Sometimes I reduced the file sizes of my jpeg images for faster uploading to the web.
Does this reduce the image quality?
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Yes it does. When JPEG compresses, it removes details by slightly altering pixels so that the image can be represented with fewer bytes.
One has to be careful how much compression to apply on a JPEG because each step down lowers image quality as well as size. JPEG quality is measured typically on a 0-100 scale (Photoshop has a 1 to 12 scale IIRC) where higher numbers represent higher quality.
When choosing to reduce image quality for the sake of size or bandwidth, you have to compromise somewhere. Going from 100 to 98 for example reduces file size but has an almost insignificant impact on image quality, so it going to 95. For web use, I typically go down to 85 which shows some obvious artifacts but still produces a recognizable image with a moderate amount of details.
Aside from what @Itai said: Take a look at this blog post, where the author dives into jpg quality analysis, determining empirically that there are actually 13 quality output levels spread out across the 0-100 Lightroom scale. While this was done on an earlier version of Lightroom, I'm fairly sure it still applies to LR4.
For JPEG, the format you asked about, yes, reducing file size does reduce quality, as JPEG compression is always* lossy.
(*The JPEG standard actually does support lossless compression, but this is rarely implemented and is not well supported. Your tools are almost certainly using only lossy JPEG compression.)
For other formats, though, the answer may differ. TIFF, for example, supports lossless compression, and in this case, exporting from Lightroom to a losslessly compressed TIFF reduces file size, but does not reduce image quality.
Support for newer file formats is slowly emerging. Unlike JPEG, JPEG-XR's maximum quality setting is lossless, so should such support appear in LR (it is already present in Photoshop), a smaller export size, in that case, would also not reduce image quality.
The answer boils down to whether the method being used to reduce the file's size is lossy (in which case, your answer is 'yes, image quality is being lost') or lossless ('no, no image quality is being lost').