Estimated maximum tolerable error and minimum sample size .

Therefore, for the parameter to be useful, the maximum allowable error and minimum sample size have to be experimentally realistic.

To estimate the error and sample size , we calculated the propagation of error in COOPu and COOPC, and used them in the student t-test to calculate statistical significance.

It is thus of interest to estimate the total size of H, and the relation between the sampling size and the portion of H that we actually observe.

Formally, the expected number of unique haplotypes (U(R)) in a sample size (R) can be estimated, assuming a truncated power law formalism as defined above, to be (see Sl—S3 Texts):

Further, estimates of the power law eXponent converged before the full sample size was analyzed (Table 3 and 83—88 Figs).

Comparison of computed and observed expected number of haplotypes in a sample of size R : U(R)forthe European American population for different sample sizes R. The gray squares are observations.

An important aspect of Eq 7 is that it does not saturate until the sample size is close to the full population size.

U(R) Expected number of unique haplotypes in a sample size of R.

R Sample size .

From the population we extract two measures—the haplotype frequency distribution (B) and the number of unique haplotypes as a function of the sample size (C).

We then fit the obsen/ed unique haplotype cun/e (C) with an log(observed (R’)) for different values of sample sizes R'.

We then validated that the resulting values fit the observed distribution all the way to the full sample size (7.8e6) and extrapolated it to the total European American population as defined by the Census [22].

We study non-neutral stochastic community models, and show that the presence of non-neutral processes is detectable if sample size is large enough and/or the amplitude of the effect is strong enough.

The power of a statistical test generally depends on three factors: first, the sample size ; second, statistical significance as measured by the threshold p-value used to assess significance; and third, the effect size, which quantifies departures from the null hypothesis.

Our results highlight the fact that the parameter I plays a more complicated role for these models than the sample size in standard power calculations, because the power does not always increase monotonically with I (Fig.

This means that the community size I plays a nonlinear role and is not a straight analogue of the sample size in standard statistical tests, so statistical power does not necessarily increase monotonically with I.

Our power calculation provides an estimate of the smallest sample size that is needed to detect non-neutrality of known intensity, and of the range strengths of non-neutrality needed to reject neutrality for a given species abundance data set.

The strength of non-neutral processes affects the sample size that is required in order to have a good chance of rejecting the neutral hypothesis (see Fig.

This appears counterintuitive because statistical power should increase monotonically with sample size .

The power of a test will depend on the magnitude of the deviation from the null hypothesis —the so-called effect size—and on the quality of the data at hand, typically, sample size .

in meta-analysis) difference in underlying sample size , if such effects are present.

However, despite growing sample sizes , the genetic variants discovered by GWAS generally account for only a fraction of the total heritability of a phenotype [2,3].

More than anything, GWAS has shown that many phenotypes, such as height [4], schizophrenia [5] and BMI [6] are highly polygenic and influenced by thousands of genetic variants with small individual effects, requiring very large sample sizes to detect them.

Gene analysis was performed on the CD data, and a joint empirical distribution gene SSM values was generated using 4,611 permutations of the phenotype (since the sample size of the CD data is 4,611).

Gene analysis was performed on the CD data, and a joint empirical distribution of the gene SSM values was generated using 4,611 permutations of the phenotype (since the sample size of the CD data is 4,611).

This result is likely due to the high noise level and low sampling size for that class, which dilutes discriminatory features between the mid/late exponential and stationary phases.

This is expected, since that class corresponds to samples that either are missing data or represent classes that have low sample sizes and are grouped together.

To adjust the non-biological experimental variation with the consideration of large number of datasets with a few samples, we used ComBat that is developed under Bayesian framework and is known to be robust to outliers in small sample sizes [62].

Classifier performance and sample size .

These differences are not likely due to sample size effects in the relatively small number of patient samples in this study because the univariate marginals and the bivariate marginal estimates are calculated with high precision in each sample due to the extremely high coverage afforded by deep sequencing and the very narrow bounds imposed on the bivariate probabilities by the univariate probabilities.

But, as the total sample size tends to infinity, ranking based on LR is asymptotically equivalent to ranking based on Fisher’s exact test of independence [64].

Therefore, the proposed procedure for deep sequencing data differs from previous analyses of MSA data [3] mainly in the necessary step of constructing lower and upper probability tables and, to a lesser extent, in the use of mutual information for ranking correlations in probability tables without depending on the total sample size .

An estimator that produces estimates that are, on average, closer to the truth for a given sample size is said to be more efficient than other estimators.

We drew 30 independent samples with sample sizes 11 = 250, 500, 1000, 2000, and 4000 from each model and computed the loss €(C, Z) for each of the five estimators.

With increasing sample sizes , all estimators converged to the ground truth (zero loss) but the estimators with correct structure outperformed the others even for large samples.

Most proposed methodologies require the collection of new data sets and thus are limited in sample size , making them difficult to validate.

The majority of currently suggested approaches are limited in sample size , and require the time consuming collection of large new data sets (such as multiple biopsies from single tumours) for validation and proof of concept.

The clinical assessment of intra-tumour heterogeneity also poses a significant challenge, with current eXperimental approaches requiring multiple biopsies per tumour leaving them severely limited in sample size [17—19].