I recommend finding a different statistics teacher, preferably one who isn’t a comic and one who knows what the difference between a standard deviation, a standard error, and a 95% interval is. Those should not be too hard to find, it’s relatively basic stuff, but many people actually kinda struggle with the concepts (made harder by various factors, don’t get me started on the misuse of bar charts).

Oops, should have multiplied those intervals with 1.96, ao here again:

9 - 49%

16 - 38%

25 - 30%

100 -16%

400 - 8%

That’s how a standard error with normal-ish data works. The more data points for the estimation of a conditional mean you have, the fewer of the data point will be within it. For a normal distribution, the SE=SD/√N . Heck, you can even just calculate which proportion of the distribution you can expect to be within the 95% CI as a function of sample size. (Its a bit more complicated because of how probabilities factor into this, but for a large enough N it’s fine)

For N=9, you’d expect 26% of data points within the 95% CI of the mean For N=16, 19% For 25, 16% For 100, 8% For 400, 4% Etc

Out of curiosity: What issue did you take with the error margin not including most data points?

To be honest, I doubt Munroe wants to say “if the effect is smaller than you, personally, can spot in the scatterplot, disbelieve any and all conclusions drawn from the dataset”. He seems to be a bit more evenhanded than that, even though I wouldn’t be surprised if a sizable portion of his fans weren’t.

It’s kinda weird, scatterplot inspection is an extremely useful tool in principled data analysis, but spotting stuff is neither sufficient nor necessary for something to be meaningful.

But also… an R^2 of .1 corresponds to a Cohen’s d of 0.67. if this were a comparison of groups, roughly three quarters of the control group would be below the average person in the experimental group. I suspect people (including me) are just bad at intuitions about this kinda thing and like to try to feel superior or something and let loose some half-baked ideas about statistics. Which is a shame, because some of those ideas can become pretty, once fully baked.

Sure, you could do some wild overfitting. But why? What substantive theoretical model would such a data model correspond to?

A more straightforward conclusion to draw would be that age is far from the only predictor of flexibility etc., but on the list nevertheless, and if you wanna rule out alternative explanations (or support them), you might have to go and do more observations that allow such arguments to be constructed.

To expand a little: you get a 95% ci by taking the expected value ±SE*1.96 . The SE you get for a normal distribution by taking the sample SD and dividing that by the sqrt of the sample size. So if you take a standard normal distribution, the SE for a sample size of 9 would be 1/3 and for a sample size of 100 it would be 1/10, etc. This is much tighter than the population distribution, but that’s because youre estimating just the population mean, not anything else.

Capturing structured variance in the data then should increase the precision of your estimate of the expected value, because you’re removing variance from the error term and add it into the other parts of your model (cf. the term analysis of variance).

It’s a 95% CI, presumably for the expected value of the conditional (on age) population mean. It looks correct, given the sample size and variance, what issue do you see with it?

Lol

Well, your comment is a better variant of mine, i should have checked. :o) Thanks!

Keep learning, and it’ll stay easier than if you didn’t. See if you can find changes for the structure of what you’re learning so you don’t get too ossified about that, either. Like, have a decade where you focus more on sciences, one more for arts, one more for languages, one more for understanding people who are very different from you… Maybe a decade is too big a chunk, but you get the idea.

Maybe, yeah, but I kinda get annoyed at this kinda dismissiveness - it’s a type of vague anti-science or something like that. Like… Sure, overfitting is a potential issue, but the answer to that isn’t to never fit any curve when data is noisy, it is (among other things) to build solid theories and good tests thereof. A lot of interesting stuff, especially behavioral things, is noisy and you can’t expect to always have relationships that are simple enough to see.

You’re probably right. But also, I was annoyed, not trying to convince. Maybe not the best place to post from. :)

I dunno, the point cloud looks to me like some kinda symmetric upward curve. I’d’ve guessed maybe more like R^2=.2 or something in that range, though.

But also: This is noisy, it’s cool to see anything.

That’s stupid, though. If you can explain 11% of the variance of some noisy phenomenon like cognitive and behavioral flexibility, that’s noteworthy. They tested both linear and quadratic terms, and the quadratic one worked better in terms of prediction, and is also an expression of a meaningful theoretical model, rather than just throwing higher polynomials at it for the fun of it. Quadratic here also would coincide with some homogenizing mechanism at the two ends of the age distribution.

https://doi.org/10.1111/bjc.12505 the paper

Also, the R^2 is even in the picture: .11

How do you think a case of “this explains some of the differences in the population, but not a lot” should look?

And that looks potentially fine for an error bar. For a mean estimate, SE=SD/√N , so depending on what error band they used this looks quite plausible.

Pretty sure that that is forbidden by the bible. Necromancy, divination, that sort of general thing…

https://www.lincolndiocese.org/news/diocesan-news/15543-ask-the-register-what-is-necromancy and other bible pages agree.

I come bearing bad news from the Ruhr valley…

Die Idee eigentlich aller kontemporaeren oekonomischen Systeme ist, dass wirtschaftliche Taetigkeit insgesamt kein Nullsummenspiel ist. Du faengst mit Zustand A an, wendest Transformation X an, und endest mit Zustand B, wobei Zustand B Mehrwert hat und Transformation X ueblicherweise Arbeit involviert.

Mehr Arbeit erlaubt mehr Transformation.

Probleme sind eher:

-wie wird der Mehrwert verteilt? (Profit fuer wen?) -welche Eigenschaften von A haben Grenzen? (Wie viel CO2 gehr klar?) -wie wird ausgewaehlt welche Transformationen gemacht werden? (Baut die Stadt Strassen oder macht das Elon Musks Firma?)

I.A. sinds in Deutschland nicht finite Rohmaterialien die gesamtgesellschaftlich das Limit stellen. Es fehlen z.B. eher Leute die Pflege durchfuehren, als es das Verbrauchsmaterial an der Quelle tut.

Malthus lag schon immer falsch.

Forscher hier, die Antwort lautet:

Nein