# Questions tagged [binomial]

The binomial distribution gives the frequencies of "successes" in a fixed number of independent "trials". Use this tag for questions about data that might be binomially distributed or for questions about the theory of this distribution.

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### Interpretation of R's output for binomial regression

I'm quite new on this with binomial data tests, but needed to do one and now I´m not sure how to interpret the outcome. The y-variable, the response variable, is binomial and the explanatory factors ...
6answers
68k views

### Test if two binomial distributions are statistically different from each other

I have three groups of data, each with a binomial distribution (i.e. each group has elements that are either success or failure). I do not have a predicted probability of success, but instead can ...
4answers
26k views

### Logistic Regression - Error Term and its Distribution

On whether an error term exists in logistic regression (and its assumed distribution), I have read in various places that: no error term exists the error term has a binomial distribution (in ...
5answers
19k views

### Probability distribution for different probabilities

If I wanted to get the probability of 9 successes in 16 trials with each trial having a probability of 0.6 I could use a binomial distribution. What could I use if each of the 16 trials has a ...
2answers
2k views

### Risk of extinction of Schrödinger's cats

I am interested in how uncertainty can be accounted for when considering the risk of extinction of a species. Forgive me for extending a rather tired thought experiment, but at least it's familiar ...
5answers
8k views

### Probability of a run of k successes in a sequence of n Bernoulli trials

I'm trying to find the probability of getting 8 trials in a row correct in a block of 25 trials, you have 8 total blocks (of 25 trials) to get 8 trials correct in a row. The probability of getting any ...
1answer
934 views

### Estimating parameters for a binomial

First of all I'd like to precise that I'm not an expert of the subject. Suppose to have two random variables $X$ and $Y$ that are binomial, respectively $X\sim B(n_1,p)$ and $Y\sim B(n_2,p),$ note ...
2answers
1k views

### Beta as distribution of proportions (or as continuous Binomial)

Beta distribution is related to binomial being also the distribution for order statistics. Probability mass function of binomial distribution is $$f(k) = {n \choose k} p^k (1-p) ^{n-k} \tag{1}$$ ...
5answers
23k views

### Relationship between Binomial and Beta distributions

I'm more of a programmer than a statistician, so I hope this question isn't too naive. It happens in sampling program executions at random times. If I take N=10 random-time samples of the program's ...
4answers
20k views

### Using offset in binomial model to account for increased numbers of patients

Two related questions from me. I have a data frame which contains numbers of patients in one column (range 10 - 17 patients) and 0s and 1s showing whether an incident happened that day. I'm using a ...
1answer
2k views

### Prediction interval for binomial random variable

What is the formula (approximate or exact) for a prediction interval for a Binomial random variable? Assume $Y \sim \mathsf{Binom}(n, p)$, and we observe $y$ (drawn from $Y$). The $n$ is known. Our ...
6answers
12k views

### Binomial confidence interval estimation - why is it not symmetric?

I have used the following r code to estimate the confidence intervals of a binomial proportion because I understand that that substitutes for a "power calculation" when designing receiver operating ...
1answer
14k views

### Fitting a binomial GLMM (glmer) to a response variable that is a proportion or fraction

I'm hoping somebody can help with what I think is a relatively simple question, and I think I know the answer but without confirmation it has become something I just can't be certain of. I have some ...
2answers
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### Removing intercept from GLM for multiple factorial predictors only works for first factor in model

I am running a binomial logistic regression with a logit link function in R. My response is factorial [0/1] and I have two multilevel factorial predictors - let's call them $a$ and $b$ where $a$ has 4 ...
2answers
31k views

### What is quasi-binomial distribution (in the context of GLM)?

I'm hoping someone can provide an intuitive overview of what quasibinomial distribution is and what it does. I'm particularly interested in these points: How quasibinomial differs to the binomial ...
1answer
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### Non-uniform distribution of p-values when simulating binomial tests under the null hypothesis

I heard that under the null hypothesis the p-value distribution should be uniform. However, simulations of binomial test in MATLAB return very different-from-uniform distributions with mean larger ...
2answers
14k views

### Logistic Regression: Bernoulli vs. Binomial Response Variables

I want to perform logistic regression with the following binomial response and with $X_1$ and $X_2$ as my predictors. I can present the same data as Bernoulli responses in the following format. ...
4answers
29k views

### Exact two sample proportions binomial test in R (and some strange p-values)

I am trying to solve the following question: Player A won 17 out of 25 games while player B won 8 out of 20 - is there a significant difference between both ratios? The thing to do in R that ...
2answers
2k views

### Why does the continuity correction (say, the normal approximation to the binomial distribution) work?

I wish to better understand how the continuity correction to the binomial distribution for the normal approximation was derived. What method was used to decide we should add 1/2 (why not another ...
4answers
17k views

### How to assess the fit of a binomial GLMM fitted with lme4 (> 1.0)?

I have a GLMM with a binomial distribution and a logit link function and I have the feeling that an important aspect of the data is not well represented in the model. To test this, I would like to ...
2answers
8k views

### Overdispersion in logistic regression

I'm trying to get a handle on the concept of overdispersion in logistic regression. I've read that overdispersion is when observed variance of a response variable is greater than would be expected ...
2answers
564 views

### Is the normal distribution a better approximation to the binomial distribution with proportions near or far from 0.5?

From the Online Stat Book: I don't understand this: The accuracy of the approximation depends on the values of N and π. A rule of thumb is that the approximation is good if both Nπ and N(1-π) ...
4answers
64k views

### Difference between binomial, negative binomial and Poisson regression

I am looking for some information about the difference between binomial, negative binomial and Poisson regression and for which situations are these regression best fitted. Are there any tests I can ...
1answer
3k views

### Generating correlated binomial random variables

I was wondering if it might be possible to generate correlated random binomial variables following a linear transformation approach? Below, I tried something simple in R and it produces some ...
4answers
29k views

### ANOVA on binomial data

I am analyzing an experimental data set. The data consists of a paired vector of treatment type and a binomial outcome: ...
1answer
16k views

### Overdispersion and Underdispersion in Negative Binomial/Poisson Regression

I was performing a Poisson regression in SAS and found that the Pearson chi-squared value divided by the degrees of freedom was around 5, indicating significant overdispersion. So, I fit a negative ...
2answers
7k views

### How to replicate Stata's robust binomial GLM for proportion data in R?

There is an example on how to run a GLM for proportion data in Stata here: http://www.ats.ucla.edu/stat/stata/faq/proportion.htm The IV is the proportion of students receiving free or reduced priced ...
2answers
974 views

### Can multinomial distribution be simulated by a sequence of binomial draws?

I wonder if single multinomial distribution (I will use the notation from JAGS/WinBUGS, but in fact, this is principial thing rather than of particular language) ...
4answers
17k views

### Maximum likelihood estimation of p in a Binomial sample

Assuming I need to find the ML estimator for p, p being the chance of success in a Binomial experiment $Bin(N,p)$, I would expect my density function to be: $$f(y) = {{N}\choose{y}} p^y(1-p)^{N-y}$$...
2answers
260 views

### The dirty coins and the three judges

All things being perfect, if we want to know if a set of coinage (all coins with the same bias) is biased, and to what degree, we would just use the outcomes and confidence intervals of the binomial ...
1answer
256 views

### Probability of getting between

...2 to 5 questions answered correctly, out of 20 of them? Each question has 5 choices. Probability of getting one right is 1/5. Probability of getting exactly 1 right is ${20 \choose 1} p^1 q^{19}$, ...
4answers
72k views