I use Audacity only for mastering mixes that I do on portable studios. Recently, I started using a Tascam 2488mkii (24 or 16 bit option). The 2488mkii does not offer dithering if I use the 24 bit rate (as far as I can tell in the manual, and the techs at Teac weren’t helpful), but whether I import the mixes into my computer by CD or by USB, it does automatically convert the 24 bit to 16 bit for transport. How do I tell if I need to use the dithering in Audacity at that point, or should I just turn it on as a matter of course because I’m dropping that bit rate?

Firstly, a “terminology” issue.
16-bit, 24-bit or 32-bit refer to the “bit format” or “bit depth”. This is different from “sample rate” or “data rate”.

The “bit-depth” refers to the numerical precision that is used for each sample value.
The “sample rate” refers to the number of samples per second.
“Bit rate” or “data rate” refers to the amount of digital data per second and is dependent on the bit-depth, sample rate and data format.

Dither should normally be applied when converting from a higher bit-format (bit depth) to a lower one. For example when converting from 24-bit to 16-bit.
The Teac should (and probably does) apply dither when converting 24-bit to 16-bit.

Whether or not to use dither in Audacity depends on exactly what you will be doing in Audacity. In most cases you should leave the default “Quality” setting at 32-bit float and have dither enabled for “high-quality conversion” (either “triangle” or “shaped”).
If you are using exclusively 16-bit audio and you are ONLY using basic editing functions (“cut”, “copy”, “paste”) and are NOT DOING ANY OTHER PROCESSING, then there is a marginal advantage to setting Quality to 16-bit and setting dither to “none”. If you are doing any processing of any sort (such as Amplify, Normalize, Equalization, Noise Removal, Equalization, or any other type of effect or processing) then leave the Quality settings at 32-bit float and triangle/shaped dither.

Thank you. This is very helpful.

One other question regarding dithering: Since I have no way of transferring samples from my Tascam/TEAC unit to my computer at anything but a bit format of 16, does it do me any good to use the 32 floating bit format in Audacity? I was told by the company that mastered my last album that once it was reduced to 16 bit I should just leave it there because increasing it would not do anything for it. I do use Audacity to compress, limit, EQ, filter, amplify, and normalize the audio when I do my own mastering, then I move it to itunes as a WAV file and burn it to a cd.

If you are ONLY doing cut/paste/trim/delete type editing, then it is best to leave it at 16-bit and turn off dither (in Preferences).
All processing in Audacity is done with 32-bit (float) so it is definitely better to convert to 32-bit float format and enable dither if you are doing any processing.

In that case you should leave the Quality setting in Preferences at 32-bit (float) and dither enabled for high quality conversion.
When you process a 1-bit audio track, Audacity uses 32-bit float processing (because it is faster and much more precise) and then converts the result back to 16-bit when it is returned to the track. This means that there will be format conversions from 16-bit to 32-bit float, back to 16-bit each time to apply any effect. It is better to convert to 32-bit once (when the file is imported) and then convert back to 16-bit on the final export so that there is no format conversion during processing.

Thank you very much, Steve, for your explanation.