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Experimental Design and Analysis in Aquaculture
Published in Hillary S. Egna, Claude E. Boyd, Dynamics of POND Aquaculture, 2017
The pooled variance allows for comparisons of treatments with different sample sizes (n1 and n2). Conceptually, consider two ponds (numbered 1 and 2) each containing thousands of fish. You sample both ponds and get a difference between mean fish weight between the ponds. You sample both ponds several more times and get more differences between mean fish weights. The t-test calculates the standard error of the difference between means using the sample variances for each pond. In practice, however, each pond is usually sampled just once. The probability that the true means for ponds 1 and 2 are significantly different from each other is based on the ratio of the observed difference between sample means from the two ponds and the standard error of the difference between means (Equation 17). In other words, the difference between mean fish weights in ponds 1 and 2 is more likely to be significant as the variability of fish weights within each pond gets smaller.
Basic Univariate Statistics
Published in Jhareswar Maiti, Multivariate Statistical Modeling in Engineering and Management, 2023
Let, σ12=σ22=σ2, but σ2 is unknown. We calculate pooled variances (sp2) as an estimate of σ2. The pooled variance (sp2) issp2=(n1−1)s12+(n2−1)s22n1+n2−2
Comparative Analysis of Standard and Advanced USL Methodologies for Nuclear Criticality Safety
Published in Nuclear Science and Engineering, 2023
Jeongwon Seo, Hany S. Abdel-Khalik, Ugur Mertyurek, Goran Arbanas, William Marshall, William Wieselquist
For the parametric methodology, the inverse-variance weighted average is −636 pcm, setting the nonconservative parameter to be zero. The pooled variance consists of two parts, one accounting for the weighted standard deviation and the other for the spread of the calculated responses. The evaluation uncertainty for all the models was selected to be 250 pcm, yielding the same value for the weighted standard deviation. By adding the impact of the response spread, the pooled variance increased to 535 pcm, which is approximately two times larger than the evaluation uncertainty. Therefore, the final parametric CM is calculated as
“Macro-structure” of developmental participation histories and “micro-structure” of practice of German female world-class and national-class football players
Published in Journal of Sports Sciences, 2019
Descriptive data include frequencies, means and standard deviations. Differences between NT and BL players were analysed using χ2, unpaired t-test or, for non-uniform (skewed) data distribution, the non-parametric U-test. Effect sizes (Cohen, 1992) are reported as Cohen’s d using pooled variance. To evaluate potential multivariate associations of senior performance with the different sport activities, a binary logistic regression analysis was conducted (dependent variable: NT/BL). Based on the hypothesised predictions, stepwise introduction of independent “macro-structure” and “micro-structure” variables considered football before other sports and within each of them coach-led practice before peer-led play variables: 1. accumulated coach-led football practice; 2. proportions of play, physical conditioning, and drill-type skills practice within coach-led football practice (3 variables); and period of participation (years) and accumulated volume (hours/sessions) of each of: 3. peer-led football play (2 variables); 4. coach-led practice in other sports (2 variables); and 5. peer-led play in other sports (2 variables), in each case until age 18 years (criterion for variable exclusion p > 0.10). Analyses were performed with SPSS 25.0. All statistical hypothesis testing was two-tailed. A value of p < 0.05 was considered statistically significant.
In-control performance of the joint Phase II
Published in Quality Engineering, 2018
Lorena D. Loureiro, Eugenio K. Epprecht, S. Chakraborti, Felipe S. Jardim
We consider that in both cases the unknown process standard deviation is estimated by Sp, the square root of the pooled variance of the Phase I samples. Mahmoud et al. (2010) showed that the three estimators Sp (biased), Sp/c4 (unbiased), and c4Sp (with the smallest mean squared error), where the value of c4 to be used is for m(n − 1) d.f., are more efficient than the estimator and “are virtually equivalent for combinations of values of m and n typically encountered in practice”, and recommended the use of any of these three instead of the former. Although the former () is the traditional estimator of the in-control process standard deviation with S charts (see Montgomery 2009), we see no point in using it instead of a more efficient one, given that the effort in computing one or the other is the same. Indeed, the Sp estimator has been the one considered in some of the most recent papers on the effect of estimation over the performance of control charts (e.g., Faraz, Woodall, and Heuchenne 2015). Anyway, some results for the estimator are available from the authors.