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How do you determine if something is a binomial experiment?
We have a binomial experiment if ALL of the following four conditions are satisfied:
- The experiment consists of n identical trials.
- Each trial results in one of the two outcomes, called success and failure.
- The probability of success, denoted p, remains the same from trial to trial.
- The n trials are independent.
What are the requirements for a binomial experiment?
The four requirements are:
- each observation falls into one of two categories called a success or failure.
- there is a fixed number of observations.
- the observations are all independent.
- the probability of success (p) for each observation is the same – equally likely.
How to perform a binomial test in R-statology?
A binomial test compares a sample proportion to a hypothesized proportion. The test has the following null and alternative hypotheses: HA: π ≠ p (the population proportion π is not equal to some value p) The test can also be performed with a one-tailed alternative that the true population proportion is greater than or less than some value p.
How to calculate the binomial distribution in R?
The binomial distribution with size = n and prob = p has density. p(x) = choose(n, x) p^x (1-p)^(n-x) for x = 0, …, n. Note that binomial coefficients can be computed by choose in R. If an element of x is not integer, the result of dbinom is zero, with a warning. p(x) is computed using Loader’s algorithm, see the reference below.
How to calculate the sum of two binomial variables?
Let (Bk)k be a sequence of iid Bernoulli distributed random variable with P(Bk = 1) = p for k = 1, 2, … Then X: = B1 + ⋯ + Bn is binomially distributed with parameters n, p and Y: = Bn + 1 + ⋯ + Bn + m is binomially distributed with parameters m, p.
How to compare two sample proportions in binomial test?
Likewise with binom.test (x=8,n=20,p=17/25) says the probability of success is 17/25 which is why these p-values differ. Therefore you are not comparing the two proportions at all.