I'm not an expert by any means, but from reading a lecture notes [1] on it, I think I have a decent idea. Any gravitational wave polarization can be considered

I'm not an expert by any means, but from reading a lecture notes [1] on it, I think I have a decent idea. Any gravitational wave polarization can be considered as a tensor. There are several constraints that reduce the dimensional of that tensor though. For example, it must be symmetric and thus reducing its dimension from 16 to 10. Further constraints reduce it to 6. For physically meaningful waves (under the most accepted theory of gravitational waves), all but 2 of those are 0. This leaves us with 2 polarizations of waves. One of the polarization applies only on the diagonal (of the tensor) and the other on the anti diagonal. From this background, I interpret "we find that the data strongly favor pure tensor polarization of gravitational waves, over pure scalar or pure vector polarizations" to mean that the polarization was not purely of the diagonal polarization and was instead a combination of the two. Alternatively, it could be a property that the tensor representation is more robust to noise or that a non-standard theory is correct and the polarization doesn't fit cleanly into the accepted theory. [1]: http://eagle.phys.utk.edu/guidry/astro616/lectures/lecture_ch21.pdf http://eagle.phys.utk.edu/guidry/astro616/lectures/lecture_c...