Attributes Control Charts with Large Sample Sizes

1996 ◽  
Vol 28 (4) ◽  
pp. 451-459 ◽  
Author(s):  
Peter A. Heimann
Keyword(s):  
Control Charts ◽  
Sample Sizes ◽  
Large Sample

scholarly journals High heterogeneity undermines generalization of differential expression results in RNA-Seq analysis

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Weitong Cui ◽  
Huaru Xue ◽  
Lei Wei ◽  
Jinghua Jin ◽  
Xuewen Tian ◽  
...  
Keyword(s):  
Gene Expression ◽  
Differential Expression ◽  
Small Sample ◽  
Differentially Expressed ◽  
Cancer Type ◽  
Rna Seq ◽  
Sample Sizes ◽  
Large Sample ◽  
Expression Levels ◽  
Gene Expression Levels

Abstract Background RNA sequencing (RNA-Seq) has been widely applied in oncology for monitoring transcriptome changes. However, the emerging problem that high variation of gene expression levels caused by tumor heterogeneity may affect the reproducibility of differential expression (DE) results has rarely been studied. Here, we investigated the reproducibility of DE results for any given number of biological replicates between 3 and 24 and explored why a great many differentially expressed genes (DEGs) were not reproducible. Results Our findings demonstrate that poor reproducibility of DE results exists not only for small sample sizes, but also for relatively large sample sizes. Quite a few of the DEGs detected are specific to the samples in use, rather than genuinely differentially expressed under different conditions. Poor reproducibility of DE results is mainly caused by high variation of gene expression levels for the same gene in different samples. Even though biological variation may account for much of the high variation of gene expression levels, the effect of outlier count data also needs to be treated seriously, as outlier data severely interfere with DE analysis. Conclusions High heterogeneity exists not only in tumor tissue samples of each cancer type studied, but also in normal samples. High heterogeneity leads to poor reproducibility of DEGs, undermining generalization of differential expression results. Therefore, it is necessary to use large sample sizes (at least 10 if possible) in RNA-Seq experimental designs to reduce the impact of biological variability and DE results should be interpreted cautiously unless soundly validated.

Control Charts for Poisson Count Data with Varying Sample Sizes

2010 ◽  
Vol 42 (3) ◽  
pp. 260-275 ◽  
Author(s):  
Anne G. Ryan ◽  
William H. Woodall
Keyword(s):  
Count Data ◽  
Control Charts ◽  
Sample Sizes ◽  
Poisson Count

Very large sample sizes

BMJ ◽  
2009 ◽  
Vol 338 (feb25 2) ◽  
pp. b737-b737 ◽  
Author(s):  
J. Fletcher
Keyword(s):  
Sample Sizes ◽  
Large Sample

Concentration inequalities for the empirical distribution of discrete distributions: beyond the method of types

2019 ◽  
Vol 9 (4) ◽  
pp. 813-850 ◽  
Author(s):  
Jay Mardia ◽  
Jiantao Jiao ◽  
Ervin Tánczos ◽  
Robert D Nowak ◽  
Tsachy Weissman
Keyword(s):  
Sample Size ◽  
Empirical Distribution ◽  
Discrete Distributions ◽  
Concentration Inequalities ◽  
Sample Sizes ◽  
Alphabet Size ◽  
Large Sample ◽  
Kl Divergence ◽  
The Difference ◽  
True Distribution

Abstract We study concentration inequalities for the Kullback–Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes of sample size $n$ and alphabet size $k$, and the improvement becomes more significant when $k$ is large. We discuss the applications of our results in obtaining tighter concentration inequalities for $L_1$ deviations of the empirical distribution from the true distribution, and the difference between concentration around the expectation or zero. We also obtain asymptotically tight bounds on the variance of the KL divergence between the empirical and true distribution, and demonstrate their quantitatively different behaviours between small and large sample sizes compared to the alphabet size.

What's the Score?

2000 ◽  
Vol 21 (1) ◽  
pp. 57-58
Author(s):  
David Birnbaum
Keyword(s):  
Confidence Interval ◽  
Infection Rate ◽  
Binomial Distribution ◽  
Sample Sizes ◽  
Negative Numbers ◽  
Large Sample ◽  
Infection Surveillance

AbstractIf you have calculated a confidence interval for an infection rate and found the interval extending into meaningless negative numbers, chances are the error is due to use of approximation formulae. Many of us unknowingly were taught to use the Wald approximation, which does not always approximate the exact binomial distribution accurately. Poor approximation can occur in infection surveillance at both small and large sample sizes.

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