Home again home again
Lickety split immediately came to mind, but Josh suggested jiggety jig, and suddenly I was afraid that the entire lickety split ending was a figment of my imagination. But, no, it isn't, it just seems less well-documented than jiggety jig.
"Home again home again jiggety jig" comes from the "To Market, to Market, to Buy a Fat Pig" nursery rhyme.
I have no idea where "home again home again lickety split" originates. I thought maybe it was "This Little Piggy Went to Market," but I don't think it is. Going home in "This Little Piggy" is connected to crying "wee wee wee" all the way there, not to any lickety splitness. Anyone know?
I'm sorry that I haven't posted anything more substantial lately. I've been a bit distracted by things like this and my paying job--you know how it is--and, of course, nursery rhymes. Ah, to be little again and have someone read nursery rhymes to me! I'll just have to find some little kid to read them to instead. (Although some are at least a little bit disturbing. Nonetheless, please disown me if you ever find me reading this to any little kid! "And brightened Miss Muffit's whole day," my foot!)
Josh thought it was "jiggedy jig," but when I Googled it, it turns out that "jiggedy jog" is more common, but both exist. And, to further confuse things, it's spelled both "jiggedy" and "jiggety."
These two versions of "To Market, To Market" are very different from each other, actually, which is a bit surprising:
Jiggety Jog: http://www.amherst.edu/~rjyanco94/literature/mothergoose/rhymes/tomarkettomarkettobuyafatpig.html
Jiggety Jig and Jiggety Jog: http://www.rhymes.org.uk/a105-to-market.htm
As to how likely it is that all those people made up the "lickety split" ending--I just did some research. I tried comparing the number of hits for plausibly misquoted nursery rhymes (and similar doggerel) to the correctly quoted words. It turns out to vary tremendously, depending on which misquote you look at, but 1 in 200 in well within the normal range. If you compare "catch a lion by the toe" to "catch a tiger by the toe," it is only one in 5000, i.e. 4 hits compared to 20,000. But if you look at "'gave her father forty whacks' 'gave her mother forty one'" vs. "'gave her mother forty whacks' 'gave her father forty one'", the ratio is almost exactly 1! (Each one gives a little over 5000 hits.) The great majority of people just don't remember which it is, and guess at random. But I did find a case that gives a ratio similar to your case. If you compare "one horned one eyed flying purple people eater" to "one eyed one horned flying purple people eater," then the ratio is 1 to 100, i.e. 7 hits vs. 700 hits.
Granted, that's not exactly the same, since it is only changing the order of the words, rather than changing the words themselves. We need to think of a case where there is a nonsense phrase that sounds similar to another well known nonsense phrase. Can you think of any examples?
ALG's dad-- I only thought "jiggety jog" / "jiggedy jog" (conflate the two, please, since they sound the same when you say them) was more common than "jigget/dy jig" because one or two people seemed to imply that that's how they knew it. Pig rhyming with "jig" (no "jiggety") and hog rhyming with "jog." Nothing as scientific as you came up with!
I am now convinced that "lickety split" is just a figment of my imagination--and a 108 other people's! It doesn't sound so much like "jiggety jig" to me, but I suppose it is a nonsense phrase with the same number of syllables and same rhythm.
(I think some of the words in this comment are misspelled, but I'm too tired to check.)
Substituting plausible sounding nonsense syllables for other nonsense syllables in song lyrics turns out to be quite common on the internet. For example, there are 420 hits for "twiddley diddley dee" and 33 hits for "fiddley diddley dee", a ratio of 13 to 1. That's for these exact spellings. You get smaller numbers of hits substituting "dum" for "dee" or "twiddledy" for "twiddley", etc.
But I haven't yet thought of an exact test case, i.e. substituting for a nonsense phrase a similar sounding phrase that means something appropriate in the context.