Track
Statistics you actually need
Distributions, inference, and the mistakes that sink analyses.
Steps in order
- 01Bayes' theoremA rule for turning the probability of the evidence given a hypothesis into the probability of the hypothesis given the evidence. The two are not the same, and the gap between them is the prior.Free
- 02CorrelationOne number for how tightly two variables sit on a straight line. It says nothing about the slope of that line, and near zero it does not mean the two are unrelated.Free
- 03OutliersValues far from the rest, which may be mistakes or may be the finding. Detecting them with a mean and a standard deviation fails in a specific way — the more of them there are, the fewer you find.
- 04Time series decompositionSplitting a series into trend, a repeating seasonal pattern, and what is left. Three readable things in place of one unreadable one, and the basis of most forecasting methods.
- 05A/B testingRandomly assigning subjects to two variants and comparing an outcome, so that the difference you measure can be attributed to the change rather than to who happened to see it.
- 06Hypothesis testingAssume there is no effect, work out how often chance alone would produce a result as striking as yours, and call it real if that is rare enough. The method is a proof by contradiction.
- 07Confidence intervalA range built so that, across repeated experiments, a stated fraction of such ranges contain the true value. The fraction is a property of the method, not of the interval in front of you.
- 08BootstrapResample your own data with replacement, recompute the statistic, and read the spread. It gives you an interval for statistics that have no formula — and quietly fails for some that do.
- 09Central limit theoremAdd up enough independent values from almost any distribution and the sum is approximately normal. Almost is doing real work — the theorem has conditions, and heavy-tailed data breaks them.
- 10ConfoundingA third variable that causes both the thing you changed and the thing you measured. Adjusting for the right one rescues an estimate; adjusting for the wrong one invents an effect that is not there.
- 11Maximum likelihoodPick the parameters that make the observed data as probable as possible. Nearly every loss function in machine learning is this rule with a minus sign and a logarithm in front of it.
- 12Multiple comparisonsRun twenty tests at the 5% level and you will usually find something. The corrections differ in what they promise, and the honest choice is which kind of mistake you would rather make.
- 13StationarityThe assumption that a series' mean, variance and correlation structure do not change over time. Nearly every time-series method needs it, and ordinary regression fails loudly without it.
- 14AutocorrelationThe correlation of a series with a shifted copy of itself. It is how you find a cycle you were not told about, and how you discover that your sample size is smaller than you thought.
- 15Generalized linear modelsOne framework that covers linear, logistic and Poisson regression at once — a linear predictor, a link function connecting it to the response, and a distribution for the noise.