Latest Posts (20 found)
Entropic Thoughts 5 days ago

90 % of the t distribution

William Sealy Gosset was great. He improved beer at Guinness by using the statistics that existed at the time. Not happy with that, he invented new statistics to brew even better beer. The things he invented are used all over the place now, but Guinness wanted to keep him a secret weapon, so they made him publish his results under the fake name Student . One thing Gosset realised is that it is wrong to compute 90 % confidence intervals for the mean by taking the standard deviation of the sample, and assume a normal distribution , like-a-so: \[\hat{\mu} \pm 1.645 \hat{\sigma}\] (Continue reading the full article on the web.)

statistics Statistics Science data-analysis Data Analysis
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Entropic Thoughts 1 weeks ago

Pythagorean Addition

TL;DR: Instead of labouriously computing \(c = \sqrt{a^2 + b^2}\), we can mentally calculate using the alpha-max plus beta-min algorithm, by estimating \[\hat{c} = \mathrm{max}\left(a, 0.9a + 0.5b \right)\] and this will be very close to the actual \(c\). This is useful for adding up sources of variance, or figuring out radiuses, or other such things. (Continue reading the full article on the web.)

programming Programming statistics Statistics
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Entropic Thoughts 2 weeks ago

Regatta Starting Stations – Chi-squared Continued

In the Henley Royal Regatta two teams at a time propel their boats up a river and compete to be first to go a distance. Teams get assigned to their starting stations – Berkshire or Buckinghamshire – at random. From there, it is a straight shot up the river, with the lane from each starting station being seemingly identical. I didn’t know any of this, but a reader reached out some time ago because they had noticed something odd about this, and they wanted to borrow me as a sounding board. Here’s the odd thing: the team that starts from the Berkshire station has won 53.5 % of the 7555 races in the historic data this reader looked at. This is highly unexpected. If teams are assigned at random, and the starting stations are practically equal, then the starting station of the winning team should be a coin flip. If we flip 7555 coins, we would never have as many as 53.5 % come up heads. (Continue reading the full article on the web.)

statistics Statistics data-analysis Data Analysis
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