critical value: meaning, definition, pronunciation and examples
Low (C1/C2). Specialised term.Formal, Technical, Academic
Quick answer
What does “critical value” mean?
In statistics and hypothesis testing, the threshold value on a test statistic that separates the rejection region from the non-rejection region.
Audio
Pronunciation
Definition
Meaning and Definition
In statistics and hypothesis testing, the threshold value on a test statistic that separates the rejection region from the non-rejection region; a point beyond which the null hypothesis is rejected.
More generally, any specific value that represents a crucial boundary or threshold in a system, process, or theoretical model, often marking a point of transition, failure, or fundamental change in state or behaviour.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling of related terms follows regional conventions (e.g., 'behaviour/behavior').
Connotations
Identical technical connotations in both dialects.
Frequency
Equally low-frequency and specialised in both UK and US academic/professional contexts.
Grammar
How to Use “critical value” in a Sentence
The [test statistic] is compared to/with the critical value.If [statistic] > critical value, reject H0.The critical value for [alpha level] and [degrees of freedom] is [number].The critical value depends on [parameter].Vocabulary
Collocations
Examples
Examples of “critical value” in a Sentence
verb
British English
- [The term itself is a noun phrase. No standard verb form.]
American English
- [The term itself is a noun phrase. No standard verb form.]
adverb
British English
- [No standard adverbial form.]
American English
- [No standard adverbial form.]
adjective
British English
- [Used attributively in noun phrases, e.g., 'the critical value approach', 'critical value tables'.]
American English
- [Used attributively in noun phrases, e.g., 'the critical value method', 'critical value analysis'.]
Usage
Meaning in Context
Business
Virtually never used in general business. Might appear in highly specialised business analytics or risk modelling reports.
Academic
Core term in statistics, mathematics, engineering, and physical/social sciences research methodologies.
Everyday
Extremely rare. Unlikely to be encountered outside educational or highly technical discussions.
Technical
The primary domain of use. Essential in statistical software output, scientific papers, and engineering safety/performance analyses.
Vocabulary
Synonyms of “critical value”
Strong
Neutral
Weak
Vocabulary
Antonyms of “critical value”
Watch out
Common Mistakes When Using “critical value”
- Using 'critical value' and 'p-value' interchangeably. They are related but distinct concepts.
- Pronouncing 'value' as /ˈvæl.uː/ instead of the standard /ˈvæl.juː/.
- Forgetting that the critical value is determined *before* looking at the test statistic in the classical hypothesis testing procedure.
FAQ
Frequently Asked Questions
No. A critical value is a point on the scale of the test statistic (like z or t). A p-value is a probability. You compare your test statistic to the critical value, or you compare your p-value to the significance level (alpha). They are two sides of the same coin but are not interchangeable numbers.
It is found using statistical tables (e.g., z-table, t-table, chi-square table) or software. You need to know: 1) The distribution of your test statistic, 2) Your chosen significance level (alpha), and 3) The degrees of freedom (for some distributions like t).
Yes, depending on the test and distribution. For example, in a left-tailed test using the z-distribution, the critical value will be negative (e.g., -1.645 for alpha=0.05).
Yes, but always with a technical sense derived from the statistical one. In engineering, it might refer to a load or stress threshold causing failure. In physics, it could be a temperature or pressure at which a phase change occurs. The core idea of a decisive threshold remains.
In statistics and hypothesis testing, the threshold value on a test statistic that separates the rejection region from the non-rejection region.
Critical value is usually formal, technical, academic in register.
Critical value: in British English it is pronounced /ˌkrɪt.ɪ.kəl ˈvæl.juː/, and in American English it is pronounced /ˌkrɪt̬.ɪ.kəl ˈvæl.juː/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “[None directly. The term itself is technical.]”
Learning
Memory Aids
Mnemonic
Imagine a critic at a talent show holding a scorecard with a specific number (the critical value). Contestants scoring below this number are 'rejected' from the next round.
Conceptual Metaphor
A BOUNDARY/GATEKEEPER (separating acceptance from rejection), a TRIPWIRE (that triggers a specific action when crossed), a RED LINE (that must not be crossed).
Practice
Quiz
What is the primary function of a critical value in hypothesis testing?