# topic/math/statistics

Bayesian vs Frequentist Inference

Bayesian and frequentist inference differ in how they interpret probability and unknown parameters.

Bootstrap and Resampling

The bootstrap estimates uncertainty by resampling from the observed data.

Central Limit Theorem

The Central Limit Theorem says that sums and averages of many independent random variables become approximately normal under broad conditions.

Confidence Intervals

A confidence interval is a procedure that produces a range of plausible parameter values from data.

Correlation and Covariance

Covariance measures how two variables vary together.

Estimators

An estimator is a rule for using data to estimate an unknown population parameter.

Experimental Design

Experimental design is about collecting data so comparisons support valid causal or statistical conclusions.

Hypothesis Testing

A hypothesis test asks whether observed data is surprising under a null hypothesis.

Law of Large Numbers

The Law of Large Numbers says that the sample average converges to the expected value as sample size grows.

Population vs Sample

A population is the full data-generating group you care about. A sample is the observed subset used to infer properties of that population.

Sampling Distributions

A sampling distribution is the distribution of a statistic across repeated samples from the same population.

Statistical Power

Statistical power is the probability that a test correctly detects a real effect.

Statistical Significance vs Practical Significance

Statistical significance asks whether an observed effect is unlikely under a null hypothesis.

Statistics Fundamentals

Statistics studies inference from finite data. The useful mental model is: probability goes from model to possible data; statistics goes from observed data back to uncertain…