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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Three binomial random variables: test null that no two have equal mean

I have a dummy variable for health (0 or 1), and for each observation a treatment (one of three possible treatments for each observation). I want to test the null hypothesis that the proportion (mean) ...
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26 views

Sample size determination contradiction

I'm struggling with a contradiction when trying to determine a sample size when proportion is small. If I use binomial formula: $n = p(1-p)z^2/ME^2$ then the smaller the proportion - the smaller ...
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30 views

Binomial proportion confidence interval

I have a sample and I've classified each member into 3 groups A,B,C. To get uncertainties on the percentages of these groups, I've been told I should use the wilson score interval. As someone who is ...
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1answer
22 views

S shaped curve for logistic regression

I was trying to fit logistic regression with a binary response variable and a continuous predictor variable. But when I plotted the fitted probabilities vs the predictor, I got an almost straight line ...
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1answer
38 views

Determine if many coins are fair

Imagine I have many coins ($>100$), and for each coin I have the data: $(n_{\rm heads}, n_{\rm tails})$ where $\sum(n_{\rm heads}, n_{\rm tails})$ is decreasing for each next coin. Any one of the ...
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18 views

How to calculate standard errors of a non-linear model prediction?

I'm trying to understand how to show the prediction error of a model fit in R using the non-linear least squares function nls. Although there is an argument ...
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7 views

How to measure whether the YES/NO (Bernoulli trials) answers have converged about their estimated mean for a specified error bound?

I have a questionnaire with questions that require a Yes or a No answer (1 or 0 input) from participants. From the set of answers I want to use the mean, $\mu$, estimated from the data for the ...
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1answer
49 views

Are binomial and McNemar's tests right for my data?

I have performed an experiment, where I have real and synthesised movie data. My participants were shown either a real movie, or a synthesised movie (of talking heads), in a random order, and had to ...
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19 views

How to handle underdispersion in GLMM (binomial outcome variable)

I'm working on the following model in R: ...
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32 views

A test for a binomial r.v. vs. sum of two binomial r.v.'s?

Suppose I draw a sample from one of the two possible random variables $X$ or $Y$ where $X\sim\text{Binomial}(p,N)$ and $Y=A+B$ with $A\sim\text{Binomial}(p,M)$ and $B\sim\text{Binomial}(q,N-M)$. ...
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56 views

At least probability question

At a university 60% of the students are male and 40% are female. If ten students are selected at random, What is the probability that we have exactly seven females? I tried $0.4^7\cdot0.6\cdot3 = ...
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152 views

Probability enemy territory captured in X turns

I am playing Warlight online (something like Risk), and my goal is to create a bot which plays against other bots. ...
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23 views

The number of coin tosses needed if the proportion of heads is to lie within 0.05 of p with probability at least 0.9?

There's a question I'm not really sure if I did it right or even understand what its trying to say. There is a coin which produces heads with an unknown probability $p$. How many times should we ...
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22 views

Interpretation of coefficient sign change and order of terms

I have a logistic regression with data that are kind of like this: ...
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2answers
139 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 ...
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2answers
122 views

How does logistic regression use the binomial distribution?

I'm trying to understand how logistic regression uses the binomial distribution. Let's say I'm studying nest success in birds. The probability of a nest being successful is 0.6. Using the binomial ...
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1answer
48 views

Simple “yes / no” question. Uncertain how to analyze the results

I am in the midst of conducting a study which compares content in a printed catalog of records to content in a much larger online catalog of similar records. I have randomly selected 50 entries from ...
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1answer
42 views

R: generate binomial sample with (pretty) exact probability

When I simulate normal data in R, I make sure that the sample have the exact mean and sd of the sampling distribution: x = scale(rnorm(n))*sd + mean. I want to do ...
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2answers
41 views

Comparing different conditions on a binomial distribution

I have some data where I have tested a binomial random variable under 4 conditions. The null hypothesis is that they all have equal means, alternative hypothesis is that one or more means differ from ...
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70 views

Non-parametric estimators for time-varying binomial proportion

I have a bunch of count data associated with time intervals (potentially overlapping and of variable lengths), say $(s_i, t_i, n_i, N_i)$ where $N_i$ is a count of the total number of events ...
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23 views

Margin of error for non-dichotomous data

I am trying to calculate the margin of error for specific survey questions. I know how to calculate this if the data are dichotomous (i.e., a 75-25 or 60-40 split). But how do you deal with questions ...
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1answer
47 views

Binomial GLMM: Model validation & ceiling effect

My data has a binary response acc(correct/incorrect), one continuous predictor score, three categorical predictors (...
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1answer
85 views

Binomial GLMM with categorical predictors: p-values?

My data has a binary response (correct/incorrect), one continuous predictor score, three categorical predictors (race, ...
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38 views

The probability that one bernoulli process has a higher p than another?

I have two data generating processes that are independent Bernoulli processes with probabilities of success $p_A$ and $p_B$. I am taking repeated samples from these two data generating processes, so ...
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32 views

Binomial mixed model with categorical predictors: model selection and getting p-values [closed]

My data has a binary response (correct/incorrect), one continuous predictor (with NaNs) and several categorical predictors. I want to add a random intercept for a ...
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1answer
52 views

Poisson vs Binomial for rare events

From Poisson's postulates, we know Poisson works for rare events. However, we also know binomial is an approximation of Poisson when the probability of an event is small. So can we use binomial and ...
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22 views

Relation between mean of the hypergeometric distribution and binomial

The mean of the hypergeometric distribution is: $n \frac{K}{N}$ where: $n$ is the number of draws $K$ is the number of successes N is the size of the finite population. As the population size, ...
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1answer
60 views

Binomial count data - use glmer, lmer or just average it all?

