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Unlearning descriptive statistics

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Re: Unlearning descriptive statistics

#21

Post by irishsultan »

somestag wrote: post #15

I think the message of the article is great: move beyond the "standard" descriptions and pay more attention to what you're trying to show and who your audience is. That said, it's a slight pet peeve of mine when people recommend the median over the mean to describe center. The median, on its own, does not describe what is "typical" any more than the mean does; it just has a small advantage in that it will always map…

> The median [..] just has a small advantage in that it will always map a real observation

Not if the number of observations is even and the two "middle" observations differ.

Re: Unlearning descriptive statistics

#22

Post by somestag »

irishsultan wrote: post #21
somestag wrote: post #15

I think the message of the article is great: move beyond the "standard" descriptions and pay more attention to what you're trying to show and who your audience is. That said, it's a slight pet peeve of mine when people recommend the median over the mean to describe center. The median, on its own, does not describe what is "typical" any more than the mean does; it just has a small advantage in that it will always map…

> The median [..] just has a small advantage in that it will always map a real observation Not if the number of observations is even and the two "middle" observations differ.

Yes that's true. I was being somewhat charitable in affording it that benefit, but I did so because the article is the one that brought up the 1.9 legs example so that was kind of an implied benefit. And it's also true that you can use a "median" that picks one of the two, instead of splitting them, without any real downside if you want to preserve the feasibility of the statistic.

Re: Unlearning descriptive statistics

#23

Post by johnmyleswhite »

nkkar wrote: post #20
johnmyleswhite wrote: post #13

Earlier quoted context omitted.

Glad you enjoyed that post so much. It really is a shame that we do such a bad job of teaching students about the inherent subjectivity of descriptive statistics and let students leave their courses with dangerous ideas about the existence of a Holy Grail statistic that will solve all of their problems.

Your followup post ( http://www.johnmyleswhite.com/notebook/2013/03/22/using-norm... ) is excellent. Thank you!

Thanks! I really should have finished and written the post about the SVD as well. One of these days...

Re: Unlearning descriptive statistics

#24

Post by alexilliamson »

somestag wrote: post #15

I think the message of the article is great: move beyond the "standard" descriptions and pay more attention to what you're trying to show and who your audience is. That said, it's a slight pet peeve of mine when people recommend the median over the mean to describe center. The median, on its own, does not describe what is "typical" any more than the mean does; it just has a small advantage in that it will always map…

But I think the author was careful to sprinkle caveats so as to avoid universal recommendations. Rather, it take on a few common abuses.

About the mean vs. median, it might be true that "mean" is appropriate in just as many contexts as "median", but at least in my opinion, people cite a "mean" when a "median" would have been appropriate more frequently than the reverse. There are times when neither are appropriate, but if you're using median, you're more likely to understand the merits of different contexts.

Re: Unlearning descriptive statistics

#26

Post by FabHK »

sp332 wrote: post #17
andy_wrote wrote: post #8

For readers who are OK with some math, I recommend John Myles White's eye-opening post about means, medians, and modes: http://www.johnmyleswhite.com/notebook/2013/03/22/modes-medi... He describes these summary descriptive stats in terms of what penalty function they minimize: mean minimizes L2, median minimizes L1, mode minimizes L0. A single-number statistic is _going_ to leave things out, so if you must boil thing…

I always pull out Anscombe's Quartet https://en.wikipedia.org/wiki/Anscombe's_quartet The four datasets have the same mean, variance, and linear regression line, but are very different from one another.

Great example, and mentioned in the article.

Re: Unlearning descriptive statistics

#27

Post by stdbrouw »

apathy wrote: post #16
shmageggy wrote: post #9

> But why do you want a number at all? Because lots of data analysis questions hinge upon the association between two data sets, and it's nice (crucial) to be able to quantify this value. Especially because > While statisticians are generally quite good at estimating a correlation from a picture and vice versa, most people are not. The author says > Still not happy and absolutely want a number? You would do well to s…

1) it is pretty amazing that normit transformations (map the quantiles of a non-normal distribution onto a Gaussian and use that) don't seem to be on this guy's radar. We use distributions with linearly additive and affine invariant properties (normal plus normal is normal, bernoulli plus bernoulli is bitwise bernoulli) because we find linear algebra very useful. Nonparametric tests and procedures erode your power; n…

> it is pretty amazing that normit transformations (map the quantiles of a non-normal distribution onto a Gaussian and use that) don't seem to be on this guy's radar

I don't mean to offend, but this is the PhD ur-response, "you didn't mention my pet theory!" :-)

You've given me some interesting stuff to chew on but I very specifically wanted to write about descriptive statistics as a way to describe data, not as a way to summarize it for computers so it can be used in inference. Mapping non-normal distributions onto a Gaussian ain't gonna cut it for that purpose, and to the extent that I care about robustness in this context it's not robustness of inference but whether a descriptive continues to provide a reasonable description of the data for human consumption in the face of outliers etc.

Re: Unlearning descriptive statistics

#28

Post by FabHK »

To be fair the article should not be called "Unlearning descriptive statistics", but "Learning just a bit more (and often better) descriptive statistics", but granted, it's not that snappy.

Certainly better than "I took a statistics course, and you won't believe what happened next!!!1!!"

Re: Unlearning descriptive statistics

#29

Post by pyromine »

I don't feel particularly convinced by this article, I feel like it misses the bullet by going beyond a reasonable standard. The article is phrased in such a manner that it acts as if typical descriptive statistics are not useful, but the more important point is more reasonable and understand when to use what statistics.

In fact, many of his examples of what to use are just other descriptive statistics, median is no less a descriptive statistic than the mean is.

I think the problem is not so much that descriptive statistics are bad, so much as they are not particularly useful when they lack context. Unfortunately, statistics is a much more complex field than your average product designer doing an A/B test thinks. The majority of statistics and models the average person utilizes has assumptions and qualifications that they don't fully understand, and frankly that's not a slight to them but rather just the additional depth of the field.

Just as an example, ask the average person to derive the degrees of freedom for their t-test without just utilizing the formula they were taught.

As in most fields this is an issue of nuance, not that beginner techniques are bad, but beginner techniques alone are not nuanced enough to capture useful or rigorous insights.

Re: Unlearning descriptive statistics

#30

Post by ykler »

pyromine wrote: post #29

I don't feel particularly convinced by this article, I feel like it misses the bullet by going beyond a reasonable standard. The article is phrased in such a manner that it acts as if typical descriptive statistics are not useful, but the more important point is more reasonable and understand when to use what statistics. In fact, many of his examples of what to use are just other descriptive statistics, median is no…

"In fact, many of his examples of what to use are just other descriptive statistics, median is no less a descriptive statistic than the mean is." I think the author would fully agree with this. He is saying we should use more easily understandable descriptive statistics.

"I think the problem is not so much that descriptive statistics are bad, so much as they are not particularly useful when they lack context. Unfortunately, statistics is a much more complex field than your average product designer doing an A/B test thinks." Whatever you say publicly is likely to be stripped of its context and to be received by an audience that does not understand the complexities of your field. The answer to this is to be change what you say, not to change the world, which verges on impossible.

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