how you intend us to say “sykology” because we know the word it stands for, thanks to the ample context. But there’s nothing inherent in that series of letters that tells us how to render the y or where to put the emphasis. It isn’t really phonetic—it’s just a somewhat simplified spelling of a known word. If I wrote, for instance, “sinekdukey” and told you it was a phonetic spelling, how would you say it? and what would you have to do to come up with the intended word?
If you’re just looking for misspellings based on how a heard expression is rendered by someone who doesn’t actually know what words are being used, they’re all over the Internet, including right here on Fluther. Unless they use a set of formal symbols for rendering sounds (a phonetic alphabet) with a one-to-one correspondence between sound and symbol, they still depend on a set of shared conventions for pronouncing letter combinations.