It takes ~20 observations to verify your first significant digit of the mean with confidence.

Do you know how many observations it takes to verify your first sig-fig of the variance? More like 1000. And that’s just to get one digit of accuracy! Higher moments (skew, kurtosis) are even worse.

That’s why I often laugh out loud when I read in the newspaper claims that rely on a certain value of the variance. Even in serious, published papers!—I often see tables with estimates of standard deviation that go out to three decimal places, just because the software spat the numbers out that way. It gives a false sense of accuracy. It’s ridiculous.

Karen Kafadar

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