binomial experiment: meaning, definition, pronunciation and examples
Low (Specialist)Academic/Technical
Quick answer
What does “binomial experiment” mean?
A statistical experiment that has exactly two mutually exclusive outcomes per trial, often termed 'success' and 'failure', with a fixed number of independent trials and a constant probability of success.
Audio
Pronunciation
Definition
Meaning and Definition
A statistical experiment that has exactly two mutually exclusive outcomes per trial, often termed 'success' and 'failure', with a fixed number of independent trials and a constant probability of success.
The fundamental model underlying the binomial distribution, used to describe processes where outcomes are binary, such as pass/fail, yes/no, or presence/absence. It serves as the basis for hypothesis testing and confidence intervals for proportions.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning. Minor potential variation in spoken emphasis (e.g., 'bi-NO-mi-al' vs. 'BY-no-mi-al').
Connotations
Purely technical; no cultural connotations.
Frequency
Used with identical frequency in academic statistics contexts in both varieties.
Grammar
How to Use “binomial experiment” in a Sentence
The [researcher/study] + [conducted/defined] + a binomial experiment + to + [estimate/test] + [the proportion/a hypothesis].A binomial experiment + is characterised by + [fixed n, constant p, independence].Vocabulary
Collocations
Examples
Examples of “binomial experiment” in a Sentence
verb
British English
- We can model the process provided it binomial-experiment conditions are met.
American English
- To analyze this, you first need to binomial-experiment the data generation process.
adjective
British English
- The binomial-experiment framework is not suitable for our multi-category data.
American English
- She provided a clear binomial-experiment design for the clinical trial.
Usage
Meaning in Context
Business
Rare; might appear in quality control (defective/non-defective items) or market research (yes/no responses) contexts.
Academic
Core concept in introductory statistics, probability theory, and research methods courses.
Everyday
Virtually never used.
Technical
Fundamental in statistics, biostatistics, engineering reliability, and psychological testing.
Vocabulary
Synonyms of “binomial experiment”
Neutral
Weak
Vocabulary
Antonyms of “binomial experiment”
Watch out
Common Mistakes When Using “binomial experiment”
- Using it for experiments with more than two outcomes.
- Confusing it with the binomial distribution (the experiment generates the distribution).
- Forgetting the requirement of independence between trials.
- Using a non-constant probability of success across trials.
FAQ
Frequently Asked Questions
Yes, provided the coin is fair (or has a constant probability of heads) and each flip is independent. It has a fixed n=10, two outcomes per trial, constant p, and independence.
A single trial with two outcomes is a Bernoulli trial. A binomial experiment consists of a fixed number (n) of independent, identical Bernoulli trials.
Yes, 'success' is merely a label for the outcome of interest. In studying defect rates, a 'success' might be a defective item.
If trials influence each other (e.g., sampling without replacement from a small population), the probability of success changes, violating the constant 'p' assumption.
A statistical experiment that has exactly two mutually exclusive outcomes per trial, often termed 'success' and 'failure', with a fixed number of independent trials and a constant probability of success.
Binomial experiment is usually academic/technical in register.
Binomial experiment: in British English it is pronounced /baɪˈnəʊ.mi.əl ɪkˈsper.ɪ.mənt/, and in American English it is pronounced /baɪˈnoʊ.mi.əl ɪkˈsper.ə.mənt/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
BI-nomial = TWO names/outcomes (like a BI-cycle has TWO wheels).
Conceptual Metaphor
A repeatable coin toss (Heads/Success vs. Tails/Failure).
Practice
Quiz
Which of the following is NOT a condition for a binomial experiment?