CLT is abused among data scientists quite often, and usually due to the points in the article.
- Convergence takes infinite time when the sampling variable has infinite variance (imagine a random number generator).
- While the distribution of an aggregate statistic tends to a Gaussian, most underlying distributions are not and most stats is done using the underlying raw data.
Junior data scientists assume everything is Gaussian (sometimes attributing it to CLT) when doing linear regression when most distributions being modeled are not. Then, analysis done using variance on the coefficients is meaningless because the assumptions are incorrect.
- Convergence takes infinite time when the sampling variable has infinite variance (imagine a random number generator).
- While the distribution of an aggregate statistic tends to a Gaussian, most underlying distributions are not and most stats is done using the underlying raw data.
Junior data scientists assume everything is Gaussian (sometimes attributing it to CLT) when doing linear regression when most distributions being modeled are not. Then, analysis done using variance on the coefficients is meaningless because the assumptions are incorrect.