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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Variance of compound distribution

The binomial distribution describes the probability of $k$ 'success' events given $N$ independent trials, each with a probability $p$ of being a success. The distribution is described by the formula ...
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Minitab question about binomial probabilities

What I have tried: My first instinct was to go to Calc>Binomial distributions> Binomial to get the graph of it. 2 questions: What does the question mean it needs values less than 21? Should ...
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Binomial Logistic regression to Compare results of multiple methods to a known value

I have a "known value" (recorded by a field observer) which I want to compare several methods of data collection with to test for significant differences between methods. Methods: 2 points along a ...
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How do I include measurement errors in a Bernoulli experiment?

I would like to understand how to combine a known measurement error in a Bernoulli experiment with the confidence interval in order to calculate error bars. I am performing an experiment that has two ...
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GLM help on proportional data [closed]

I'm trying to run a GLM on proportional data. I'm analysing how deer vigilance (proportion of 2mins spend vigilant) varies between sexes and also positioning in the herd (Inside Vs Outside). I've ...
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A simple question about MAP and MLE

I recently got this simple question from a friend. But I am quite confused about it. Suppose we toss a coin $N$ times, and got heads $m$ times. Assume the binomial distribution with $p$ which is the ...
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How to address the problem of underdispersion in a binomial GLM (data in proportions)

We explored the effect of seed size, and seed-coat thickness on seed removal rates (proportion of seeds removed) and seed predation rates (proportion of seeds preyed upon)by rodents. Seed size was a ...
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Berry-Esseen bound for binomial distribution

From the Berry-Essen theorem I can deduce $$\sup_{x\in\mathbb R}\left|P\left(\frac{B(p,n)-np}{\sqrt{npq}} \le x\right) - \Phi(x)\right| \le \frac{C(p^2+q^2)}{\sqrt{npq}}$$ with $C \le 0.4748$. My ...
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Why doesn't a sample proportion also have a binomial distribution

In a binomial setting, the random variable, X, that gives the number of successes is binomially distributed. The sample proportion can then be calculated as $\frac{X}{n}$ where $n$ is your sample ...
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Relation between power and sample size in a Binomial Test?

$\beta$ (also called sensitivity or power) is a function of the sample size. It totally makes sense to me when we're performing a regression for example. The intuition is not that clear when we ...
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Analyzing binomial distributed variables

I have the following situation. A subject comes to the clinic at day 1 and is evaluated using a 10 item checklist. The sum of those 10 items is the subjects score. A intervention is performed. The ...
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21 views

Calculate the average rate of success

It sounds like a simple problem but I am unsure about the methodology I should follow. A company developed processor with a new innovative way and they tested the processors to see if they pass the ...
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LRT for one-sided Bernoulli parameter

Suppose $X_1,X_2,...,X_n$ are i.i.d. $\mathrm{Bernoulli}(\theta)$. We are interested in testing the hypotheses $$H_0:\theta\leq\theta_0$$vs. $$H_1:\theta>\theta_0$$ Show that if we use the ...
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1answer
71 views

R: prop.test - Chi-squared approximation may be incorrect

I am trying to compare the proportions of two populations, using prop.test My data is straightforward - first population is 6/26 and second is 15/171. I am trying ...
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Nominal/Categorical Data Set

I have a nominal data set of a sample(species) floating characteristic(vertical floating, horizontal floating, bottom horizontal, and etc.) over a period of time. im interested to study the most ...
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Does binomial distribution have the smallest possible variance among all “reasonable” distributions that can model binary elections?

Imagine an election where $n$ people make a binary choice: they vote for A or against it. The outcome is that $m$ people vote for A, and so A's result is $p=m/n$. If I want to model these elections, ...
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Huge increase in predicting values when removing intercept from a negative binomial model (glmmadmb function in r)

I am trying to fit a negative binomial model for predicting the intensity of deforestation (measured as a number of hectares deforested per year) from population change data, using glmmadmb function ...
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Comparing four classifiers

I have trained and tested four different classifiers, and I would now like to compare them. The classifiers have accuracies 95, 90, 81, 75. I know that there is no unbiased estimator of the variance ...
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Correct Sample Size N in a Relative A/B Test with Binomial Variates

I randomly assign users to two distinct groups and track their return rate to the website (the return rate on each day for each group is simply $\frac{Number Of ReturningUsers}{TotalUsersOnDayZero}$). ...
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Conceptual problem for binomial distribution

I'm reading this book (Implementation: How Great Expectations in Washington Are Dashed in Oakland. 1973) and they discuss how hard it is to gain agreement of actors. They set up a conceptual ...
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What are the effects of continuity correction in binomial meta-analysis in the metafor package?

The metafor package in R can be used to fit the random effects model with the exact binomial likelihood as described in Stijnen et al. (2010). The ...
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Standard Error of the ratio of Binomial variates

What's the right way to compute the Standard Error of the Mean of the ratio of two random variables that follow a binomial distribution? I asked a similar question here using Weibull distributions ...
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Confidence interval for function of the parameter - small sample size

I am trying to come up with a solution for this problem. Consider the following set of random variables: \begin{align*} X_{11},...,X_{1n_{1}}\quad &\text{i.i.d. Bernoulli(1-$e^{-\lambda_{1}}$)}\\ ...
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analytically finding the dispersion of beta distribution in multilevel bayesian model

I want to create a multilevel bayesian model of the format depicted in the in figure below. I am examining # of conversions (out of total number of exposures) in multiple subgroups. The conversion ...
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Distribution of p-values - Binomial test

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 ...
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How to process Binomial-Binomial data on SPSS for hypothesis testing?

