Two things strike me about this. Firstly, it is a statistical analysis of how often chords appear, though they don't seem to measure how long chords are held for, which seems pretty important. Secondly, it is a probability analysis of the likelihood of one chord following another. If you scroll down you will see a chart titled "Chords following em [E minor]". That looks pretty wacky too. 59% of the time E minor is followed by F major in the key of C major? That's a pretty weak progression. But maybe that is, statistically, true. The problem is that all this seems quite oblivious to the function of harmony.
I've been raging about pseudo-science lately and how researchers doing research into music who know absolutely nothing about music are just embarrassing. This site is a little different. For one thing, it is digging into the music itself instead of coming at if from left field somewhere. Remember the yellow-bellied marmot in this post? Hooktheory has a page where they put all their analyses. Here that is. Here is the analysis of "California Gurls" by Katy Perry.
The first thing I did was look for a Beatles song to see how that came out. Take the analysis of "Hey Jude" for example. The authors know something about music theory, which is refreshing, but not quite enough. Look at the "outro" (I think "coda" might be the better word) for "Hey Jude". They give the progression as I, IV of IV, IV, I. The idea of a secondary dominant is a long-standing one in music theory, but it really can't be extended to the idea of a secondary subdominant which is what is being claimed so blithely here. IV of IV? S'existe pas!
The idea of a secondary dominant is a powerful one because the relationship of V or better, V7, to I is so strong that it can be transferred to any chord. There is no strong relationship of IV to I. IV, in traditional theory, prepares V, that is its role. So the progression I, IV of IV, IV, I just isn't plausible because the relationships claimed are not plausible. The progression is actually I, bVII, IV, I. This is interesting because it is so very coda-like. In common-practice harmony, the coda has the role of lowering the tension and it very commonly uses subdominant harmony to do so. Interesting that this song, with its huge coda, does the same. But what is also happening here is the creation of an ambiguity. Any time you have an ambiguous progression that fades out, it can be an undecided question just what the final chord is. For example, suppose that the key is not F but Bb? We then have the progression V, IV, I, V. That's a lot more probable than the one they suggest and just as probable as the one I first suggested. What is actually happening here is something that always happens when you have IV I progressions. It either sounds like a plagal cadence, which is inherently weak, or it sounds like the IV is actually the I. The coda to "Hey Jude" is interesting, I suggest, because it floats between both possibilities.
Well, that's my stab at doing some popular music theory. I would suggest to the authors of Hooktheory that instead of doing a statistical analysis of 1300 songs (and not coming up with much), that they pick a few good songs and try and figure out how the harmony functions.