My name is Charlie Hagedorn. I’m an experimental physicist by day (and night, I guess) and curious outdoorsperson much of the rest of the time.
Need precision torque/force/angle-sensing instrumentation? I might be your guy. I’ll be graduating soon, and I’m interested in building custom hardware in addition to continuing precision tests of nature in the academic world. In our lab, we can measure angle-deflections of a nanoradian in a second and torques of one hundred-trillionth of a Newton-meter in a second.
Want to support continued production of measuredmass posts? Find any of my reviews/measurements/musings helpful? You can send a Bitcoin tip to 1Fsz3rMN5opx93th8JavG2reDy4bYnvnNe . These posts take time and effort; if they become self-sustaining, I’ll do more!
Why this blog?:
In the lab, we measure physical quantities. Our measurements come with an associated uncertainty, like 1.0 ± 0.1 kg. If the uncertainty isn’t stated, it’s related to the number of significant figures; the uncertainty is in the last digit.
I’d like to see people who sell things do the same.
It’s easy to do. Here’s the recipe:
- Randomly select fourteen or more samples of a product, taken from different lots, if possible.
- Measure (for example, weigh) them individually.
- Compute the average weight by adding up the weights and dividing by however many samples you have.
- Individually calculate the differences between each sample’s weight and the average.
- Compute the variance by squaring each of the differences, summing up those squares, and dividing that sum by the number of samples.
- It’s customary to use the standard deviation when stating an uncertainty. To compute it, take the square root of the variance.
- Check your answer. The standard deviation should be smaller than the biggest difference between samples and larger than the smallest difference between samples.
- You’re done! Label the packaging like this: “average ± standardDeviation” !
- Bonus: Point it out to customers! To a discerning customer, done correctly, it highlights consistent products.
I should note that this errorbar does not encompass all of the weights of your set of products. If your products are ‘normally distributed‘, then the ± interval will encompass 68% of your products. If you double the standard deviation, then the ± will incorporate 95% of your products. Triple it, and it will include 99%.
I’m an experimental physicist by day (and night, I guess)…
I love it!
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quibbling query: why not divide by n-1–aren’t you taking sample std dev?
You’re exactly right. I believe my intent when I wrote it was to keep the instructions as simple and clear as I could. I want the barrier to entry to be as low as possible for manufacturers to quote uncertainties.
Understanding the N-1 requires care, and at N=14, amounts to a 4% shift. When I compute the standard deviation for measurements reported on this site, I use N-1. In addition, for low N measurements (almost every measurement on this site), I incorporate a correction for the uncertainty in the standard deviation  as well. Getting an uncertainty even remotely right with N=2 is a shady business; it is my inclination to be as conservative as I can. In the one instance where I really called out a company for under-quoting a weight, I doubled my one-sigma errorbars before computing a significance.
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