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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How to combine/pool binomial proportion confidence intervals after multiple imputation?

After I multiply imputed my dataset m times I wanted to calculate a binomial proportion confidence interval. I did that formerly using the Hmisc::binconf() function ...
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Probability than empirical mean of one binomial RV smaller than another

Lets suppose I have two binomial random variables: $X \sim B(n_1, p_1)$ and $Y \sim B(n_2, p_2)$. I would like to calculate the probability than the empirical mean of $X$ be smaller than the empirical ...
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What is the probability that the matrix is orthogonal?

Let $X$ and $Y$ be independent $Bin(3,\frac{1}{3})$ random variables. Then what is the probability that the matrix, $$ P=\begin{bmatrix} \frac{X}{\sqrt2}&\frac{Y}{\sqrt2}\\\frac{-1}{\sqrt2}&\...
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binomial distribution and rolling dice

I play a tabletop game and we roll dice for game outcomes. The dice have 8 sides and a certain result (lets call it a success) appears on 2 sides, so 25% of success. If I roll 4 dice, the chance of ...
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13 views

Error Rate Confidence

I have a very basic understanding of statistics and have the following question: Given a test that can be run and give either a Pass or Fail result, how do I calculate how many times I must run the ...
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Expected number of points in k turns?

I'm not too familiar with expected values so I'm wondering if people could verify if I'm on the right track with my thought process here. If the probability of winning one point in a turn is 1/9, ...
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28 views

Binomial proportion statistics for variable $n$?

Using the standard definition of the sample proportion random variable: We first suppose $X \sim binomial(n, p)$ is the count of "successes" in $n$ trials where each trial has probability $p$ of ...
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Integration of product of functions of “x” with exponents/powers (binomial problem)

Original problem: A point X is randomly chosen from the interval (0,1). Suppose X=x is observed. Then a coin with P(Heads) = x is tossed independently n times. Let Y be the number of heads in n ...
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Limiting distribution of $\frac{\bar{x}-p}{\frac{pq}{n}}$ from mean of $Bin(1,n)$?

I found some difficulties in here. We know that if $X$ has Binomial distribution with $1$ trial and $p$ success, or what we called $X$~$Bin(1,p)$, we have $\mu=p$ and $\sigma^2=p(1-p)=pq$. From that, ...
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Beta binomial GLMM dispersion statistic issue

I am analyzing proportion data with GLMM in which the number of occurrence a behaviour of interest has been displayed and has not been displayed are concatenated and fitted as a single response ...
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1answer
61 views

What is the probability of the first positive event in an sequence of binary events where sequences have finite but random lengths?

I have a time series of observations from a longitudinal study of individual objects. These observations are seen as discrete sequences of features, one sequence per object. The sequences have ...
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Interpretting Confidence Interval Questions

Q.In a survey conducted by a mail order company a random sample of 200 customers yielded 172 who indicated that they were highly satisfied with the delivery time of their orders. Calculate an ...
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Product of binomial probability

I am trying to get an estimate for the Drake Equation by simulation (context doesn't matter to this question) I have reached a point where I have a number of planets, $n_e$, and 3 probabilities; $f_l,...
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1answer
20 views

Extracting Standard Errors for a combination of factorial predictors in binomial GLM

Suppose I run a binomial GLM (in R) with response variable [0,1] and 2 predictor variables that are both categorical. Let's call them a and ...
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Using variables measured at different scales in a binomial GLMM with successes and failures

I have seed and seedling abundance data for several plant species. I am trying to model the effect of my treatment on how many seeds successfully transition into seedlings (seed-to-seedling ...
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23 views

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 ...
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Consecutive sampling from a pool

I am new to stats. I have a straightforward ball drawing situation. If I have certain red balls (r) among blue balls in a pool (total: N), and I sample the balls with replacement for a certain times (...
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Calculating binomial distribution in R [migrated]

I want to do some calculations on a binomial distribution Bin(100,0.55). In particular: P[μₓ - σₓ ≤ X ≤ μₓ + σₓ] I also want to calculate it using the normal approximation for the binomial: f(x)=1/√...
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Uncertainty in a fractional count

What is the uncertainty (68% confidence level) of $N/M$, where $N$ is the number of entries that pass a cut and $M$ is the total number of entries? ($N$ and $M$ are both integers, and I'm interested ...
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Unbiased estimator of binomial parameter

Let 4,3,5,2,6 are 5 observations of the binomial(10,p) random variable.What will be an unbiased estimate of $(1+p)^{10}$ ? I have tried to solve the problem in this way. We know that $E[\frac{\bar{(...
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how to test multiple binomial events

Suppose I have a million coins, they have different propabilities for heads, and I known the probability of each of them. Now, I flip each of them once and record the head/tail events. How can I test ...
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14 views

Alternatives to Google's weighted sort for binomial experiments with n=1

An interesting data scientist interview question: "We are looking at the failure rate for opening files on websites for many clients. We want to rank the files by failure rate; but, with our current ...
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19 views

Poisson regression with offset vs logistic regression

I am thinking to use Poisson regression with an offset variable instead of a logistic regression in case where event is rare, since p (probability of success) is very small and n (sample size is large)...
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36 views

Binomial glmer with data between 0-1, not count data, not normal proportion

I have a special case of a binomial glmer and I can't figure out how to properly model it. I have a random factor (1|Species) to account for differences in species....
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What's the problem with my sports streaks problem solution?

