Glossary of probability and statistics

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Relationship between mean and median under different skewness

Glossary of Probability and Statistics

The Glossary of Probability and Statistics provides definitions and explanations of key concepts in the fields of probability and statistics, which are branches of mathematics concerned with the analysis of random phenomena and the collection, analysis, interpretation, and presentation of data. This article aims to introduce some of the most fundamental terms and concepts.

A

• Algorithm - A step-by-step procedure for calculations. Algorithms are used for data processing, mathematical computation, and automated reasoning.

• Analysis of Variance (ANOVA) - A collection of statistical models and their associated procedures which compare means among three or more groups based on sample data.

B

• Bayesian Probability - A theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a degree of belief in an event.

• Binomial Distribution - A probability distribution that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions.

C

• Confidence Interval (CI) - A range of values, derived from the sample statistics, that is likely to contain the value of an unknown population parameter.

• Correlation Coefficient - A numerical measure of some type of correlation, meaning a statistical relationship between two variables.

D

• Data Mining - The process of discovering patterns and knowledge from large amounts of data. The data sources can include databases, data warehouses, the internet, and other sources.

• Descriptive Statistics - Statistics that quantitatively describe or summarize features of a collection of information.

E

• Expected Value - The anticipated value for a given investment. In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur, and summing all of those values.

F

• Frequency Distribution - A summary of how often different values occur within a set of data.

G

• Gaussian Distribution - Also known as the normal distribution, it is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

H

• Hypothesis Testing - A method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis.

I

• Inferential Statistics - The branch of statistics that attempts to infer the properties of a population based on a sample.

J

• Joint Probability Distribution - A probability distribution that captures the likelihood of two or more random variables simultaneously taking on specific values.

K

• Kurtosis - A measure of the "tailedness" of the probability distribution of a real-valued random variable.

L

• Likelihood Function - A function that measures the goodness of fit of a statistical model to a sample of data for given values of the unknown parameters.

M

• Mean - The average of a set of numbers, calculated by dividing the sum of these numbers by the count of the numbers.

N

• Normal Distribution - See Gaussian Distribution.

O

• Outlier - An observation point that is distant from other observations in a data set.

P

• P-Value - The probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct.

• Probability - A measure of the likelihood that an event will occur.

Q

• Quantile - Values that divide the range of a probability distribution into continuous intervals with equal probabilities, or divide the observations in a sample in the same way.

R

• Random Variable - A variable whose values depend on outcomes of a random phenomenon.

• Regression Analysis - A set of statistical processes for estimating the relationships among variables.

S

• Sample Size - The number of observations or replicates to include in a statistical sample.

• Standard Deviation - A measure of the amount of variation or dispersion of a set of values.

T

• T-Test - A type of inferential statistic used to determine if there is a significant difference between the means of two variables.

U

• Uniform Distribution - A type of probability distribution in which all outcomes are equally likely.

V

• Variance - A measure of the dispersion of a set of data points around their mean value.

W

• Wilcoxon Signed-Rank Test - A non-parametric statistical hypothesis test used when comparing two related samples or repeated measurements on a single sample.

Z

• Z-Score - Also known as a standard score, it indicates how many standard deviations an element is from the mean.

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