[kristjansson]

A better summary would be that those two quantities explain about half of the variation, not that they predict accurately half the time.

If you took a random sample of cases, half of them wouldn’t exhibit a direct relationship b/w SAT and first year GPA and half nothing (unless the data is _super_ weird). Instead, SAT would be instructive-ish in predicting first year GPA for all those cases.

[ordinaryperson]

Explaining half the variation, and the other half?

The point was to draw a connection for the general audience, not present the most scientifically accurate description of a relationship between two variables -- that's what the links to the research are for.

[kristjansson]

It's good to communicate for a general audience, but your presentation misleads rather than simplifies.

> meaning the combined measurement accurately predicts how a potential college applicant will perform in their first year of college 56% of the time.

"accurately predicts...56% of the time" implies that half of predictions are 'accurate', which most readers would interpret as 'correct' i.e. knowing SAT + HSGPA allows you to state FYGPA _exactly_ for about half of cases. That's not what the research you cited says. Rather, the square of the multiple correlation R (which is exactly R^2, the coefficient of determination) indicates how much of the variance in the output variable is explained by the input variables. That quantity _must_ be communicated in terms of the strength of the relationship, not accuracy for a given or share of cases as it doesn't tell us anything about a given case. One could say it tells us about 30% (0.56^2, correction from my statement above) of the information we'd need to know to perfectly predict the outcome, or that the relationship is better than random, but doesn't predict perfectly, or ...

Additionally, table 5 of the link you cited indicates the adjust correlation coefficient b/w FYGPA and the combination of HSGPA and SAT is 0.62. None of the numbers in that table are 0.56, so I'm not sure where you pulled that exact number from. I've used 0.56/56% above to be clear which quantity I'm referring to.

[ordinaryperson]

Uh...this is exactly what I mean. Your description is 100% scientifically accurate but probably way beyond the average reader.

Again, if you can simplify this in a way more accurate than I have, great, be my guest-- I look forward to reading it.

R^2, coefficient of determination, output variable variance, etc etc -- most readers aren't going to go that deep in the math. For those who do, like you, the links to the actual research is provided.

But so far all I see are data scientists complaining about how my description is not 100% statistically accurate without providing any alternative explanation that doesn't devolve into variance of output variables.

Again, be my guest to show me I'm wrong, but what you wrote above is not something that would be easy to understand for the general audience, IMHO.

[kristjansson]

The concerning (mis)interpretation of your statement is what I said on the third line above:

> "accurately predicts...56% of the time" implies that half of predictions are 'accurate', which most readers would interpret as 'correct' i.e. knowing SAT + HSGPA allows you to state FYGPA _exactly_ for about half of cases.

This interpretation is easy to arrive at, and clearly does not correspond to a reasonable understanding of the source, even for a general audience.

I provide two suggestions above:

> One could say it tells us about 30% of the information we'd need to know to perfectly predict the outcome, or that the relationship is better than random, but doesn't predict perfectly

[ordinaryperson]

OK, but that only makes it more confusing. You say it tells us about 30% of the information we'd need to know...which makes it sound (to the lay person) like there's no connection because 70% of the information is elsewhere!

I appreciate your commitment to academic rigor but sometimes oversimplifying things, even at the cost of mathematical accuracy, is enough for a general audience who aren't going to compute variance of output variables.

[kristjansson]

This isn't about academic or mathematical rigor - this is about responsible communication of statistics.

You're right that a general audience isn't going to look at the source, nor think about variance of output variables. Therefore, it's the responsibility of us as communicators of statistics to relate the conclusions that can be drawn from the data in a way that first and foremost is not wrong or misleading, and secondly captures the concept as accurately as possible for the audience.

The first principle is the overriding obligation. Your simplification can capture as little of the information and conclusions supported by the data as you want, but it cannot imply or state conclusions that are not supported.

You're getting this response to your statement, from me and others, because your interpretation of the source can easily be read as drastically overstating the character (and strength) of the relationship supported by the data - even if that's not what you intended.

[thanatropism]

No, man.

1) Your description is 0% correct; and 2) It's not a complaint. Maybe you don't know what a correlation coefficient is. That's okay -- I don't know what polyfinite rings are.

[ordinaryperson]

So funny how all the data scientists complain about incorrectness and yet fail to produce a plain English description...

[thanatropism]

The problem is not plain English, the problem is that you want to make claims that are more specific than your numbers allow you to.

"Correlation is a number in [-1,1] where -1 means predictably inversely related and 1 means predictably directly related". What is correlation 0.5? There isn't even an unique definition of "correlation", man.

The best thing you could do is to produce a table of correlation coefficients for comparison. That would communicate some qualitative nuance as to what a 0.5 correlation really means.

You can also try to do something like a bootstrap or kernel density or use a prior distribution to claim that the probability that increment dx leads to an increment of dy or more is... That's more technically involved, but satisfies your desire of saying something specific that correlation coefficients do not allow you to say.