statistical independence: meaning, definition, pronunciation and examples

Low Frequency (C1/C2)
UK/stəˌtɪs.tɪ.kəl ˌɪn.dɪˈpen.dəns/US/stəˌtɪs.tɪ.kəl ˌɪn.dəˈpen.dəns/

Technical/Academic

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Quick answer

What does “statistical independence” mean?

The property whereby the occurrence or value of one event or variable has no influence on the probability or value of another.

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Pronunciation

Definition

Meaning and Definition

The property whereby the occurrence or value of one event or variable has no influence on the probability or value of another.

A fundamental concept in probability theory and statistics signifying a complete lack of relationship or predictive power between two or more random variables or events. It implies that knowledge of one provides no information about the other.

Dialectal Variation

British vs American Usage

Differences

No significant differences in meaning or usage between British and American English. Spelling follows national conventions (e.g., 'modelling' in British contexts, 'modeling' in American contexts when used in surrounding text).

Connotations

None beyond its strict technical meaning in both varieties.

Frequency

Identical, very low frequency outside technical contexts in both varieties.

Grammar

How to Use “statistical independence” in a Sentence

statistical independence of X from Ystatistical independence between X and YX and Y exhibit statistical independence

Vocabulary

Collocations

strong
assume statistical independencetest for statistical independencemutual statistical independenceviolation of statistical independence
medium
condition of statistical independenceproperty of statistical independencestatistical independence betweenachieve statistical independence
weak
complete statistical independencefundamental statistical independencekey statistical independence

Examples

Examples of “statistical independence” in a Sentence

adjective

British English

  • The two measurements were shown to be statistically independent.
  • A statistically independent sample is crucial for the validity of the test.

American English

  • We need to verify that the variables are statistically independent.
  • The model assumes statistically independent observations.

Usage

Meaning in Context

Business

Rare; used in advanced analytics or risk modelling contexts (e.g., 'The model assumes statistical independence of default risks across the portfolio.').

Academic

Primary context; central to papers and textbooks in statistics, probability, machine learning, econometrics, and quantitative social sciences.

Everyday

Virtually never used. Would be replaced by phrases like 'they're not related', 'one doesn't affect the other', or 'pure chance'.

Technical

Core term; used with precise mathematical definition in data science, engineering, physics, and research methodologies.

Vocabulary

Synonyms of “statistical independence”

Strong

stochastic independence

Neutral

probabilistic independence

Weak

non-correlationlack of association

Vocabulary

Antonyms of “statistical independence”

Watch out

Common Mistakes When Using “statistical independence”

  • Using it to mean 'autonomy' or 'political independence'.
  • Confusing it with 'linear independence' in linear algebra.
  • Saying 'statistically independent' as an adjective but omitting the '-ly' adverb form (e.g., 'statistic independent').

FAQ

Frequently Asked Questions

No, they are distinct. Independence means no relationship at all. A lack of causation is a stronger claim than independence; two variables can be dependent (related) without one causing the other (e.g., they may have a common cause).

For two variables, zero correlation (specifically, zero linear correlation) does not necessarily imply statistical independence, except in special cases like normally distributed variables. Independence is a stricter condition meaning no relationship of any kind.

True, perfect statistical independence is often an assumption or approximation used to simplify models (e.g., assuming coin tosses are independent). In complex real-world systems, variables are often dependent, and testing for independence is a key analytical step.

The direct opposite is 'statistical dependence', meaning that the probability of one event is affected by the occurrence of another. Related common antonyms include correlation, association, and covariance.

The property whereby the occurrence or value of one event or variable has no influence on the probability or value of another.

Statistical independence is usually technical/academic in register.

Statistical independence: in British English it is pronounced /stəˌtɪs.tɪ.kəl ˌɪn.dɪˈpen.dəns/, and in American English it is pronounced /stəˌtɪs.tɪ.kəl ˌɪn.dəˈpen.dəns/. Tap the audio buttons above to hear it.

Learning

Memory Aids

Mnemonic

Think of two separate coin tosses. The result of the first toss (Heads) gives you NO CLUE about the result of the second toss. This 'no-clue' relationship is statistical independence.

Conceptual Metaphor

ISOLATED ISLANDS (Two events are like islands with no bridges or communication between them; what happens on one island doesn't change what happens on the other.)

Practice

Quiz

Fill in the gap
For the t-test to be valid, we must assume the of the two samples.
Multiple Choice

What does 'statistical independence' between Event A and Event B imply?