Statistics
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
1RM Estimation
One-repetition maximum (1RM) estimation is a method to predict an athlete's maximum strength in a given lift without performing an actual maximal single repetition. Developed systematically by Matt Brzycki (1993) and refined by numerous res...
2PL IRT
The two-parameter logistic item response model, formalised by Frederic Lord (1980), describes the probability that a respondent answers a binary test item correctly as a smooth S-shaped function of the respondent's latent ability. By estima...
2SLS Regression
Two-Stage Least Squares is a two-step instrumental-variables estimator that addresses endogeneity, the situation where a regressor is correlated with the error term. In the first stage the endogenous regressor is predicted from instrumental...
3PL IRT
The three-parameter logistic (3PL) model, introduced by Allan Birnbaum in 1968, is an item response theory model that describes the probability of a correct response to a binary test item as a function of three item-level parameters — diffi...
A/B Test
An A/B test is a randomized controlled experiment that simultaneously exposes two groups of users to a control variant (A) and a treatment variant (B) in order to determine whether a measured outcome differs significantly between them. The...
ANCOVA
ANCOVA is a parametric hypothesis test that compares the adjusted means of two or more independent groups while statistically controlling for one or more continuous covariates. By removing the portion of outcome variance explained by the co...
APARCH
APARCH, introduced by Ding, Granger, and Engle (1993) while studying long-memory properties of stock market returns, extends the GARCH family by allowing both the power transformation of conditional volatility and an asymmetric response to...
ARCH model
The ARCH model, introduced by Robert Engle in 1982, captures time-varying volatility in financial and macroeconomic time series. It models the conditional variance of today's error as a function of past squared errors, explaining why volati...
ARCH-LM Test
The ARCH-LM test is Robert Engle's (1982) Lagrange multiplier diagnostic for autoregressive conditional heteroscedasticity in the residuals of a fitted time-series model. It checks whether the error variance changes over time and clusters i...
ARDL Bounds Test
The ARDL bounds test is an autoregressive distributed lag method that tests for a cointegrating (long-run level) relationship between time series, introduced by Pesaran, Shin and Smith in 2001. Unlike the Johansen procedure, it remains vali...
ARFIMA Model
ARFIMA is a time series model that captures long-memory behaviour using a fractional differencing parameter d, generalising the integer differencing of ARIMA. It was introduced by Granger and Joyeux (1980) and formalised by Hosking (1981) t...
ARIMA
ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins met...
ARIMA model
The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear frame...
ARMA model
The ARMA(p,q) model describes a stationary time series as a combination of two components: an autoregressive part that regresses the current value on its own past p values, and a moving average part that accounts for past q error terms. It...
Abusive Supervision Scale
The Abusive Supervision Scale measures subordinates' perceptions of the extent to which their supervisors engage in sustained displays of hostile verbal and nonverbal behaviors, excluding physical contact. Bennett Tepper introduced both the...
Accelerated Failure Time Model
The Accelerated Failure Time model is a parametric regression approach to survival analysis — formally reviewed and advocated by L. J. Wei in 1992 — in which covariates act as multiplicative factors that directly stretch or compress the tim...
Accelerometer Cut-Point Calibration
Accelerometer cut-point calibration solves the central translation problem of objective physical-activity measurement: a wearable accelerometer outputs dimensionless 'counts,' but researchers and health guidelines speak in intensities — sed...
Active Life Expectancy Estimation
Active life expectancy (ALE) estimates how many of an older person's remaining years are expected to be lived in an active, independent state — free of disability in basic activities of daily living — as opposed to a dependent state requiri...
Actor-Partner Interdependence Model
The Actor-Partner Interdependence Model (APIM), formalized by Kenny, Kashy, and Cook, is the standard framework for analyzing dyadic data in which two people's outcomes depend on both their own and their partner's characteristics. For each...
Acute-Chronic Workload Ratio
The acute-chronic workload ratio (ACWR) is the ratio of acute training load (typically the past 1 week) to chronic training load (typically the rolling 4-week average). Formalized by Tim Gabbett (2016), ACWR is a widely adopted metric for p...
Adaptive Clinical Trial Design
Adaptive clinical trial design is a flexible experimental framework, formalised by Bauer and Köhne in 1994, in which pre-specified rules allow the trial to be modified mid-course — adjusting sample size, treatment arms, or randomisation rat...
Adjusted Boxplot
The Adjusted Boxplot is a robust descriptive tool introduced by Hubert and Vandervieren (2008) that corrects the classical IQR-based boxplot for skewness using the medcouple statistic, reducing the false labelling of outliers in asymmetric...
Age-Crime Curve Modeling
Age-crime curve modeling fits statistical functions to the well-known relationship between age and offending: crime rises sharply in adolescence, peaks in the late teens or early twenties, and declines through adulthood. Brought to prominen...
Age-Period-Cohort Analysis
Age-period-cohort (APC) analysis decomposes variation in disease or mortality rates into three temporal components: the effect of age (biological and accumulated risk), the effect of period (influences hitting everyone alive at a given cale...