"The internal transparent dither circuit dramatically improves the ADC’s SFDR response well below 100dBc for low level input signals, allowing the ADC to maintain its high dynamic range specification with only a small degradation to the noise floor."
We've all seen those check boxes in Setup > General > HPSDR: "Dither" and "Random". If you are wondering what they are for, look no further than the data sheet for the ADC used in all of the ANAN series radios:
http://cds.linear.com/docs/en/datasheet/2208fc.pdf
Those check boxes directly control the Dither and Random control lines on the ADC.
Everything you need to know about what these control lines do is in the datasheet. However, the datasheet is lengthy and perhaps difficult for some to read and understand. The much more important of two controls is the Dither control. Therefore you may want to read this application note first as it is quite a bit shorter and to more to the point:
http://www.analog.com/media/en/reference-design-documentation/design-notes/DSOL44.pdf
If you are looking for the math, this link is an excellent reference:
http://www.analog.com/en/analog-dialogue/articles/adc-input-noise.html
Adam Farson, VA7OJ/AB4OJ, who does such a fantastic job measuring radio performance, shows exactly how well Dither and Random work in his measurements of an ANAN-8000DLE:

As you can see, there is substantial improvement at lower signal levels, and little improvement at higher signal levels.
You'll note that Adam put a couple of reference lines on the graph that represent ITU-R P.372-13 radio noise levels at the 20M measurement frequency he used. It can be clearly seen that there is little difference at signal levels higher than the ITU radio noise levels Adam referenced regardless of how the Dither and Random settings are selected.
Personally I always run with both Dither and Random turned on. There is little penalty in the noise floor, sometimes none depending on conditions, and the resulting increase in SFDR and IP3 certainly can't hurt when you are faced with a great many S9-plus-a-lot signals on the band. In other words, it is better to have it and not need it, then need it and not have it.
Also, consider the ITU radio noise level recommendation data:

If your conditions are good and/or you are operating on higher frequency bands, there may be ample opportunity for both Dither and Random to contribute to better radio performance. Indeed, I live in a rural to quiet rural environment, depending on the appliances in my house

At any rate, you can decide for yourself if "it is better to have it and not need it or need it and not have it." Experiment!
Finally, it is worth noting that turning on the "IP+" feature on the Icom IC-7300 is equivalent to the Dither check box in PowerSDR. I'm not sure if there is a similar control on Flex radios.
73,
Scott