What is a Noncentrality Parameter?
A noncentrality parameter (NCP) is a way to distinguish noncentral distributions, which have nonzero means, from their “central” counterparts which have zero means. In other words, if a population mean is μ0, then the NCP represents the normalized difference between μ0 and μ.
If no NCP is stated, it’s usually assumed the distribution is the default: a centralized distribution.
The noncentrality parameter, usually denoted as δ, is used in many areas of statistics, like hypothesis testing and sample size calculation . In power analysis, many equations are stated in terms of the NCP . The NCP is also used to find confidence limits for effect sizes, because effect sizes are linear functions of noncentrality parameters .
Noncentrality Parameter in Hypothesis Testing
In a hypothesis test, the noncentrality parameter describes the degree of difference between the alternate hypothesis (H
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 Luh, W. & Gou, J. (2011). Developing the Noncentrality Parameter for Calculating Group Sample Sizes in Heterogeneous Analysis of Variance. Journal of Experimental Education, v79 n1 p53-63 2011.
 Newsom, J. (2020). Power. Retrieved November 30, 2021 from: http://web.pdx.edu/~newsomj/uvclass/ho_power.pdf
 Howell, D. Confidence Intervals on Effect Size.
Stephanie Glen. "Noncentrality Parameter: Definition" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/noncentrality-parameter-definition/
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