Alpha Level
The alpha level, also called the significance level, is the predetermined probability threshold below which the null hypothesis is rejected in a statistical test.
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Research Glossary
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Statistics and Analysis Terms
The statistical ideas behind every results section: describing data, testing hypotheses, estimating effects and building models. Each term explains what a method does, when to use it and the mistakes that trip researchers up, with cited sources and worked examples.
A
ANCOVA (Analysis of Covariance)
Analysis of covariance, or ANCOVA, is a statistical method that combines elements of analysis of variance (ANOVA) and linear regression to compare group means on an outcome variable while controlling for one or more continuous covariates.
ANOVA (Analysis of Variance)
Analysis of variance, or ANOVA, is a statistical method that tests whether the means of three or more groups differ significantly from one another.
B
Bayesian Statistics
Bayesian statistics is a branch of statistical inference based on Bayes' theorem that treats probability as a measure of belief or uncertainty rather than as a long run frequency.
Bivariate Analysis
Bivariate analysis is a statistical approach that examines the relationship between exactly two variables simultaneously.
C
Censored Data
Censored data are observations in survival analysis for which the exact time to the event of interest is not known because the event has not yet occurred by the end of the study period, the participant was lost to follow up before the event, or the…
Central Limit Theorem
The central limit theorem (CLT) is a foundational principle in statistics stating that the sampling distribution of the sample mean approaches a normal (Gaussian) distribution as the sample size increases, regardless of the shape of the underlying population…
Chi Square Test
The chi square test is a statistical test that evaluates whether the distribution of observed frequencies across categories differs significantly from the frequencies that would be expected under a specified hypothesis, most commonly the hypothesis of…
Clinical Significance
Clinical significance refers to the practical importance of a treatment effect, indicating whether the observed change is large enough to be meaningful in real world patient care.
Coefficient of Variation
The coefficient of variation (CV) is a standardized measure of dispersion calculated as the ratio of the standard deviation to the mean, typically expressed as a percentage.
Complete Case Analysis
Complete case analysis, also called listwise deletion, is a statistical approach that includes only participants who have complete data for all variables of interest in the analysis, excluding anyone with any missing values.
Confidence Interval
A confidence interval is a range of values, calculated from sample data by a method that, across repeated samples, captures the true population parameter at a specified rate called the confidence level.
Conjoint Analysis
Conjoint analysis is a survey based statistical technique used to understand how individuals value different attributes of a product, service, or intervention by presenting them with hypothetical scenarios that require trade offs.
Correlation
Correlation is a statistical measure that quantifies the degree and direction of the association between two variables.
Correlation Coefficient
A correlation coefficient is a numerical statistic that quantifies the strength and direction of the relationship between two variables on a standardized scale from negative 1 to positive 1: linear for Pearson's r, monotonic for rank based coefficients.
Cox Regression
Cox regression, also known as the Cox proportional hazards model, is a semiparametric statistical method used in survival analysis to examine the relationship between one or more predictor variables and the time to an event of interest (such as death,…
Credible Interval
A credible interval is the Bayesian counterpart to the frequentist confidence interval. It provides a range within which an unknown parameter falls with a specified posterior probability, given the observed data and a prior distribution.
D
Data Mining
Data mining is the process of discovering patterns, correlations, anomalies, and meaningful structures in large datasets using statistical, mathematical, and computational techniques.
Data Visualization
Data visualization is the graphical representation of data and information using visual elements such as charts, graphs, maps, diagrams, and infographics to communicate patterns, trends, relationships, and insights that might be difficult to perceive in raw…
Descriptive Statistics
Descriptive statistics are statistical methods used to summarize, organize, and describe the main features of a dataset without making inferences about the broader population from which the sample was drawn.
Distribution
In statistics, a distribution is a mathematical function or empirical description that shows all possible values of a variable and how frequently they occur.
E
F
F Test
The F test is a statistical test that compares variances, for example to test whether group means differ significantly.
Factor Analysis
Factor analysis is a statistical method that reduces a large number of observed variables to a smaller set of underlying factors or latent constructs by identifying patterns of correlation among the variables.
Fisher Exact Test
The Fisher exact test is a statistical test used to determine whether there is a significant association between two categorical variables in a 2 x 2 contingency table.
Frequency Distribution
A frequency distribution is a summary of how often each value or category (or range of values) occurs in a dataset. It can be presented as a table, histogram, bar chart, or frequency polygon.
G
Generalized Estimating Equations (GEE)
Generalized Estimating Equations (GEE) is a statistical method for analyzing correlated or clustered data, such as repeated measurements on the same individuals over time, observations nested within groups (schools, clinics, families), or multi site studies.