There are 2 groups of 100 pregnant women: the first are malnourished and the second are well-nourished. A COHORT research is being done on them to determine if malnutrition is a risk factor for low ...
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Variance of binomial vs. multinomial distribution in cross-validation

Suppose we have a dataset with $N=100$ observations. We do $K$-fold cross-validation with $K=10$ and $K=100$. In the first case, the classification decisions are sampled (can I say it like this?) ...
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Fitting a GLM for binomial data in R

I am an R beginner and out of my depth! I am trying to build a model to analyse data regarding fertility in 2 populations of different levels of sexual selection(M and P), both of which have undergone ...
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Hypothesis test of 2 proportions, with $np < 5$

We are frequently conducting one-tailed hypothesis tests for 2 proportions ($H_0: p_1-p_2=0;\, H_1: p_1-p_2 > 0$). However, $p_2$ is relatively small in terms of $n, x$ and in some cases we find ...
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Is chi-squared valid in this scenario?

I'd like to know whether I am misusing Pearson's chi-squared test. And if so, what should I be doing instead. I've a game-playing program, a "bot", for a zero-sum two-player game. To improve it, many ...
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1answer
15 views

Comparing survival times in small samples for two groups

I am working on a dataset of big cats. 18 cats have a particular antigen and the rest (58) do not. We have contact times for when blood samples were taken - so when the cats were identified as having ...
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1answer
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Censored Binomial model - log likelihood

I have a dataset with multiple samples of batches of observations (e.g. one batch of 20 obs., one batch of 50 obs,, etc.). There is a probability that the batches have contaminated observations, with ...
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What measures the y-axis in stat_smooth, ggplot2 in R? [closed]

I am fairly new with logistic regression. I have a binary response. And did this plot. The binary response is: Y = 0: The student fails Y = 1: The student succeed ...
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Problem with pbinom in R (and binom.dist() in Excel)

I understand that the R-function pbinom(0, 100, 0.5, lower.tail=FALSE) returns the probability of getting 0 or more heads in 100 trials. R gives the correct ...
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Beta-binomial logistic regression model for binomial data with small samples

I have fitted a nonlinear beta-binomial logistic regression model on data y_i: y_i ~ beta-binom(n_i,mu_i,\Phi) where mu_i = exp(\eta_i)/(1+exp(\eta_i)) , and \eta_i=\beta_0+\beta_1/(1+exp(\beta_2x_i ...
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Bivariate distribution: beta and binomial

Consider a pair of RVs $X$ and $Y$, with the following conditional distributions: $$X | Y=y \sim Binom(L, y)$$ $$Y | X=x \sim Beta(\alpha + x, \nu)$$ where $L$, $\alpha$, and $\nu$; are all ...
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Post-hoc test after a GLM with binary data

I have run various logistic regressions (GLM) from the binomial family and they have produced some very interesting results. I would now like to run post-hoc tests to find out which levels of the ...
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Probability of students in a test

So I know this may seem like a simple question, but i'm a student and the difference seems trivial but confusing to me. So basically you have 2 types of students in a class, guessers and swaters. ...
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Generalised Likelihood Models

Why would you use a re-scaled binomial distribution rather than just the standard binomial distribution as the distributional assumption in a GLM?
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rbinom() produces NA values. What's wrong?

I have to generate RV from a binomial distribution with R . I have a vector for $n$ and a vector for $p$ and for each component I have to generate a random variable. My idea was the following for ...
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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} ...
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Estimate probability mass function from observed samples?

This question is related to but is distinct from Estimation of probability mass function using finite samples. As in the related question, suppose we have a discrete random variable $X$ with known ...
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binomial confidence including run to run variation for overdispersion

I'm trying to determine the model to correct a confidence interval (binomial proportion for example) but to also include overdispersion affects that arise from a Run-to-Run variation. Example, case ...
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192 views

Probability distribution for a proportion based on (continuous) quantities

I have a problem related with probability distributions and parameter estimation, which comes from a real case. I would be very grateful if you could help me. Let us suppose that we have a continuous ...
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Binomial regression does not give coefficients for all IVs [duplicate]

I have a dataset with the dependent variable presence / absence (0 and 1) for a certain species. I have three categorised IV's (2 IV's with 3 categories and 1 with 2 categories). To test the response ...
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How to calculate the absolute central moment of a Binomial distribution?

There is an experiment. The coin is tossed $n$ times with $p = 0.5$. The experiment is repeated $k$ times. I need to calculate the average central moment. For example, let $n = 5$ and $k = 3$. $[0, ...
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Expectation-Maximization Algorithm for Binomial

I have a multinomial distribution with four outcomes, with a pdf: $$p(x_1,x_2,x_3,x_4)=\frac{n!}{x_1!x_2!x_3!x_4!}p_1^{x_1}p_2^{x_2}p_3^{x_3}p_4^{x_4}, \sum_{i=1}^4x_i=n, \sum_{i=1}^4p_i=1$$ The ...
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Molecules movement distribution puzzle

Let's say I have blood samples of whiteblood cells ($x$) and viruses ($v$). Space has been discretized in $LL$ spaces. They have a $p_v$ probability of interacting when found in the same space. I want ...
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Which test should I use to determine whether multiple binomial experiments results are different, with p not equal to 0.5 for all? [duplicate]

I have four subject A,B,C,D, I asked 500 students whether they like each subject, there are two choices: Yes/No. I want to test, do students have a preference for any of A/B/C/D? Originally I used ...