IMO using any adc with a Vref tied to the Arduino usb powered Vcc is a recipe for disaster. There are several options from a TIL431 "Adjustable Zener" to a full Precision voltage source but whatever method used does require a separate dedicated reference supply.
Noise or variation of Vref is the same as noise or variation of the Arduino USB Vcc source if it is used for the external ADC Vref. The TIL431 is a cheap low tempco adjustable zener with a 100 uA min zener current and the max is 100 mA. The device has a reasonably good tempco in of itself... Probably very good for an enob of 10. However as has been mentioned the Arduino board has several glaring PCB layout errors.. the least is that is isn't a star topology where all the supply returns individually come to the same point which is the PSU return point. There is also little attention to the AVref supply for both noise filtering and ground or supply common mode noise. Individual Pi section LC type filtering in both the Vref and ground returns are a good idea and or a separate low noise linear or dedicated reference... This is very applicable when more than 10 bits of accuracy are required and finally the ADC on the Arduino board is an SAR type architecture which isn't really intended for high accuracy. I always mistrust the LSB and frequently will add some clean buffering and gain so I can drop the LSB. The best option by ar is a dedicated off board ADC of 12 - 14 bits as the PCB layout for that level of accuracy isn't nearly as demanding as are higher resolution parts. Finally the National Semiconductor Linear App notes (Vol 2 I think) describe in great detail the requirements for high accuracy ADC's. Unfortunately the books have been out of print for many years... the issues are the same though and both TI and National (owned by TI now) have available app notes that are applicable to your issues.. I would first read all I could find on layout and good wiring practices from both sources... Burr Brown also had some great stuff for care and feeding of high resolution ADC's... Old to be sure but most applicable.
Doc