It's good to question things. If you don't do so, you'll never really "own" the answers that you're looking for.
The accuracy for shunt and series measurements are different because the partial derivatives of the impedances with respect to the reflection coefficients are different. I used standard metrological methods for evaluating uncertainties. The reason why there are 3 sigma standard deviations is that metrology is a statistical science. There are no fixed, "defined" accuracies, only a confidence interval within which one can expect to find a particular measurement. This was explicit in the article. You can't arrive at the correct answers by banging away at it numerically in Excel. I used 3 sigma statistics in particular because almost all manufacturers of test equipment use this confidence interval when setting data sheet specifications. With a 3 sigma confidence interval, we can say that 99.7% of the time, your measurement should fall within a certain error tolerance. It goes without saying that 0.3% of the time, your measurement may be outside of the data sheet tolerance.
There
is an error in the chart. As I stated in the article, the expected measurement error does not go to 0 for the shunt measurement. I was simply uninterested in the value at 50 ohms and only concerned about the crossover points with the two other curves.
Adding a series resistor for the Shunt-Thru measurement to extend measurement range is potentially useful, but there are limitations. Calibration must be performed with the resistors in place in order to compensate for them. This creates a problem for for the reflection measurements on each side. If the attenuation of the series resistors looking into the 50 ohm cal kit is greater than about 15 dB, the raw S11 and S22 measurements will suffer and the corrected S21 will have greater inaccuracy. If the attenuation is closer to 20 dB, then the S21 measurement cannot be trusted at all.
For reference, the most relevant doc for VNA uncertainties is "Guidelines on the Evaluation of Vector Network Analyzers (VNA), EURAMET calibration guide No. 12, Version 3.0
https://www.euramet.org/Media/news/I-CAL-GUI-012_Calibration_Guide_No._12.web.pdfBest,
Brian