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Statistical Foundations terms
Probability, inference, sampling and the arguments statisticians have.
Anomaly detection Identifying data points or patterns that deviate significantly from expected or normal behavior. Autocorrelation The correlation of a time series with a lagged, delayed copy of itself, used to detect repeating patterns and dependence over time. Bayesian inference A statistical approach that updates the probability of a belief as new evidence arrives, starting from a prior assumption. Bootstrapping A technique for estimating the uncertainty of a statistic by repeatedly resampling the observed data with replacement. Central limit theorem The principle that the average of many independent samples tends toward a normal distribution, regardless of the data's shape. Chi-square test A statistical test that checks whether observed frequencies in categorical data differ from what chance would produce. Confidence interval A range calculated from sample data that, under repeated sampling, would contain the true value a stated percentage of the time. Correlation A statistic between -1 and 1 that measures the strength and direction of a linear relationship between two variables. Cross-validation A method for estimating how well a model generalizes by repeatedly training and testing it on different splits of the same data. CUPED (controlled-experiment using pre-experiment data) A variance-reduction technique that uses each user's pre-experiment behavior to sharpen an experiment's estimate without adding more traffic. Design of experiments (DOE) A structured, statistical approach to planning experiments so the effect of each factor can be estimated efficiently. Differential privacy A mathematical technique for publishing aggregate statistics while guaranteeing no individual record can be inferred from the results. Effect size A standardized measure of the magnitude of a difference or relationship, independent of sample size. Expected value (EV) The probability-weighted average outcome of a bet or decision, used to judge whether it is favorable over the long run. Exploratory data analysis An open-ended first pass through a dataset to understand its structure and spot patterns before formal analysis. False discovery rate (FDR) The expected share of "significant" results that are actually false positives, when many statistical tests are run and checked at once. Hypothesis testing A statistical framework for deciding whether observed data provides enough evidence to reject a default assumption. Interquartile range The range covering the middle 50% of a dataset, from the 25th to the 75th percentile, used to measure spread. Likert scale An ordinal rating scale, typically five or seven points, running between two opposite attitudes or opinions. Logistic regression A statistical model that estimates the probability of a binary outcome as a function of input variables. Margin of error The range added to and subtracted from a survey estimate to express the uncertainty from sampling only part of a population. Median The middle value of a dataset when sorted from lowest to highest, splitting it into two equal halves. Minimum detectable effect (MDE) The smallest true effect an experiment is designed to reliably distinguish from no effect, given its sample size and power. Multilevel regression and poststratification (MRP) A method for estimating opinion in small geographic or demographic groups from a national survey by modeling and reweighting. Multiple comparisons problem The increased risk of a false positive that comes from running many statistical tests and highlighting any one significant result. Nonresponse bias Distortion in survey results that occurs when people who decline to participate differ systematically from those who respond. Normal distribution A symmetric, bell-shaped probability distribution defined entirely by its mean and standard deviation. Null hypothesis The default assumption in a statistical test, typically that there is no effect or no difference, until evidence says otherwise. P-value The probability of observing data at least as extreme as the result, if the null hypothesis were actually true. Percentile The value below which a given percentage of observations in a dataset fall. Questionnaire design Writing and structuring survey questions and response options to minimize bias and measure reliably. Record linkage Matching records that refer to the same person or entity across datasets that lack a shared unique identifier. Regression analysis A statistical method for estimating the relationship between one outcome variable and one or more predictor variables. Regression to the mean (in sports) The statistical tendency for unusually good or bad performances to move back toward a player's or team's underlying average. Response rate The share of people selected for a survey who actually complete it, a key indicator of potential nonresponse bias. Sample size The number of observations in a study or test, which determines how precisely and reliably an effect can be measured. Sampling bias A systematic distortion that arises when the method used to select a sample favors some members of the population over others. Sampling frame The list or source, such as a voter file or address database, from which a survey's respondents are actually drawn. Sampling in analytics Computing a report from a subset of the underlying data rather than the complete data set, to return results faster. Selection bias A distortion that occurs when the sample analyzed is not representative of the population it is meant to describe. Sequential testing An analysis method that lets experiments be checked continuously without inflating the false-positive rate from repeated peeking. Simpson's paradox A pattern where a trend appears in several groups of data but reverses or disappears when the groups are combined. Spurious correlation A statistically strong relationship between two variables that has no causal or meaningful connection. Standard deviation A measure of how spread out a set of values is around its mean, expressed in the same units as the data. Standard error The estimated variability of a sample statistic, such as the mean, if the study were repeated across new samples. Statistical power The probability that a hypothesis test correctly detects a real effect, given that one truly exists. Statistical process control (SPC) Using control charts and statistical limits to tell normal process variation apart from a genuine problem in real time. Statistical significance A threshold judgment that an observed effect is unlikely to be due to chance alone, given the data and test used. Survey mode effects Systematic differences in how people answer identical questions depending on the survey's mode of delivery. Survey weighting Adjusting survey responses so the sample's demographic makeup matches the target population's known composition. T-test A statistical test that compares the means of one or two groups to judge whether an observed difference is likely real. Type I and Type II errors The two ways a hypothesis test can be wrong, rejecting a true null, or failing to reject a false one. Variance The average of the squared differences between each value and the mean, quantifying spread before returning to original units. Z-score The number of standard deviations a value lies above or below the mean of its distribution.