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The binomial probability mass function (equation 6) provides the probability that x successes will occur in n trials of a binomial experiment.
A binomial experiment has four properties: (1) it consists of a sequence of n identical trials; (2) two outcomes, success or failure, are possible on each trial; (3) the probability of success on any trial, denoted p, does not change from trial to trial; and (4) the trials are independent.
Note that also "no transition" is possible outcome of the binomial experiment.
State Y(t + 1) is the result of a binomial experiment with the probabilities obtained in (ii).
This is difficult to understand because a power calculation can only be done before specifying the outcome of the binomial experiment, and not after.
Event types were generated by the binomial experiment of the two-step algorithm, substituting the CSHs by the increments of the cumulative CSHs.
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The transposition of the beta parameters of the Haldane and the uniform priors in fixed binomial experiments into the beta-J distribution yields bias-corrected versions of these priors in multistage designs.
Statistical entropy is derived from the negative binomial distribution where an experiment with two equally likely outcomes, labeled success or failure, is considered.
The proportion of participants choosing either AB or CE did not differ in Experiment 1A (binomial test, p =.327) and, contrary to the prediction of the noisy-OR rule, a reliably high proportion of participants chose AB over CE in Experiment 1B.
The performance of two-level experiments for binomial responses is explored by investigating the dependence of the determinant of their information matrix on their location, orientation, range, presence or absence of interactions and on the relative allocation of runs to support points, and in particular, on the type of fractionating involved.
To introduce binomial uncertainty into those experiments with an SAR of 0 or 1, we set the binomial probability to 0.1 or 0.9, respectively.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com