i googled it, but still understood nothing 😛
What’s this thing??
In: Mathematics
Imagine you measure the height of every adult male (or adult female, but maybe not both to ensure that you don’t get two peaks) in a single country (let’s go with my country of the UK). If you plot the number of people (y-axis) measuring a given height (x-axis), you’ll probably get some sort of bell-curve. The mean height would be the height of the bell-curve at its centre. The width of the bell, however, would be represented by the standard deviation.
The standard deviation is an important quantity for the following reason. Let’s say you find from your graph that the mean adult male height is around 5’9” (1.75m). Now let’s say you come across a guy who’s 6’0” (1.83m). Would you consider him particularly tall? Well, if the standard deviation of adult male height in the UK was six inches, then 6’0” would be half a standard deviation above the mean, which means that around 30% of the British adult male population would be his height or taller, ie nothing particularly special. What about if the standard deviation was three inches? Then he’d be one standard deviation from the mean (‘one sigma’), so around 16% of the adult male population would be taller than him, so he’d be on the tall side but still nothing to cry home about. What if it was only one inch (‘three sigma’)? Then only around 0.15% of the population would be taller than him. We’ve now got a BFG on our hands.
So let’s say you’re a scientist looking for methane (a possible sign of life) in an exoplanet atmosphere. Suddenly you come across a spike that looks like an absorption feature of methane. But your data is noisy, so how can you be sure that it’s genuinely methane and not just noise? Well what you can do is you can measure the average amount of noise in your spectra, which gives you your one standard deviation noise distribution. Now, if your methane spike is 5 times larger than your average noise level, then you have a ‘5 sigma detection’, which means that there’s about a 1 in a million chance that your methane detection is due to noise in the data, which reassures your reviewer that what you’ve discovered on your planet is indeed methane beyond any reasonable doubt.
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