Generalized Linear Model
A generalized linear model (GLM) is a flexible extension of ordinary linear regression that accommodates dependent variables following non normal distributions from the exponential family, including binomial, Poisson, gamma, and negative binomial…
H
Hazard Analysis
Hazard analysis is a systematic process for identifying potential hazards associated with a product, process, or system, estimating the severity and probability of harm from each hazard, and determining appropriate risk control measures.
Hazard Ratio
The hazard ratio (HR) is a measure used in survival analysis that compares the rate at which events (such as death, disease recurrence, or hospitalization) occur in one group relative to another at any given point in time.
Hierarchical Linear Modeling (HLM)
Hierarchical Linear Modeling (HLM), also called multilevel modeling or mixed effects modeling, is a statistical method for analyzing data that have a nested or hierarchical structure, such as students within classrooms, patients within hospitals, or repeated…
Hierarchical Model
A hierarchical model, also called a multilevel model, is a statistical framework designed to handle data organized at multiple nested levels, such as patients within hospitals, students within schools, or repeated measurements within individuals.
Hypothesis Testing
Hypothesis testing is a formal statistical procedure that uses sample data to evaluate a claim about a population parameter.
I
K
Kaplan Meier Estimate
The Kaplan Meier estimate is a nonparametric statistic used in survival analysis to estimate the probability of surviving (or remaining event free) beyond successive time points.
Kruskal Wallis Test
The Kruskal Wallis test is a nonparametric statistical test used to determine whether there are statistically significant differences in the distributions (assessed through mean ranks) of a continuous or ordinal dependent variable across three or more…
L
Linear Regression
Linear regression is a statistical method that models the relationship between a continuous dependent variable and one or more independent variables by fitting a linear equation to the observed data.
Log Rank Test
The log rank test is a nonparametric statistical test used in survival analysis to compare the time to event distributions between two or more groups.
Logistic Regression
Logistic regression is a statistical method used to model the relationship between a binary dependent variable (one with two possible outcomes, such as disease present or absent) and one or more independent variables.
M
Mann Whitney U Test
The Mann Whitney U test is a nonparametric statistical test that compares the distributions of a continuous or ordinal dependent variable between two independent groups.
Margin of Error
The margin of error is a statistic expressing the amount of random sampling error in a survey's results.
Maximum Likelihood Estimation
Maximum likelihood estimation (MLE) is a method for estimating the parameters of a statistical model by finding the values that maximize the likelihood function, which gives the probability (or probability density) of the collected data for specific…
Mean
The mean, or arithmetic average, is a measure of central tendency calculated by summing all values in a dataset and dividing by the number of values.
Median
The median is the middle value in a dataset when all observations are arranged in ascending or descending order. If the number of observations is odd, the median is the central value; if even, it is the average of the two central values.
Missing Data
Missing data are observations or measurements that are absent from a dataset, arising from a variety of causes including participant dropout, nonresponse to survey items, equipment malfunction, data entry errors, or administrative gaps in record systems.
Mixed Model
A mixed model, also called a mixed effects model, is a statistical framework that contains both fixed effects (population level parameters that apply to the entire sample or population) and random effects (parameters that vary across groups, individuals, or…
Mode
The mode is the most frequently occurring value in a set of observations. A dataset can have one mode (unimodal), two modes (bimodal), or more (multimodal), and it is the only measure of central tendency applicable to nominal (categorical) data, where…
Multicollinearity
Multicollinearity is a statistical condition that occurs when two or more independent variables in a regression model are highly correlated with each other.
Multiple Regression
Multiple regression is a statistical technique that models the relationship between a single dependent variable and two or more independent variables, allowing researchers to estimate the unique contribution of each predictor while controlling for the…
Multiple Testing Correction
Multiple testing correction refers to a set of statistical adjustments applied when multiple hypothesis tests are performed simultaneously.
Multivariate Analysis
Multivariate analysis encompasses a set of statistical methods designed to analyze data involving several variables jointly, typically more than one dependent variable, accounting for the relationships and correlations among them.
N
Nonparametric Statistics
Nonparametric statistics are a class of statistical methods that do not assume the data follow a specific probability distribution, such as the normal distribution.
Normal Distribution
The normal distribution, also called the Gaussian distribution or bell curve, is a symmetric, continuous probability distribution defined by two parameters: the mean (mu) and the standard deviation (sigma).
Null Hypothesis
The null hypothesis (Hâ‚€) is the default proposition in statistical hypothesis testing that states there is no effect, no difference, or no association between variables.
