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Applying Newton's binomial formula to the left-hand-side of (14) yields the left-hand-side of (13).
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The Sign test uses the binomial formula to check whether min{x, N-x} would have been expected to have occurred by chance if the two possible outcomes were equally likely; if this is not the case then we can assume that the two methods are significantly different (two-tailed test) or that one method is significantly better than the other (one-tailed test).
LQAS applies cumulative probabilities calculated with a binomial formula to select small sample sizes and decision criteria for judging a group of providers.
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Qualitative variables were summarized as percentages and associated with 95% confidence intervals (95% CI, provided in squared brackets) calculated with an optimized binomial formula similar to that presented in [ 28].
The approximation of the binomial formula by the normal distribution is guaranteed by the Central Limit Theorem.
Because we know that the probability of heads and tails are the same, (or that each of the 16 outcomes is equally likely) we can ignore the second half of the binomial formula with the probabilities.
Exact binomial probabilities for the situations of n out of n genes were calculated in each sample using the standard binomial formula, where the n is the number of genes identified using ESTs in each sample, and the probability that the differentially expressed gene of ESTs will exist in the same sample type of the MPSS is the proportion of the DES among total MPSS in each sample.
When it happens that (left| mathbf {a} right| in mathbb {N}_{0}) expansion by the binomial formula and application of the Cauchy integral formula completes the proof of Theorem 1.
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The first part of the binomial formula may look unfamiliar this is the binomial coefficient and is often stated as 'n choose k').
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com