The problem is from the book "Think stats". It's formulated as follows: If there are 10 players in a basketball game and each one takes 15 shots during the course of the game, and each shot has ...
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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 ...
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51 views

Some basic probability dilemma

So I started studying probability and while it seemed all ok I'm having trouble wrapping my head around this one. So the question is: We have 100 balls , 10 black and 90 white. In 50 tries what is the ...
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Test Retest of highly skewed dichotomous variables

Does anyone have recommendations on how to evaluate test retest reliability with 95% CI (individuals took the same survey 1 week apart) on data that is dichotomous (yes = 1; no = 0) where the data is ...
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43 views

Level of factor taken as intercept?

I am using a GLM to analyze binomial data from one factor (Group) with three levels: Control, Control Treatment and Treatment. ...
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Predicting viewer's cultural heritage from glmer and lmer versions of formula with different results?

I'm trying to understand why I'm getting different results when comparing anovas for glmer(binomial) and lmer versions of a formula. I am interested in whether a participant/viewer's cultural ...
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25 views

Diagnostic device hypothesis testing for superiority to a fixed value

I am designing a study to demonstrate that a diagnostic medical device is more sensitive than a fixed performance goal of 70%. Currently I am attempting to determine the appropriate sample size. My ...
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1answer
24 views

Determining coin biases, given some information

I have a real-life problem which essentialy boils down to the following: Given n biased coins, given to you ordered from highest to low bias, determine the last coin (by index) whose bias is still ...
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37 views

Can I use a binomial model with logit link function when dealing with continuous proportions?

I have continuous proportion data (i.e. ranges from 0 to 1). Or it could be percentage too if multiplied by 100. This is the proportion/percentage of overlap in home range between animals, therefore I ...
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Probability that two people get a certain number of heads on 100 coin tosses and all other outcomes with lower probability?

2 people flip a coin 100 times. The first person get 42 heads, the second person gets 58 heads. What is the probability of this outcome and all other possible outcomes that have an equal or lower ...
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Voting: probability of outcome flip

Assume you have a set of $N$ persons who should vote in a poll "for" or "against" an issue. The outcome of the poll is taken with simple majority. Each person's vote is independent of the rest and ...
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Estimating The Probability Of Success For Text Data

Imagine the phrase toy maker and by itself, it has 1 success and 887 trials for a success ...
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17 views

Test if two binomial distribution are significantly different from each other

I obtained two groups of data from my experiment and calculated the binomial distribution for each group, trying to see if they are significantly different from each other. However, the z sore I got ...
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should the product of 2 independent binomials converge to a normal distribution for large sample sizes?

I have been studying 2x2 contingency tables and specifically I have been looking at situations where the marginals are fixed by design for one categorical variable. As an example, suppose a ...
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51 views

How do I test difference in Percentages?

I have some survey data and know the number and percentage of "yes" responses. How do I determine if any of the percentage yes regional responses are statistically different from the national yes ...
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74 views

log ratio of Poisson means versus logit of binomial probability

Assume that two observed counts C1 and C2 are independent realizations of two Poisson processes: ...
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Comparing large and small populations

Here is a hypothetical that mimics my actual data (sensitive so cannot post actual details). I have 149 students in a class. In preparation for the final exam (which is pass/fail, NOT ranked), I held ...
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53 views

Inverse Sampling according to Haldane (1945)

According to the inverse-sampling method (Haldane 1945) you continue sampling until m of the rare items have been found. Let p be the frequency of the rare item ...
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73 views

Learning how to compute confidence intervals

Say we have tossed a coin $n$ times and have counted $s$ times of heads (success). So our estimated success probability for this binomial model is $p=s/n$. Now we are interested to compute the ...
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Calculate false negative probability for "fair coin” type problem:

Imagine the problem of determining whether a new wine vintage is better than one offered to customers in the past. Our null hypothesis is that both wines are equally good, i.e., 50% would rank it ...
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94 views

analyzing binary mortality data collected at different remeasurement intervals. Bonus for R implementation

I am replicating an analysis that models tree mortality data. Data are structured such that forest sites are revisted at some random interval, which is recorded. It is then determined if a tree lived ...
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Why is multinomial variance different from covariance between the same two random variables?

We know that if $\big(X_1,X_2...X_k) \sim multinomial(n;p_1,p_2...p_k)$ then $X_i \sim bin(n;p_i) $ Then, $var(X_i) = np_i(1-p_i)$. But we have $cov(X_i,X_j) = -np_ip_j$. So doesnt that imply ...
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How many boxes have balls?

I have N boxes, each of which may or may not contain a ball. I want to know how many boxes have balls by sampling the boxes in the following way. For each box in the N boxes: I open this box with ...
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Nonlinear regression vs. GLMs for estimating ED50

Are binomial GLMs better than nonlinear regression for model-fitting, and predicting ED50s and other effective dose point intercepts? In toxicology it is typical to run an experiment with a ...
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Strange predictions from binomial glmm?

I am analysing the dominance of a Species, i.e. its relative abundance in a community. Since these data are proportions I use binomial models. However, the predictions from these models are ...