The sample from Monday's test, 4 days ago, was done at my primary care doctor's parking lot in Folsom by a gowned nurse who came out to my car's window to swab me (but only 1 nostril). That swab was sent to the lab at Quest Diagnostics and my online Quest account is where I viewed the result last night. The type of test was "SARS CoV 2 RNA(COVID 19), QUALITATIVE NAAT". Another online resource says that test "includes RT-PCR or TMA".
Off hand, I don't know which lab or which type of test it was from the testing done last Thursday (now 8 days ago) when we both were tested by the same PA at Med-7 in Roseville. Both nostrils were swabbed and my wife's came back positive. I don't have online access to the test -- they notified me of the result by phone. It is not showing up in my Quest Diagnostics account, so I assume they didn't process it at a Quest lab.
Practical follow-up
Going for an additional test may increase the odds of a negative disease state, if negative but certainty is hard to achieve here. And then, if the test is positive, there's always the possibility that it's a false positive. Also, being free of disease today does not mean free of disease tomorrow.

Statistical follow-up (just in case somebody is interested)
Just like in any decision making process (health-related, investment etc), what you want are sensitive and specific 'tests' that help you keep or reject hypotheses (or investment targets).
Disease
Y N
Y a b
Test result
N c d
Where false negatives come is from the sensitivity aspect (a/a+c). Specificity is (d/d+b). That's the disease perspective. Another instructing aspect is the predictive value (test) perspective. Positive predictive value = a/a+b. Negative predictive value = d/d+c.
So for a disease (or an investment) you want high sensitivity and high specificity tests for screening and high positive and negative predictive value on results to help delineate where the value is within the selected group.
This may seem dry and irrelevant but it's quite useful (people do it all the time without realizing it) when, for instance, you meet people for the first time. You may ask them if they like sports to screen and then calibrate by asking if they enjoy rugby.
By repeating the exact same test, you increase the odds for more precision but repeating the exact same test carries the same statistical limitations.
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On the home oximetry.
i've been following an interesting company that offers home services for people affected by chronic lung conditions. i think it is becoming increasingly overvalued (i may be wrong) and think that they wrongly focus on the equipment rather than the services side at this point although this may be related to how insurers deal with 'product' under present conditions. Anyways, they have the potential to provide, in real time, online monitoring of different parameters including oximetry in order to timely intervene and likely reduce complications, hospitalizations etc
It's still unclear if the introduction of home oximetry would be cost effective on a large scale (for Covid-19 or otherwise) but, from an individual point of view, it's a reasonable option. There are smart watch options which are becoming interesting. Also, there are places where the idea is being tested.
https://www.bmj.com/content/371/bmj.m4151One characteristic of Covid (not unique but quite representative) has been the combination of a relatively comfortable person with unusually low oxygen saturation levels at the initial measure. These people were often clinical ticking bombs with very real and rapid deterioration shortly thereafter so the idea to detect a significant and relatively asymptomatic aspect is an interesting feature. The oxygen saturation to oxygen concentration (pressure) curve is interesting and offers valuable lessons for other disciplines.

A very interesting feature happens when saturation reaches around and below 90%. This is related to a long evolutionary process meant to facilitate efficient oxygen unloading in peripheral tissues but has the side effect that the slope change around 90% can have sudden and disastrous consequences when it becomes systemic in the main circulation.
i've seen this this play out many times (ages ago it seems) when making money around securities entering or leaving financial distress as the cost of capital has historically been quite volatile during these transitions. Of course, i've become increasingly confused as the changing slope concept has existed for centuries and has recently become irrelevant with firms entering financial distress no longer submitted to this natural law. In fact, in parallel to the Covid spread in 2020, firms entering financial distress often had access to lower cost of capital options!? i continue to wonder if historical easy money conditions have anything to do with this. It seems it's the same concept that Mr. Minsky used to elaborate his unstable stability concept.
Anyways, home oximetry seems like a good and reliable idea if you're into self-monitoring. It is probably a better tool than home blood pressure monitoring. Home blood pressure devices are known to be quite imprecise. If you take it under standardized circumstances (ie once a day before breakfast), it may offer a reliable documentation of the underlying efficacy of non-pharma or pharma changes that are introduced. With blood pressure, there's the white coat syndrome aspect which basically means that your blood pressure may rise simply because you have reasons to believe that it should be, or needs to be, measured.