Chi-squared from fundamentals and the Trial of the Pyx
We figure out how the mysterious Chi-squared test comes about, and learn how we could have illicitly profited from a very important English government position in the 1300s, had we had our modern knowledge then.
I hope your week is going well!
New articles
Chi-Squared From Fundamentals
There are many mysterious things in the large toolbox of frequentist statistics. I keep discovering that if one understands how the things in there work, they stop being so mysterious. This week, we'll look at how the Chi-squared test comes about.
Full article (6–20 minute read): Chi-Squared From Fundamentals
Flashcard of the week
One of the earliest examples of statistical process control was the Trial of the Pyx, instituted sometime in the 1300s. During the year, random samples of coins from the London Mint would be set aside. Every now and then, these coins would be tested for many things, among others how close to their intended weight they were.
(Obviously, if the coins were underweight the Master of the Mint was pocketing the difference in shiny metals. If the coins were overweight that was just as bad, because then clever business people could shave off metal from the coins and hand it back to the Mint to issue new coins from!)
The weight threshold for individual coins at the Trial of the Pyx was set at about two standard deviations, but individual coins were rarely weighed. Instead, they weighed batches of 100 coins.
Where was the threshold set at for a batch of a hundred coins?
They did realise the variation of a sum of independent errors grows, but they got the order of magnitude wrong.
Hundred times a single coin, i.e. 20 standard deviations away.
At the time, they did not know that variation of a sum of independent errors grow with the square root of the number of samples. In practice, this means a statistically cunning Master of the Mint could have profited quite handsomely, with practically no risk of punishment. Of course, at the time, there was not a single human who was that statistically proficient.
Premium subscription
The first premium newsletter went out three weeks ago. It had:
- three links to external articles that I thought were really good;
- a two-page review of the first half of Working Backwards: Insights, Stories, and Secrets from Inside Amazon.
- a brief mention of Craft Stories by Chuck Palahniuk and why it matters.
- a preview of what it might look like if one takes The Economist's The World Ahead and tries to squeeze out of it verifiable claims that one can forecast on.
If any of this sounds interesting, you should upgrade to a premium subscription! For a limited time, premium subscriptions are $1/month. As always, you can cancel at any time. To upgrade, click the subscription link at the top of this newsletter and fill in your email again.
Your opinions
As always, I cannot improve without feedback. Reply to this email to share your thoughts on any of the topics above, or anything else!