Statistics Abbreviations
88 abbreviations · part of Units of Measurement Abbreviations
Abbreviations used in statistics, probability, data analysis and research reporting: descriptive measures (SD, IQR, CV), inference (CI, df, H0, p), regression and model diagnostics (OLS, R², RMSE, AIC), named methods (ANOVA, PCA, ARIMA, MCMC) and probability terms (PDF, CDF, iid). Style guides such as the APA Publication Manual specify how statistical symbols are written, usually in italics for letters such as M, SD, n, p and t.
| Abbreviation | Stands for | Description |
|---|---|---|
| a.s. | Almost surely | Probability term meaning an event has probability 1, even though it is not logically certain. |
| ACF | Autocorrelation function | The correlation of a time series with lagged copies of itself, plotted against the lag. |
| AIC | Akaike information criterion | A model-selection score that balances goodness of fit against complexity: AIC = 2k − 2 ln(L), where k is the number of parameters and L the maximized likelihood. |
| ANCOVA | Analysis of covariance | ANOVA extended with one or more continuous covariates, comparing group means after adjusting for variables such as baseline scores or age. |
| ANOVA | Analysis of variance | A family of methods that test whether the means of three or more groups differ, by comparing variance between groups with variance within groups through an F-test. |
| ARIMA | Autoregressive integrated moving average | A class of time-series models combining autoregression (AR), differencing to remove trends (I) and moving-average error terms (MA), written ARIMA(p, d, q). |
| ATE | Average treatment effect | The average difference in outcomes between receiving and not receiving a treatment across a whole population, the central quantity in causal inference. |
| avg | Average | Shorthand for average, usually the arithmetic mean: the sum of the values divided by their number. |
| BIC | Bayesian information criterion | A model-selection criterion similar to AIC but with a heavier penalty for extra parameters, BIC = k ln(n) − 2 ln(L). |
| BLUE | Best linear unbiased estimator | The estimator with the smallest variance among all linear unbiased estimators. |
| CDF | Cumulative distribution function | The function giving the probability that a random variable is less than or equal to a value, F(x) = P(X ≤ x). |
| CFA | Confirmatory factor analysis | Statistical technique that tests whether data fit a pre-specified model of how observed variables, such as questionnaire items, relate to underlying latent factors. |
| CI | Confidence interval | A range computed from sample data that would contain the true population value in a stated share of repeated samples, most commonly 95 percent. |
| CLT | Central limit theorem | The theorem that the sum or average of many independent random variables with finite variance is approximately normally distributed, whatever the shape of the original… |
| Cov | Covariance | A measure of how two variables vary together: positive when they rise together, negative when one rises as the other falls. |
| CV | Coefficient of variation | The standard deviation divided by the mean, often given as a percentage. |
| df | Degrees of freedom | The number of independent values free to vary when computing a statistic, which sets the shape of the t, chi-square and F distributions. |
| DiD | Difference-in-differences | A method for estimating causal effects by comparing the change in outcomes over time for a treated group with the change for an untreated comparison group. |
| DOE | Design of experiments | The planning of experiments so that the effects of several factors can be estimated efficiently and without confounding. |
| EDA | Exploratory data analysis | The first stage of a data analysis, in which analysts summarize and visualize a dataset with statistics, histograms, scatter plots and correlations to understand its… |
| EFA | Exploratory factor analysis | A technique for discovering the underlying factors that explain correlations among many observed variables, such as survey items, without specifying a structure in… |
| EM | Expectation-maximization | An iterative algorithm for maximum likelihood estimation when data are incomplete or involve hidden variables. |
| F | F-statistic | The test statistic in ANOVA and regression, a ratio of two variances: the variance explained by the model or groups divided by the unexplained variance. |
| FDR | False discovery rate | The expected proportion of false positives among all results declared significant. |
| FPR | False positive rate | The proportion of actual negatives that a test wrongly flags as positive, equal to 1 minus specificity. |
| GARCH | Generalized autoregressive conditional heteroskedasticity | A time-series model for volatility that changes over time, capturing the tendency of large price swings to cluster together. |
| GLM | Generalized linear model | A framework extending linear regression to outcomes such as counts, proportions and yes-or-no results by combining a link function with a distribution from the… |