I'm new to both mixed-effects models and R, so please excuse me if this is a bit of a silly question! I'm struggling with choosing the best method to analyse my data for a speech perception study, and ...
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49 views

Modeling binary outcomes - inaccurate model when using logistic regression?

I am trying to model the probability of a binary outcome with the independent variable being an hour variable. I understand that linear regression is not the correct method for this type of task (I ...
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2answers
51 views

Probability of getting an equal number of ones and twos from 10 dice rolls

If a die is rolled 10 times, how do you calculate the probability that an equal number of ones and twos occur? Let A be the number of ones, B the number of twos I first thought it might be equal to ...
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1answer
66 views

Computation of a binomial probability: nan result

I am computing binomial probabilities for many parameters. I am using the library scipy.stats: b = scipy.stats.binom(n,p) probability = b.pmf(k) I have noticed ...
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1answer
182 views

lme4: glmer problems with offset()

this is my first post, so I hope everything is in the right format. I have some problems with glmer and don't know how to fix it, so I hope somebody can help me out with this. I could not find an ...
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1answer
26 views

Question on Probability and Binomial

I'm doing a self-study. I am currently at part IV of the question. After several attempts, I still can't seem to figure out why $p = 0.75$ for part IV. QUESTION SHEET ANSWER KEY
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368 views

Why do I always fail to reject the null hypothesis on a binomial test for `p=.5`?

When performing a two-tailed test on a binomial process with p=.5, why are my p-values all over the place, and I virtually never reject the null hypothesis? I answered a question on stackoverflow ...
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30 views

Sample size calculation to demonstrate reliability of physical test method

I'm preparing a procedure for validating attribute physical test methods (e.g. vision system) by demonstrating the reliability of the test method to detect known good/bad samples.I have sourced the ...
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1answer
23 views

Binomial regression with categorical explanatory variable

When doing a multiple binomial regression, is it possible to do the regression with a categorical variable as x at the same time as y is categorical? Most of my x-variables are continuous except for ...
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Is there a way to calculate the probability of drawing X+ > y% of time given X- [closed]

Say I have a bag with 10 balls (either red or blue), and I know that there are 8 balls that are red. How do I calculate the probability of drawing a a red ball $>75\%$ of the time if the first ball ...
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23 views

Exposure in Negative Binomial regression and other distributions

For a Poisson regression we can model exposure $\epsilon_i$ in observation $Y_i$ as $Y_i \sim Poisson(\epsilon_i*\lambda)$. For instance, in a Poisson regression, if we observe: $y = \begin{bmatrix} ...
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30 views

plot for a binomial glm

Can any one help? I am trying to graph the probability of predicting a male bird based on tarsus length according to the GLM. I have run a GLM and I am not sure why I can't plot the predictions. My ...
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1answer
26 views

Scoring validation database based on estimates from test database in R

I divided my dataset into Test and Validation (50-50 split). I ran glm function (link=binomial) on Test dataset and got the parameter estimates. How do I score the Validation dataset based on these ...
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1answer
71 views

X is binomially distributed, and Y is binomially distributed. What distribution does X+Y follow?

We know that $X$ follows $\mathrm{Bin}(n_1,p_1)$, $Y$ follows $\mathrm{Bin}(n_2,p_2)$, $X$ and $Y$ are independent. What does $X+Y$ follow? I know the answer, that if $p_1=p_2=p$ then $X+Y$ follow ...
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41 views

Random forest for binomial data

I have data where the response is of the form (k,n) - k successes, n trials for a given subject. The covariates are just some subject-specific predictors. Is it possible to use randomForest for ...
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64 views

How to plot binomial regression model in R

I´m trying to visualize a glm model with a binomial response variable, I want to put a line in the plots, but neither lines or ...
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20 views

Sports winning percentage distribution

I am doing a study where I am measuring parity in sports. To do this I am looking at how well a year's winning percentages (WP) are distributed. I am currently comparing them to a binomial ...
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1answer
34 views

Variance of average of Bernoulli variables

What is the variance of the average of n Bernoulli distributed random variables Ber(p)? So Var(sum(xi)/N)
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A model for multiple nested proportions?

I think this is more of a stats advice than code question so I've posted here rather than SO. My data looks like this (~300 more sample rows). ...
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1answer
98 views

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 ...
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41 views

Hierarchical model: question on frequentist estimation

I am interested in understanding the differences between Bayesian and Frequentist estimation in the context of hierarchical models. Consider $n$ subjects, where for subject $i$ there are $k_i$ ...
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Deep learning: what is done with sampling in practice?

I have come against a small issue when implementing some deep learning techniques. Sometimes, if one is implementing a classic binary-binary Restricted Boltzmann Machine (RBM), the sampling ...
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Variance of sample proportion decreases with n but of a count increases with n - why?

I've got an intuitive block with this. For a binomial problem, the standard deviation of a count is $\sqrt{np(1-p)}$. Conversely, the standard deviation of the sample proportion decreases with ...