I got some wonky nonsense while trying to show that S was more appropriate than sigma. Maybe making the disparity in numbers bigger would help? I do not know, I'll keep fiddling.

Write a function for standard deviation without built-in functions that take arrays (can use mean and such). There should be no loops this part. Use it to calculate standard deviation among a population (N=1e3), then take a subset (N=10) of the population **without altering the original population**. Do it a bunch of times with random samples, appending each of the values to an array so that you can compare them. Do this with s (N-1, you know) as well. With a loop, do it 100 times, look at the averages and standard deviations of the standard deviations to create error bars for a plot with the true sigma, see where it lies. This should theoretically show that s is a better value than sigma. Write the journal as though it is meant to convince the reader that s is a better value than sigma.

Think about a numerical experiment to show how accuracy of estimates increases by sqrt(n)

IPython notebooks showing up in Nature magazine

http://cs.marlboro.edu/ courses/ fall2014/jims_tutorials/ gschacht/ nov_6
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