---
client: lesswrong
project_id: curated
narrator: pw
qa: km
narrator_time: 2h45m
qa_time: 1h00m
---

Thanks to Drake Thomas for feedback. I. Here’s a fun scatter plot. It has two thousand points, which I generated as follows: first, I drew two thousand x-values from a normal distribution with mean 0 and standard deviation 1. Then, I chose the y-value of each point by taking the x-value and then adding noise to it. The noise is also normally distributed, with mean 0 and standard deviation 1. Notice that there’s more spread along the y-axis than along the x-axis. That’s because each y-coordinate is a sum of two independently drawn numbers from the standard normal distribution. Because variances add, the y-values have variance 2 (standard deviation 1.41), not 1. Statisticians often talk about data forming an “elliptical cloud”.

Original text:

https://www.lesswrong.com/posts/nnDTgmzRrzDMiPF9B/how-much-do-you-believe-your-results

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