Statistical Glossary
Comprehensive definitions of statistical terms, concepts, and methods.
Basic Concepts
Population
The entire group of individuals, objects, or measurements of interest for a statistical study.
Sample
A subset of the population selected for study.
Variable
A characteristic or attribute that can be measured or categorized.
Data Types and Measurement Scales
Nominal Scale
Categorical data without any inherent order.
Ordinal Scale
Categorical data with a meaningful order but no fixed intervals.
Interval Scale
Numeric data with meaningful intervals but no true zero.
Ratio Scale
Numeric data with meaningful intervals and a true zero.
Descriptive Statistics
Mean
The arithmetic average of a set of numbers, calculated by summing all values and dividing by the count of values.
x̄ = (Σx) / nMedian
The middle value when data is arranged in order.
Standard Deviation
A measure of variability that indicates the average distance between data points and their mean.
s = √[Σ(x - x̄)² / (n-1)]Data Collection Methods
Survey
Method of collecting data from a sample to infer about the population.
Experiment
A controlled study where variables are manipulated to determine effects.
Observational Study
A study where data is collected without intervention, observing naturally occurring variables.
Probability
Probability
A numerical measure of the likelihood of an event occurring.
Independence
Two events are independent if the occurrence of one does not affect the probability of the other.
Bayes' Theorem
A formula for updating probabilities based on new information.
P(A|B) = [P(B|A) * P(A)] / P(B)Central Limit Theorem
The theorem that the distribution of sample means approximates a normal distribution as the sample size increases.
Distributions
Normal Distribution
A symmetric, bell-shaped distribution characterized by its mean and standard deviation.
Skewness
A measure of the asymmetry of a probability distribution.
Inferential Statistics
Hypothesis Testing
A statistical method for making decisions using data, involving null and alternative hypotheses.
Confidence Interval
A range of values that likely contains the true population parameter with a specified level of confidence.
CI = point estimate ± (critical value × standard error)Statistical Tests
t-test
A statistical test used to determine if there is a significant difference between the means of two groups.
ANOVA
Analysis of Variance - a statistical test used to analyze differences among means of three or more groups.
Chi-square Test
A test for relationships between categorical variables, often used in contingency tables.
Errors and Power in Hypothesis Testing
Type I Error
A false positive, rejecting the null hypothesis when it is actually true.
Type II Error
A false negative, failing to reject the null hypothesis when it is actually false.
Statistical Power
The probability of correctly rejecting the null hypothesis (1 - Type II error probability).
Regression and Correlation
Correlation
A measure of the strength and direction of the relationship between two variables.
Simple Linear Regression
A method to predict a response variable based on one predictor variable.
y = a + bxMultiple Regression
A regression model with multiple predictor variables to predict an outcome.
Multivariate Analysis
Principal Component Analysis (PCA)
A technique for reducing dimensionality of large data sets while retaining most variation.
Cluster Analysis
A method for grouping data points into clusters based on similarities.
Effect Size and Practical Significance
Effect Size
A measure of the strength or magnitude of an effect, useful for understanding practical significance.
Cohen's d
An effect size measure for the difference between two means.
d = (M1 - M2) / SDCan't find what you need?
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