| H0 | Null hypothesis | The default claim in a statistical test, usually of no effect or no difference, written H₀ and read "H-naught". |
| H1 | Alternative hypothesis | The claim a statistical test seeks evidence for, contradicting the null hypothesis, written H₁ or Ha. |
| HR | Hazard ratio | Ratio of instantaneous event rates in two groups over time, estimated in survival analysis, usually with a Cox proportional hazards model. |
| ICC | Intraclass correlation coefficient | A measure of reliability or agreement for measurements made by different raters or within groups, from 0 (no agreement) to 1 (perfect). |
| iid | Independent and identically distributed | Describes random variables that all follow the same probability distribution and do not influence one another, such as repeated rolls of a fair die. |
| IQR | Interquartile range | The spread of the middle half of a data set: the third quartile minus the first quartile (Q3 − Q1). |
| IV | Instrumental variable | A variable used in econometrics to estimate a causal effect when a predictor is correlated with the error term: it must affect the outcome only through that predictor. |
| KDE | Kernel density estimation | A nonparametric way to estimate a smooth probability density by placing a small bump (kernel) on each observation and adding them up. |
| KS | Kolmogorov-Smirnov (test) | A nonparametric test comparing a sample's empirical distribution with a reference distribution, or two samples with each other, based on the largest vertical gap… |
| LASSO | Least absolute shrinkage and selection operator | A regression method that adds a penalty on the sum of absolute coefficient values, shrinking some coefficients to exactly zero and thereby selecting variables. |
| LDA | Linear discriminant analysis | A classification and dimensionality-reduction method that finds linear combinations of features that best separate two or more classes. |
| LLN | Law of large numbers | The principle that the average of many independent trials converges to the expected value as the number of trials grows. |
| M | Mean (APA style) | In APA-style research writing, an italic M reports the arithmetic mean of a sample, usually paired with SD. |
| MAD | Mean absolute deviation | The average of the absolute differences between each value and the mean, a simple measure of spread taught in middle school. |
| MAE | Mean absolute error | The average of the absolute differences between predictions and actual values, expressed in the outcome's units. |
| MANOVA | Multivariate analysis of variance | An extension of ANOVA that tests group differences on several correlated outcome variables at once, such as multiple test scores or symptom measures. |
| MAP | Maximum a posteriori | A Bayesian estimate equal to the parameter value with the highest posterior probability, combining the likelihood with a prior distribution. |
| MAPE | Mean absolute percentage error | The average of absolute errors expressed as percentages of the actual values, a popular accuracy measure in sales and demand forecasting. |
| MAR | Missing at random | A missing-data mechanism in which the probability of missingness depends only on observed data, not on the missing values themselves. |
| MCAR | Missing completely at random | A missing-data mechanism in which the chance that a value is missing is unrelated to any observed or unobserved data, as when a lab sample is accidentally dropped. |
| MCMC | Markov chain Monte Carlo | A family of algorithms that draw samples from complex probability distributions by running a Markov chain whose long-run distribution is the target. |
| Mdn | Median | APA-style abbreviation for the median, the middle value of ordered data, used in tables and results sections of psychology and social science papers. |
| MGF | Moment-generating function | The function M(t) = E[e^(tX)], whose derivatives at zero give a distribution's moments: the first is the mean, and the second leads to the variance. |
| MLE | Maximum likelihood estimation | A method of estimating model parameters by choosing the values that make the observed data most probable. |
| MOE | Margin of error | Half the width of a confidence interval, usually at 95 percent confidence, reported with opinion polls and surveys. |
| MSE | Mean squared error | The average of squared differences between predictions and actual values, a standard loss function in regression and machine learning. |
| n | Sample size | The number of observations in a sample or subgroup, written lowercase n in research reports. |
| NPV | Negative predictive value | Probability that a person with a negative test result truly does not have the condition, calculated as true negatives divided by all negative results. |
| OLS | Ordinary least squares | The standard way to fit a linear regression, choosing coefficients that minimize the sum of squared differences between observed and predicted values. |
| OR | Odds ratio | Ratio of the odds of an outcome in one group to the odds in another, the standard effect measure in case-control studies and logistic regression. |
