Measuring a Small Number of Samples and the 3v Fallacy Shedding light on confidence and error intervals. M Hanspeter Schmid and Alex Huber any solid-state circuits papers today report the mean n and the standard deviation v of measurement results obtained from a small number of test chips and then compare them with numbers other authors obtained. Almost none of them discuss confidence intervals, ranges of values for that standard deviation within which the true value lies with a certain probability. Many implicitly assume that the n ! 3v range would contain all but 0.27% of chip samples to be expected in volume production. This is incorrect even if it is certain that the measured quantity is exactly normal distributed. In this tutorial article, we shed some light on confidence and error intervals and show how the naive approach to interpreting n ! 3v can lead to a misjudgment of error probabilities by orders of magnitude. We show that using standard deviations only works for normal distributions, and then we propose a better, distribution-independent way to report measurements in the future. Along the way we show how many ICs you actually need to measure to obtain a range that contains, with a probability as small as 75%, all but 0.27% of the ICs coming from the same batch as the measured ICs. This number is 1,027. Digital Object Identifier 10.1109/MSSC.2014.2313714 Date of publication: 24 June 2014 52 s p r i n g 2 0 14 IEEE SOLID-STATE CIRCUITS MAGAZINE 1943-0582/14©2014IEEE