Measuring a Small Number of Samples, and the 3σ Fallacy: Shedding Light on Confidence and Error Intervals. Schmid, H. & Huber, A. *IEEE Solid-State Circuits Magazine*, 6(2):52–58, June, 2014. Citation Key Alias: schmid2014measuringPaper doi abstract bibtex Many solid-state circuits papers today report the mean and the standard deviation 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 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.

@article{schmid_measuring_2014,
title = {Measuring a {Small} {Number} of {Samples}, and the 3σ {Fallacy}: {Shedding} {Light} on {Confidence} and {Error} {Intervals}},
volume = {6},
issn = {1943-0582},
shorttitle = {Measuring a {Small} {Number} of {Samples}, and the 3v {Fallacy}},
url = {https://ieeexplore.ieee.org/document/6841797},
doi = {10.1109/MSSC.2014.2313714},
abstract = {Many solid-state circuits papers today report the mean and the standard deviation 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 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.},
number = {2},
journal = {IEEE Solid-State Circuits Magazine},
author = {Schmid, Hanspeter and Huber, Alex},
month = jun,
year = {2014},
note = {Citation Key Alias: schmid2014measuring},
keywords = {3σ fallacy, Error probability, Gaussian distribution, Measurement uncertainty, Semiconductor device measurement, Stress measurement, Temperature measurement, Tutorials, confidence intervals, error intervals, integrated circuit measurement, integrated circuit testing, probability, solid-state circuits, standard deviation, test chips, volume production},
pages = {52--58}
}

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