ACCEPTANCE REGION Meaning and
Definition
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Acceptance region is a concept in statistical hypothesis testing, specifically in the field of statistical inference. It refers to a range of values within which the null hypothesis is accepted or deemed credible, based on the observed data or test statistic. In hypothesis testing, the acceptance region is formulated to determine the statistical significance of an observed sample or experimental result.
When conducting a hypothesis test, researchers propose a null hypothesis, which assumes that there is no significant difference or effect between the observed data and a specified population parameter. To evaluate the null hypothesis, a statistical test is performed, resulting in a test statistic.
The acceptance region is then defined by selecting a certain significance level, often denoted as α. This significance level represents the probability of rejecting the null hypothesis when it is actually true. The acceptance region is determined by calculating critical values or regions within the test statistic’s distribution, such as t-distribution or normal distribution, depending on the type of test.
If the calculated test statistic falls within the acceptance region, the null hypothesis is accepted, meaning that there is insufficient evidence to reject it. Conversely, if the test statistic falls outside the acceptance region, the null hypothesis is rejected in favor of the alternative hypothesis, indicating that there is statistically significant evidence to suggest a difference or effect.
The acceptance region plays a crucial role in hypothesis testing as it helps researchers make sound conclusions about the population characteristics or treatments being studied while minimizing the chances of committing a Type I error (erroneously rejecting a true null hypothesis).
Etymology of ACCEPTANCE REGION
The etymology of the phrase "acceptance region" can be traced back to the individual words that constitute it.
1. Acceptance: The word "acceptance" originates from the Latin word "acceptantia", which is derived from the verb "accipere", meaning "to receive". In English, it refers to the act of receiving something willingly or approvingly, often used in the context of accepting an offer, idea, or belief.
2. Region: The word "region" comes from the Latin word "regio", which means "direction" or "boundary". It refers to a specific area or part of a larger whole, typically having distinct characteristics or boundaries.
When combined, "acceptance region" refers to a specific area or range of values within a statistical test where a null hypothesis is accepted or not rejected, often used in hypothesis testing.