O
P
p Value
The p value is the probability of obtaining a result at least as extreme as the one observed in a study, assuming that the null hypothesis is true.
Parametric Statistics
Parametric statistics are a class of statistical methods that make specific assumptions about the distribution of the underlying population from which the data are drawn, most commonly that the data follow a normal (Gaussian) distribution.
Path Analysis
Path analysis is a statistical method used to examine the directed relationships among a set of variables according to a hypothesized causal model.
Pearson Correlation
The Pearson correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two continuous variables.
Point Estimate
A point estimate is a single numerical value derived from sample data that serves as the best estimate of an unknown population parameter.
Post Hoc Analysis
A post hoc analysis is any analysis conducted after data collection that was not specified in the original study protocol or statistical analysis plan.
Post Hoc Test
A post hoc test is a statistical procedure applied after an analysis of variance (ANOVA), usually one that yields a significant result, in order to identify which specific group means differ from one another.
Power (Statistical Power)
Statistical power is the probability that a study's statistical test will correctly detect a true effect when one exists, calculated as one minus the probability of a Type II error (beta).
Power Analysis
Power analysis is a statistical calculation performed during the planning stages of a study to determine the minimum sample size needed to detect an effect of a given magnitude with a specified level of confidence and statistical power.
Predictive Modeling
Predictive modeling is the use of statistical algorithms or machine learning techniques to build a model that forecasts future outcomes or classifies observations based on patterns identified in historical data.
Principal Component Analysis (PCA)
Principal component analysis (PCA) is a dimensionality reduction technique that transforms a set of correlated variables into uncorrelated linear combinations called principal components, each capturing the most variance left by earlier ones, with the first…
Propensity Score
A propensity score is the estimated conditional probability that an individual receives a particular treatment given a set of observed baseline covariates.
Propensity Score Matching
Propensity score matching (PSM) is a statistical technique that pairs treated and untreated individuals who have similar estimated propensity scores, creating a matched sample in which the distribution of observed baseline covariates is balanced between…
R
Regression Analysis
Regression analysis is a family of statistical methods used to model the relationship between one or more independent (predictor) variables and a dependent (outcome) variable.
Regression Coefficient
A regression coefficient is a numerical value in a regression equation that represents the estimated average change in the dependent variable for each one unit change in the corresponding independent variable, while holding all other variables in the model…
S
Sample Size
Sample size is the number of participants, observations, or units included in a study.
Sampling Error
Sampling error is the difference between a statistic calculated from a sample and the true parameter of the population from which the sample was drawn.
Sensitivity Analysis
A sensitivity analysis is an analytical procedure that tests how the results of a study, model, or systematic review change when key assumptions, decisions, or parameters are varied.
Spearman Rank Correlation
Spearman rank correlation is a nonparametric measure of the strength and direction of the monotonic relationship between two variables, calculated using the ranks of the data rather than the raw values.
Standard Deviation
Standard deviation is a measure of the dispersion or spread of values in a dataset around the mean.
Standard Error
The standard error is the standard deviation of the sampling distribution of a statistic, most commonly the sample mean. It quantifies the precision of a sample statistic as an estimate of the corresponding population parameter.
Statistical Significance
A result is statistically significant when its p value, the probability of obtaining data at least as extreme as those observed if the null hypothesis were true, falls below a threshold set in advance, typically 0.05.
Survival Analysis
Survival analysis is a collection of statistical methods designed to analyze time to event data, where the outcome of interest is the time elapsed until a specific event occurs, such as death, disease recurrence, treatment failure, or hospital discharge.
T
T Test
A t test is a parametric statistical test used to determine whether there is a statistically significant difference between the means of two groups or between a sample mean and a known population value.
Two Tailed Test
A two tailed test is a statistical hypothesis test in which the alternative hypothesis specifies that the parameter of interest differs from the null value in either direction, without specifying whether the difference is positive or negative.
Type I Error
A Type I error, also called a false positive, occurs when a statistical test incorrectly rejects a true null hypothesis, concluding that an effect or difference exists when it does not.
Type II Error
A Type II error, also called a false negative, occurs when a statistical test fails to reject a false null hypothesis, concluding that no effect or difference exists when one actually does.
V
W
Y
Z
Z-Score
A z-score, also known as a standard score, is a dimensionless quantity that expresses how many standard deviations a data point lies above or below the mean of its distribution.
Zero-Inflated Model
A zero-inflated model is a statistical regression model designed for count data that contains more zeros than would be expected under a standard Poisson or negative binomial distribution.