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> DK doesn't mean no correlation, it means inverse correlation. It's the correct analysis at the bottom that shows what no correlation actually looks like (at l
by andersource 4y ago
> DK doesn't mean no correlation, it means inverse correlation. It's the correct analysis at the bottom that shows what no correlation actually looks like (at least no correlation in tend, there is heteroskedasticity).
Not sure I follow, inverse correlation between what? The analysis at the bottom (assuming you mean fig. 11) is too dense to show if there's a correlation or not (between skill and self-assessment bias), and looking at the relevant figure from the paper itself gives me the impression that there is a correlation.
>> a world in which people are very bad at estimating their own skill, therefore, statistically, people with lower skills tend to overestimate their skills, and experts tend to underestimate it.
> Be careful here, the conclusion you drew doesn't actually follow.
Can you elaborate? If X and Y are two independent random variables, X representing skill and Y representing self-assessment of skill, X and Y will be negatively correlated - this is exactly what the first part of the article is about, although from my perspective it's the author who's drawing the wrong conclusion.
>> y - x ~ x, this is called the residual plot
> You're giving x and y meaning that they don't have. In the article these are uncorrelated random variables - the plot of y-x ~ x will always look that way. That's however not the case if you're plotting y_hat - y ~ y_hat for a y_hat taken out of a model. That won't be a random variable in your setup.
Not following again. Other than calling x y_hat, and having y_hat be your own estimate vs. x be the subjects' estimate, what is the distinction? What do you mean by "the plot of y-x ~ x will always look that way" - what way? The shape of the plot will necessarily depend on the relationship between x and y.
- pedrosorio 4y ago> If X and Y are two independent random variables, X representing skill and Y representing self-assessment of skill, X and Y will be negatively correlated “If two variables are independent, then their correlation will be 0” https://web.stanford.edu/class/archive/cs/cs109/cs109.1178/lectureHandouts/150-covariance.pdf https://web.stanford.edu/class/archive/cs/cs109/cs109.1178/l... “ If the variables are independent, Pearson's correlation coefficient is 0” https://en.wikipedia.org/wiki/Correlation#Correlation_and_independence https://en.wikipedia.org/wiki/Correlation#Correlation_and_in... Proof: https://www.themathcitadel.com/uncorrelated-and-independent-related-but-not-equivalent/ https://www.themathcitadel.com/uncorrelated-and-independent-...
- andersource 4y agoRight, sorry, my bad - X and Y - X will be negatively correlated
- leto_ii 4y ago> If X and Y are two independent random variables, X representing skill and Y representing self-assessment of skill, X and Y will be negatively correlated 1. As mentioned in another comment, X and Y can't be independent and correlated at the same time 2. The point of the article is to show that you can replicate the results of the DK paper starting from purely random data. In the article X and Y don't mean anything, they're just random variables that the author draws samples from. The fact that you can get DK results from this very strongly suggests that DK is just an artifact of statistics, not an actual result. > What do you mean by "the plot of y-x ~ x will always look that way" - what way? See Figure 8 in the article, also panel B in Figure 10. > The shape of the plot will necessarily depend on the relationship between x and y. What I meant to say is that since X and Y are simulated data, not actual observations, the shape in Figure 8 will not actually depend on any possible relationship between ability and self-assessment. It's just a statistical artifact. Figure 9 is based on this simulated data as well, and since it closely replicates Figure 2 there's good reason to believe that Figure 2 itself is actually just a statistical artifact and that the DK data don't actually show the purported correlation. This point is further strengthened by referring to a few papers and by showing some corrected results in Figure 11.
- andersource 4y ago> 1. As mentioned in another comment, X and Y can't be independent and correlated at the same time And as I replied to that comment, "sorry, my bad - Y - X and X will be negatively correlated." > 2. The point of the article is to show that you can replicate the results of the DK paper starting from purely random data You (and many others) are using "purely random data" as if it's always the null hypothesis and using it to cast doubt on the results. But assuming as the null model 0 correlation between skill and self-assessment of that skill makes no sense to me, and is in fact more extreme than the claim DK is making. So in other words, sure, if you assume something more extreme than the claim and generate data based on this assumption, you'll get the same effect and more extreme.
- ramblenode 4y agoThe hypothesis and distribution of data are irrelevant. The artifact comes from x being on both sides of the regression equation.