Like <PERSON> explained, the refractive properties if a material result from several properties, including conductivity. Other factors include atomic energy levels, dielectric properties (how much the material tends to make dipoles), density, and maybe a few more I can't think about.
If you're not looking for a physical explanation, rather a quick way to know what will happen, you need only look up the complex index if refraction of that material which accounts for all of those factors. Look at this site: http://refractiveindex.info. A material's index of refraction is different for varying wavelengths, so you have to take that into consideration. The real part, $n$, represents how much light is slowed (or sped up, if $n<1$) in the medium, which determines how much refraction occurs as well. The imaginary part, listed there as $k$, relates how much the radiation is absorbed in the medium. The skin depth is how far a wave penetrates before the magnitude of the wave falls off by a factor of $e$. A material with a high $k$ for a given wavelength doesn't just absorb the light, however, it's usually reflected. 70
Silver, for example, has a $k$ of around 3 to 4 for visible light, which it's why used in mirrors. Absorption occurs more due to resonance than conductive properties, but I'm near the limit of my understanding there.
Now to correct a few things about your question: the comparison between the wavelength of the radiation and the physical size of the object it will be passing through doesn't have anything to do with refraction. That is, the refractive properties of a material are independent of how thick or how big the material is. Now, you're thinking about this because you're asking about radio waves. Radio waves have wavelengths on the order of meters to kilometers. While they can pass through materials, and also be reflected and/or refracted by them, they're more likely to bend around the objects than anything else. This, however, is called diffraction, not refraction (see also this wikipedia article about radio propagation).
So, in summary, yes, there are ways to think about materials that can clue us in on how they behave optically, and measured values that contain this information. However, refraction isn't necessarily responsible for the phenomena you're thinking of. 70