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Degrees of Freedom, Actually Explained - The Geometry of Statistics | Ch. 1

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Tags: statisticslinear-algebradegrees-of-freedom

The most confusing concept in statistics must be degrees of freedom. Students everywhere leave their introductory stats courses totally bewildered about what degrees of freedom means, and why it seems to show up all over the place, such as in the t, chi-square, and F distributions, and also dividing by n minus 1 instead of n in the sample variance. The answer turns out to be complex but delightful, related to the dimensions of random vectors. Along the way we'll learn a powerful visual way to understand data analysis: the geometry of statistics. If you follow along closely, not only will degrees of freedom make way more sense to you, but lots of other statistical concepts will click too.

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7 Overall score*

24 Rank

14 Votes

7 Comments

Comments

8.7

The introduction of the video is magnificent and immediately engages the audience. You did a great job explaining who the video is directed to, which not every creator does. I personally think this is a good idea because it saves the audience time and, at the same time, protects you from unjustified criticism. The goal of the video is presented very clearly and, by the end, it is fully accomplished. Congratulations!

6.6

The visualizations of how a vector corresponds to several samples were great, as were the depictions of degrees of freedom. I would highly recommend showing this to a student who’s confused how to count the degrees of freedom.

The beginning of the video made it seem like this video would explain why the sample variance divides by the number of degrees of freedom, or what is meant by the rank of the quadratic form corresponding to the statistic.

The video explains things very well, only where you fulfill the prerequisites. I don’t have a good history with statistics in HS.

7.1

Simple and easy to understand explanation of why the residual vector has fewer degrees of freedom that I hadn’t encountered before

4.2

Visuals are nearly perfect but this content is a typical textbook one you can easily find

8.1

Someone who has taken an introductory statistics course could follow this well, I think. But the best target audience would be someone who’s done slightly more statistics — just enough to get to the t and F distributions, and be frustrated with strange and vague explanations of degrees of freedom.

I have taught a course on linear regression, for students who had previously taken roughly a semester’s worth of statistics courses. I think these students would have benefitted from this video greatly.

The step from considering a set of observations of a random variable as a set of points on a number line, to viewing it as the coordinates of a vector, can be fairly confusing for students initially. The video did a good job of explaining and showing this.

The visualisations were generally well put together and clear. However, some of the 3d visualisations might be a bit confusing for some people (depending on how easily one can visualise things in 3d).

Not self-contained, it requires to watch a full series which is currently incomplete.