Statistics Iceberg Levels

Mean Probabilities as percent Standard deviation Median LEVEL 1 Expected value Probability distribution Variance Binomial distribution Poisson distribution LEVEL 2 Random variable Normal distribution ANOVA Wilcoxon test T-test p-value simple linear regression GLM CLT probit Monte-carlo simulation Shapiro-Wilk test Kolmogorov-smirnov test Markov chain LEVEL 3 Bayesian inference power analysis stochastic process beta distribution MCMC method log-normal distribution Z-test putting data instead of using mathematical analysis logarithming everything mathematical analysis Distributions with undefined E(X) Checks for assumption violations Constructs his own statistical tests characteristic function likelihood LEVEL 4 philosophical analysis of statistics Using frequentist and bayesian inference at once likelihood ratio Chebyshev inequality measure theoretic interpretation of probability Lebesgue integral sigma-algebra writing R packages using C++ instead of R LP spaces remedian making memes about statistics Not graduating reading papers in spare time robust statistics making fun of mean, because median is just so much better CASUAL SCUM "GAMER" THAT WEIRD GUY JADED OUTCAST HARDCORE

An iceberg-style chart descends from basic statistical concepts into increasingly obscure mathematics and obsessive statistical practices, alongside progressively more extreme cartoon characters. The joke is that casual learners stop at means and probability, while hardcore statistics enthusiasts study measure theory, write packages, avoid graduating, and mock the mean in favor of the median.

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