There are many approaches to assess your resizing algorithms. Researchers typically use PSNR to compare quality of image. See http://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio .
Note that, they use the same set of images as the standard. Please see http://www.hlevkin.com/ in the "test still images".
Anyway, If you want to calculate the PSNR, you need two images (Original one, and your test image). So, when you resize image with resolution a1 to a2, you have to resize it backward to original (a1). you can then evaluate it by calculating PSNR. (We generally use the same algorithm as the downsizing step to upsize (a2-->a1).)
The point is, if you want to test the downsizing algorithm alone, what is the proper method? Let's see what others have done.
- Downsizing with test algorithm and Upsizing with FIXED algorithm. (Normally be conventional e.g. Bilinear, Bicubic.)
Likewise, to work with upsizing algorihm,
- Downsizing in traditional way and then upsizing with test algorithm.