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Phenomenological Creep Models of Fibrous Composites (Probabilistic Approach)
Published in Leo Razdolsky, Phenomenological Creep Models of Composites and Nanomaterials, 2019
In statistics, a binomial proportion confidence interval is a confidence interval for a proportion in a statistical population. It uses the proportion estimated in a statistical sample and allows for sampling error. There are several formulas for a binomial confidence interval, but all of them rely on the assumption of a binomial distribution. In general, a binomial distribution applies when an experiment is repeated a fixed number of times, each trial of the experiment have two possible outcomes (labeled arbitrarily success and failure), the probability of success is the same for each trial, and the trials are statistically independent. The simplest and most commonly used formula for a binomial confidence interval relies on approximating the binomial distribution with a normal distribution. This approximation is justified by the central limit theorem. The formula is: p¯±Z1-α/2p¯(l-p¯)n $$ \bar{p} \pm Z_{{1 - \alpha /2}} \sqrt {\frac{{\bar{p}(l - \bar{p})}}{n}} $$
Relative age effect reversal on the junior-to-senior transition in world-class athletics
Published in Journal of Sports Sciences, 2023
Paolo Riccardo Brustio, Mattia Stival, Gennaro Boccia
Part II:Successful junior-to-senior transition rates among the different birth quartiles were defined by calculating how many junior athletes ranked in the Top 200, Top 100 and Top 50 of the Under 18 remained at the top level in the Senior category (>20 years old). To give a broad view of the transition rates, the binomial proportion confidence interval (90% CI) for each quartile was calculated to describe the proportion of athletes able to maintain the top levels in the Under 18 and Senior categories. Finally, a series of binary regressions with logit link were performed to ascertain how the transition rates were affected by the birth quartile. Gender, discipline, birth decade and continental birth place entered the model as covariates. Thus, considering the Top 200, Top 100 and Top 50 levels of performance separately, transition rate (i.e., yes or no) was entered in the model as the dependent variable, while birth quartile (i.e., Q1, Q2, Q3 and Q4), gender (i.e., male and female), discipline (i.e., sprinters and jumpers), the decade of birth (i.e., the 1980s and the 1990s) and nation of birth (i.e., Europe, Asia, Africa, Oceania and America) variables were entered as independent factors.