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Additionally, 95% confidence intervals (CIs) were calculated using a binomial approximation of a normal distribution for acute and chronic diagnoses and medication utilization.
The statistical significance of GO group enrichment is determined using a binomial approximation to the hypergeometric distribution with a p-value cut-off of 0.005, as described in detail elsewhere (www.dchip.org) [36].
Complexity here depends on the statistical method used to compute S j (e.g. O(h) using a binomial approximation).
Using a binomial approximation, and assuming 479 clusters with an average of 42 records per cluster and a baseline survival proportion of 50%, this gives 85% power at 0.05% significance to detect a difference in survival proportions of 2%.
We first present in details how the delta-method can be used to get a Gaussian approximation for the distribution of S N (using a binomial approximation to compute the pattern statistics).
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In this paper, we have chosen to use a binomial approximation as it provides an expression which is analytically differentiable and is known to be a good heuristic to the problem [ 8].
Survival was modeled using a binomial error distribution.
A binomial approximation to the normal distribution was used to calculate the Z-score where: A Z-score > 1.64 (P < 0.05, one-sided test) was considered significant when testing for overrepresentation of a given HT.
In this case, we can still use a Binomial or Poisson distribution but the dependencies lead to an error in the approximation.
We calculated 95% CIs for standardized prevalence rates using a normal approximation and Breslow-Day standard errors, after being modified to use a binomial assumption for the variance of the crude stratum-specific rates (9).
The main advantage in using the binomial approximation is that the confidence intervals can be estimated from TP and P using standard methods and implementations.
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