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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“All of Statistics” questions [on hold]

I am not able to solve a couple of questions asked in the exercise 10.11 of book - All of Statistics. Question 1 Question 2 How do I start ? Any hints would be helpful ? I do not want complete ...
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Alternative answer to choose k people out of n, then choose 1? [migrated]

The question is fairly simple, we first choose k people out of n, that is $C(k,n)$ as the combination function, then we choose 1 person out of k, we have k choices. The total number of choice is given ...
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Estimating variance of a function of multiple random variables?

What are some strategies for estimating the variance of a statistic that is an arbitrary function of multiple random variables? I am familiar with the Delta method which uses asymptotics to estimate ...
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Testing the difference between two parameter estimates in binomial GLM

There are some related posts on this issue, but no answers actually demonstrate the mechanics of how to accomplish the task that I could find. I want to compare two parameter estimates in a binomial ...
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Significance in beta regression and glm binomial

While performing betaregression using betareg R package I noticed that the terms in my model are often significant, even with very small sample sizes. I tried the same model using glm with binomial ...
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Compare two binomials with unequal groups of trials

I'm attempting to determine if store B is 'better' than store A. Let's say that the two stores are identical in every way except for the sales assistants. I'd like to determine if one store makes more ...
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Conditional distribution function of sum of correlated Bernoulli variables

Let $X_i$ be a Bernoulli variable with probability $p$ for $i=1,...,N$. Hence $\sum_i X_i$ is binomial and approximately normal$(p,(1-p)p/n)$ for large $N$ The conditional probability distribution of ...
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Determining preference using a binomial test. Is this the right way to go?

Let's say you are running a blind essay on preference of a new product. You make people taste two different drinks and record their response. They prefer A and you record it as a failure in a ...
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Can I run a multivariate quasi-binomial analysis of proportion data?

I am trying to best analyse a set of foraging ecology data with >10 behaviour categories (DVs) and 3 levels of IV (season, sex, age). The time which an animal spent engaged in a behaviour was recorded ...
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Are sensitivity and specificity complement of each other?

Sensitivity : probability that a person with the condition will be classified in one's study as having the condition. ...
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86 views

Arcsin CI for proportion

I'm trying to replicate a study. I have 165 observations of a proportion variable (the distribution is skewed to the right as many proportions are low). I need to report the CI. I've applied ...
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Is there a formula for a general form of the coupon collector problem?

I stumbled across the coupon collectors problem and was trying to work out a formula for a generalization. If there are N distinct objects and you want to collect at least k copies of each of any m ...
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SPSS regression discrete number of outcomes

Patients were asked whether they experienced 6 different health consequences following a procedure. As well as looking at the predictors for each individual health consequence, I am also interested in ...
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Derivation of cumulative Binomial Distribution expression

I have a binomial distribution, with Random Variable Y and n trials. r is an integer. How can I show that P(Y ≥ r) = P(Y ≤ n − r)? I think it involves using the binomial theorem. I have tried taking ...
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calculating the statistical significance of overrepresentation of a substring in a string

I have a sequence of characters in a long string like this 'ATCGCGCGCGATCGACGCGTACGTCGGATCTA.....' And I know that for example the substring 'ATCG' has been ...
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1answer
49 views

Why not use always a binomial exact test to compare two proportions instead of chi square?

I am trying to figure out what test I should use in the following scenario: I know that there is a lot of room for improvement in a specific area at work - being extremely critical, let's say that ...
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Laplace approximation for binomial distribution in matlab

i using bionrnd() function to generate a random vector and Laplace approximation formula to approximate the binomial distribution. but Laplace histogram dose not ...
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Is there a way to do a statistical test if an independent variable has only 1 level?

I have a repeated measures design in which I tested multiple individuals with three different sounds (playbacks). The playbacks were 20 seconds in length and I recorded 1) how individuals responded ...
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Assessing fit of binomial glmer() in R with only categorical predictors

I am trying to validate a mixed effects logit regression model with a categorical dependent variable and categorical predictor variables - I have nothing that is continuous. One of my predictor ...
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Developing probability distributions

An event occurs, and after this event has occurred there is a set of conclusions which can be drawn. All of these conclusions have results which are distinct. I am trying to keep this as general as ...
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Difficulty with power analysis

I need to estimate sample size for an experiment but I am not very knowledgeable about power analysis. In my experiment, I am asking if a user can notice the two possible states of a system. I ...
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Uniformly Most Poweful Hypothesis test for the difference between two means

I have data for two groups, $G_1$ of n trials and $G_2$ of m trials, of which datasets $x_1$ and $x_2$ have been collected. These can be binomially distributed, $X_1$ ~ B(n,p), $X_2$ ~ B(m,q). I ...
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How to tell the probability of failure if there were no failures?

I was wondering if there is a way to tell the probability of something failing (a product) if we have 100,000 products in the field for 1 year and with no failures? What is the probability that one of ...
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What is the best approach to measuring significance in two binomial distributions?

