Noise comparisons of E20
Rumor has it that a circular polarizer increases noise, especially in the blue channel.  Some believe a UV filter will increase noise a little as well.  Here is a comparison of shots with No filter, Hoya Multicoat UV filter, and non-coated Circular Polarizer.

Method:

1) A Kodak pantone color sample was shot at ISO 80, 160, 320 with (A) No filter, (B) UV Multicoat, (C) non coated Plain Circ-Polarizer.   Shots were taken under Incandescent lighting with a Manual WB, using P-mode, 0 exposure compensation, and zoomed at 36mm(140mm equiv). All images were recorded using SHQ at 5mp and 1:2.7 JPG compression. Artifacts could be a factor, but results are relative to each other so artifacts weren't seen as a handicap.
2) Mean, Median and standard deviation measurements were taken from nine 2340 pixel-sized areas of each image (see green boxes of the example pantone)
3) Additionally, since histograms on E20 showed that the exposure for all shots was slightly under, a +0.7 exposure compensation was taken at ISO80 without filter for comparison.

Results:

The ISO 80 data can be viewed here.  Or downloaded as an Excel 97 spreadsheet here.

Image swath comparison is here for a qualitative view.  (The TIF version of the swaths is linked here.)

Conclusions:

1. The addition of a UV filter changed the exposure from 1/80 to 1/50, but the mean was raised using the filter by roughly 25-30%.  Perhaps a shutter of 1/60 should have been used for the filter.

2. The UV filter gives mixed results at ISO80: noise seems to raise on the RGB swaths, but not as much or even lowers on the CYM and Grey swaths.  Results seem to indicate a nearly imperceptible increase in noise when using the UV filter.

3.The Polarizer cut the exposure of the UV filter by two (expected) but maintained a mean closer to the No Filter image, indicating that it reduces the overall exposure to about a third.  The blue channel for yellow swaths, however, seems to be more efficient than the others, suggesting the polarizer is passing more efficiently on the blue end (expected).

4.  The Polarizer does not seem to substantially increase the noise in most swaths except Blue and Green, where it is increased by almost 20-30%.  The Cyan swath, surprisingly, did not increase.   Results seem to indicate skynoise will increase with the use of a polarizer, seemingly because it absorbs more on the red end.