rejection region: meaning, definition, pronunciation and examples
C2Formal, Technical, Academic
Quick answer
What does “rejection region” mean?
In statistical hypothesis testing, the set of sample outcomes for which the null hypothesis is rejected.
Audio
Pronunciation
Definition
Meaning and Definition
In statistical hypothesis testing, the set of sample outcomes for which the null hypothesis is rejected.
A predefined range of values for a test statistic that, if the observed data falls within it, leads to the conclusion that the observed effect is statistically significant and not due to random chance. The threshold(s) for this region are determined by the chosen significance level (alpha).
Dialectal Variation
British vs American Usage
Differences
No substantive difference in meaning or usage. Spelling conventions follow general patterns (e.g., 'behavioural' vs. 'behavioral' in related texts).
Connotations
Purely technical, identical in both varieties.
Frequency
Equally frequent in academic statistics texts in both regions.
Grammar
How to Use “rejection region” in a Sentence
The test statistic fell within the rejection region.We define the rejection region for alpha = 0.05.The rejection region lies in the upper tail of the distribution.Vocabulary
Collocations
Examples
Examples of “rejection region” in a Sentence
adjective
British English
- The rejection-region boundary is clearly marked on the plot.
American English
- The rejection-region boundary is clearly marked on the plot.
Usage
Meaning in Context
Business
Rare, except in highly quantitative analysis or Six Sigma contexts.
Academic
Core term in statistics, psychology, economics, and other research-method driven fields.
Everyday
Virtually never used.
Technical
Fundamental term in statistical hypothesis testing, data science, and quality control.
Vocabulary
Synonyms of “rejection region”
Neutral
Weak
Vocabulary
Antonyms of “rejection region”
Watch out
Common Mistakes When Using “rejection region”
- Using it interchangeably with 'p-value' (the p-value is a probability used to *determine* the rejection region).
- Saying 'rejection area' is non-standard.
- Thinking the rejection region contains 'bad' data; it contains statistically *unlikely* data under the null hypothesis.
FAQ
Frequently Asked Questions
Yes, in standard statistical terminology, 'rejection region' and 'critical region' are synonymous and used interchangeably.
Yes. For a two-tailed test, the rejection region is split between both extremes (tails) of the sampling distribution. For a one-tailed test, it is located entirely in one tail.
You fail to reject the null hypothesis. This is not the same as 'accepting' the null; it means there is insufficient statistical evidence against it based on your chosen significance level.
Less likely. A smaller rejection region (e.g., from alpha=0.01 vs. alpha=0.05) requires more extreme evidence (a more extreme test statistic) to reject the null hypothesis.
In statistical hypothesis testing, the set of sample outcomes for which the null hypothesis is rejected.
Rejection region is usually formal, technical, academic in register.
Rejection region: in British English it is pronounced /rɪˈdʒɛkʃən ˌriːdʒən/, and in American English it is pronounced /rɪˈdʒɛkʃən ˌridʒən/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Imagine a judge's gavel coming down in a specific 'region' of the courtroom to signify 'REJECT!' the defendant's claim of innocence. The statistical test 'gavel' comes down when the data lands in the rejection region.
Conceptual Metaphor
JUSTICE SYSTEM: The rejection region is like the 'guilty verdict zone' for the null hypothesis. If the evidence (test statistic) is extreme enough to be found in this zone, the null hypothesis is convicted (rejected).
Practice
Quiz
What determines the boundaries of the rejection region?