I’m riddled with anxieties and have no faith whatever. My book is dopey and nobody’s reading it and I have no ideas for another one. Print publishing is dying anyway. And the deader it gets, the less likely it is to publish anything I write, even if I did have an idea. I could take care of these anxieties with some nice pills, but I thought I’d try a calming statistical assessment first. Science, of course, excels at such assessments and what I really admire is when it steels its nerves, narrows its eyes, and assesses its own work. “We’ve found an exoplanet and it’s at the 2-sigma level,” they say, while they silently try to radiate confidence.
Sigma, the Greek sign σ, means “standard deviation” which I understood once and hope to again, but we needn’t worry our heads about it because scientists use it to mean something that’s probably related but sounds different. Sigma, for scientists, is a measure of their certainty about their results, of the distinctiveness of the signals from the noise, of their confidence. And I’m delighted to tell you that confidence has been been quantified. A 1-sigma result is a confidence level of around 0.7; 2-sigma, 0.95; 3-sigma, 0.9 with another 9 after it; 4-sigma, 0.9 with several 9’s after it; 5-sigma, 0.9 with a whole lot of 9’s after it. The sigmas go higher, but 5-sigma is the gold standard and if it’s good enough for physicists, it’s good enough for me.
I found all this out because I was trying to get a physicist to let me write a story about her experiment, and she wouldn’t. She showed me a power point presentation of a talk she gave on the experiment, and the last slide was:
“In my life, I have seen a lot of 2σ signals survive and a lot disappear.
I am not ready to place any bets yet.
What I want is more data.”
Ok then. I’ll wait a bit, then ask her whether more data – i.e., more signal to rise above the noise — has improved her sigmas. Meanwhile, I have a new way to inform my uncertainties. The editor who was going to call me right back? 0.2 σ. The book is going to bob along for a while, then tank? 4 σ. The universe will expand forever and disorder will only increase? 23 σ, and not a help. Aim lower: pesto, pasta, and sausages for dinner? 5 σ, gold standard and with pleasure. Nice to know what is and isn’t certain in this world.
Credits:
Storm: Wikimedia Creative Commons, no attribution
Rays of sun: Eusebius (Guillaume Piolle)
Well, if it cheers you up Ann, I’ve just ordered your dopey book from Amazon. Sigma ratings will follow.
Immensely cheered already, and thank you for it. If you think the book is dopey, you don’t need to tell me.
Well, if it cheers you up Ann, I love your blog. Ask Tim to sing you a song, that is a proven sigma million.
I’d love for Tim to sign me a song. And now I’m so cheery I’m going to have to find some pills to calm down.
Nice post.
Sigmas and higher level statistics have shown up in particle physics more and more as data has gotten more complex. Certainly, partly by necessity, but also to give people a sense they are doing things “right”.
And if an MIT physicist doesn’t know that, then nobody does. Thank you, Peter. It’s interesting, the small amount of soothingness about sigma even for physicists.