That is the study that was conducted by Andrew Dickerson and his colleague at Georgia Tech, and was published in Fluid Dynamics journal.
The team built a mathematical model of the processes involved, reasoning that surface tension between the water and the dog's hair is what keeps the dog wet. Overcoming that tension requires a centripetal force that exceeds it.
As centripetal force varies with distance from the centre of the creature, its radius is therefore crucial to work out the speed of the oscillations. The team arrived at an equation that calculates the frequency of that oscillation as R0.5.
To test that hypothesis, the team filmed a wide range of dogs shaking, and used the images to calculate the period of oscillation. For a labrador retriever, that turned out to be 4.3 Hz. He then expanded the search, filming animals as small as mice (27Hz) and as large as bears (4 Hz).
Here's the video that accompanied this article:
So the bigger the animal, the slower it can shake to achieve comparable drying, but the relationship isn't linear. Instead, it approaches a limit of 4Hz as an animal grows in size.
A preprint version of the paper can be found on Arxiv.
How many wet investigators that resulted in this study? :)
Can I say it once again how much I love things like this. You guys can go ahead and try to find the meaning of life, and why we're here, and how the universe began. Go at it and call me when you find out. But give me stuff like this that, while it appears to look mundane, can have wide-ranging application that most of us don't know about when we study such things. These things can be fascinating by itself, and the fact that they can have important implications for other systems is simply a pleasant bonus. Kids and students should be exposed to these kinds of curiosity, because these are the things that they can see and understand. Being curious and trying to understand how things happen is what physics is all about.