| p | p-value | The probability, assuming the null hypothesis is true, of obtaining a result at least as extreme as the one observed. |
| PCA | Principal component analysis | A technique that transforms correlated variables into a smaller set of uncorrelated components ordered by how much variance they explain. |
| Probability density function | A function describing the relative likelihood of a continuous random variable taking values near a point; probabilities are areas under its curve. | |
| PI | Prediction interval | A range expected to contain a single future observation with a stated probability, as opposed to a confidence interval for a mean or parameter. |
| PMF | Probability mass function | For a discrete random variable, the function giving the probability of each possible value, such as P(X = 3) for the number of heads in five flips. |
| PPV | Positive predictive value | The probability that a positive test result is truly positive: true positives divided by all positive results. |
| Q1 | First quartile | The value below which 25 percent of observations fall, the 25th percentile. |
| Q3 | Third quartile | The 75th percentile: three quarters of the observations lie at or below it. |
| Quantile-quantile (plot) | A graph that plots the quantiles of a data set against those of a theoretical distribution, usually the normal. | |
| r | Pearson correlation coefficient | A number from −1 to 1 measuring the strength and direction of the linear relationship between two variables. |
| RMSE | Root mean square error | The square root of the mean squared error, giving typical prediction error in the same units as the outcome. |
| ROC | Receiver operating characteristic | A curve plotting the true positive rate against the false positive rate of a classifier or diagnostic test across every possible threshold. |
| RR | Relative risk | Ratio of the risk of an outcome in an exposed or treated group to the risk in an unexposed or control group, used in cohort studies and trials. |
| RSS | Residual sum of squares | The sum of squared residuals, the differences between observed and fitted values in a regression. |
| RV | Random variable | A variable whose value is a numerical outcome of a random process, such as the number of heads in ten coin flips. |
| R² | Coefficient of determination | The proportion of the variance in an outcome explained by a regression model, from 0 to 1. |
| SD | Standard deviation | A measure of how spread out values are around their mean, equal to the square root of the variance and expressed in the same units as the data. |
| SE | Standard error | The standard deviation of a statistic's sampling distribution, measuring how much an estimate such as a mean or regression coefficient would vary across repeated samples. |
| SEM | Standard error of the mean | How much a sample mean would vary across repeated samples, estimated as the sample SD divided by the square root of the sample size. |
| SPC | Statistical process control | Use of statistical methods, especially control charts, to monitor a manufacturing process and detect when variation exceeds what is normal, so problems are corrected… |
| SRS | Simple random sample | A sample in which every possible group of n units has the same chance of being chosen, the basic design behind much of statistical inference. |
| SS | Sum of squares | The sum of squared deviations from a mean or from model predictions, the building block of variance, ANOVA and regression. |
| SSE | Sum of squared errors | The total of the squared differences between observed values and model predictions, also called the residual or error sum of squares. |
| SSR | Sum of squares due to regression | In many textbooks, the variation in the outcome explained by a regression model: the sum of squared differences between predicted values and the overall mean. |
| SST | Total sum of squares | The total variation in an outcome: the sum of squared deviations of each observation from the overall mean. |
| STDEV | Standard deviation (spreadsheet function) | The Excel and Google Sheets function that returns the sample standard deviation of a range, dividing by n − 1. |
| t | t-statistic | The test statistic in a t-test: an estimate divided by its standard error, compared with Student's t distribution to obtain a p-value. t-tests compare a mean with a… |
| TPR | True positive rate | The proportion of actual positives that a test or classifier correctly identifies, also called sensitivity or recall. |
| Var | Variance | The average squared deviation of values from their mean, the square of the standard deviation. |
| VIF | Variance inflation factor | A diagnostic for multicollinearity in regression, measuring how much a coefficient's variance is inflated because its predictor is correlated with the others. |
| z | z-score | The number of standard deviations a value lies above or below the mean: z = (x − mean) / SD. |
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