I have been using the Wilson score interval to determine whether the registration rate from two different website flows are significantly different. I want to see if there are suggestions for better ...
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Asymptotic distribution of the max (min) of IID binomial variables

I would like to know the limiting distribution when $k \uparrow \infty$ and $k/n \rightarrow \lambda$ of $$ \max(X_1, \ldots, X_k), \text{ where $X_i$ are IID $B(n,p)$}.$$ This is most likely a ...
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Bit Error Rate - Multiple Bernoulli trials with different probabilities

If you transmit a sequence of bits over some line, errors may creep in. For instance, if the Bit Error Rate of this line is 1%, on average, every 1 out of 100 bits will flip to the opposite value. ...
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How to calculate probability that another player has a card

In a poker game, how would we calculate the probability that another player has at least one certain card? Lets say that there are five other player, there are four cards in middle of the table, and ...
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Chi-square test p-value = 1

I am attempting to use the chi-square test as a goodness-of-fitness test in R, but I keep getting a p-value = 1. I expect a high p-value, but less than one. Can anyone point out what error I might be ...
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Hypothesis Testing for survey

Suppose my null hypothesis is “Not more than 50% person prefer milk” and alternate hypothesis is “More than 50% (or majority) prefer milk”. Actually the null and alternate hypothesis are set so only ...
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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 ...
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Probit regression with misclassified binary dependent variable in R

Is there a generalized linear mixed-effects model implementation for R that could handle misclassified binary data? Unless I have overlooked something in the documentation, glmer with ...
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2answers
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When is calculating probability based on a poisson distribution preferred over a binomial distribution?

I'm trying to understand why a poisson distribution may be preferred over a binomial one when modeling binary cases. Is there a case where you can't use a binomial distribution to solve a problem ...
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Using proportional data with a binomial error structure in R… a worked example needing answers!

I am trying to test if the proportion of herbivores in spider's diets is related to the proportion of herbivores in their grassland, but am struggling to understand if I should be using a binomial ...
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Solving formula for confidence intervals on two proportions

I'm interested in comparing two independent proportions from two samples. The formula for doing so is available in the Internet (e.g. here). So far, so good. But my main purpose is not to build a ...
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Does $\sqrt{n}(Y_n-1)$ converge in distribution?

Let $n\in \mathbb{N}$ and consider, for each $n$, independent real valued stochastic variables $Z_{1n}\ldots Z_{nn}$, such that $$ P(Z_{nk}=n)=1-P(Z_{nk}=0)=\frac{1}{n} $$ for $k=1,\ldots,n$. Thus ...
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Show that $P(X \ge r ) = P (Y \le p)$ [duplicate]

Let $ X \sim \text{Bin}(n,p) $ and $ Y \sim \text{Beta}(r,n-r+1) $. Show , without integration by parts, that $P(X \ge r ) = P (Y \le p)$. From which point of view I answer this question.
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Negative Binomial Regression?

I have a dependent count variable that measures the number of days spent in a hospital (LOS) for a group of patients who received two different medical interventions upon hospitalization. I'm trying ...
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what is the Probability of selecting 10 SNPs from a list of 5000 SNPs simply by chance

We conducted a study to predict deleterious mutations from a list of around 5000 mutations (which contains both neutral and deleterious mutations; the real state of each mutation is unknown), using ...
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Standard error for aggregated proportions

In order to obtain confidence intervals for proportions I'm trying to calculate the standard error, but I'm having difficulty working out what N should be in a case such as mine. My data is such that ...
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Confidence Intervals for a relative risk where i lack the underlying data

I have two estimated rates and their 95% confidence intervals but not the underlying data. I take the ratio of the two to get a relative risk, but how do I determine the 95% confidence intervals for ...
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Has the free kick spray in soccer an effect? Binomial Testing

In Germany a referee supported the use of the free kick spray introduced on the World Cup 2014. He reported some statistics. His data supported the assumption using the spray leads to more goals after ...
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What coefficients do I use for a binomial distribution problem?

I'm studying for an exam and my study guide explained combinations, permutations, and binomial distributions, but didn't cover much how to recognize where each comes into play in problems. I'm having ...
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Independent events in sequence

If I flip a fair coin twice, the probability of at least one Head is 0.75 (HH, HT, TH and TT). I flip the coin once and it lands Tails. In order to get at least one Head, the probability of the ...
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Show that if $X \sim Bin(n, p)$, then $E|X - np| \le \sqrt{npq}.$

Currently stuck on this, I know I should probably use the mean deviation of the binomial distribution but I can't figure it out.
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Residual variance for glmer

I am running a glmer model and I want to determine the total variance. My data is for survival and it is coded as 0 and 1, where 1 represents that the individual survived and 0 represents that the ...
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Mixed logistic model with complete separation

I want am trying to produce a mixed logistic model but certain explanatory variables suffer from complete separation. I am aware that I need to either use exact logistic regression or a firth ...
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Is it possible to model the conditional expectation of a binary outcome using an additively-separable link function?

Logit and probit link functions aren't additively separable. So, fitting a model using these link functions implies that the effect of one predictor in determining the outcome is not independent of ...
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multi stage binomial “process”

I wish to model the retransmission time of a file that divided into K blocks. I know the successful blocks of first transmission obey the binomial distribution $$ X_1 \sim \text B(K,p) $$ , p is the ...
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Put constraint on max (or min) predicted value (mgcv)

I want to fit my data using a logistic GAM model with cubic regression splines. I know for sure that in reality my estimated probability should not go above 0.5 (due to mislabeling). So I thought ...
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A binomial test with repeated measures?

I'm working on a study with a single trained animal (ie. our only participant). He is making a binary choice on a number of consecutive trials (we are essentially trying to teach him a rule -- if A, ...