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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1answer
24 views

How do I interpret this interaction between a continuous variable and a binary variable from a log binomial model?

I'm new to modelling and not sure how to interpret this interaction for a results section. The model output tells me that the interaction between cancer (binary) and age (continuous - one year ...
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7 views

Analyzing repeatability using rptR package with binary data, CI doesn't match estimated R [on hold]

I'm using the rptR package in R with the following code: rpt(SUCCESS ~ TRIAL + (1|SUBJECT), data=phase1, datatype ="Binary", grname="SUBJECT", nboot = 100, npermut = 0, ratio = TRUE) I've also ran ...
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2answers
37 views

Binomial proportion confidence interval when rigid bounds on population proportion (0.5 < p < 1)

A standard problem is estimation of confidence intervals for a population proportion given that one has observed f successes out of n independent trials. There is a reasonable discussion of this ...
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20 views

How do I determine goodness of fit for a test of n binary decisions?

Let's say I have $n$ pairs of items. For each pair I select one item over another due to some perceived trait. This could be anything, for example, identifying which image is brighter than the other ...
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1answer
19 views

What is the probabilty that X > 2 conditioning on Y = 2? (Homework)

another homework question here. Let 𝑌 be a binomial random variable with 10 number of trials and 0.2 probability of success. Let X be a uniformly distributed random variable over the interval [0, 3]. ...
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21 views

Are the beta distribution and binomial distribution related? [on hold]

I've seen questions like this and this, but it hasn't quite answered my question. How intertwined are the Beta and Binomial distributions? A quick sidenote: the Poisson distribution and the ...
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1answer
18 views

(Binomal Distribution) With n = 20, p = 0.2, calculate the probability that 2X >4 (Homework) [duplicate]

This is a homework question. The scenario is as follows: A dishwasher can accommodate 20 plates in one loading. With every loading, there is a 20% chance that 1 plate will not be cleaned properly. ...
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1answer
42 views

How to find P(2X>4)?

This is a Binomial question. I am required to find P(2X>4), and given that X~B(10,0.2), how do I convert it to 2X~B(n,p)? Have tried converting from P(2X>4) to P(X>2), but understand that it doesn't ...
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1answer
47 views

Does a 2*2 chi-square test give the same results as a binomial test?

This is a conceptual question. Suppose we have an experimental design with two grouping variables (e.g., the subjects are either male or female) and the variable we are measuring is a binary variable, ...
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8 views

Equivalence test for one proportions test

I want to apply an equivalence test on my sample to infer whether they are equivalent or not. Since my data are binominal [0,1] I don’t know whether the TOST procedure (tost() in R) can handle my ...
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14 views

Bernoulli Cusum Chart?

Can I use the R package named 'cusum' to make bernoulli cusum charts or should I use another package? I've been asked to explore using Bernoulli cusum chart for trending a parameter that's usually 0 ...
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1answer
46 views

Probability statistics - probability that 10 or more of the donors are Rh-negative?

In a certain population, 18% of the people have Rh-negative blood. A blood bank serving this population receives 95 blood donors on a particular day. So my teacher posted a solution to a problem ...
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1answer
56 views

Bayesian inference for Beta distribution after an uncertain outcome

Normally, when we have $$p\sim Beta(a,b)$$ and an observation of $x=1$ (''success'') from a Bernoulli trial with ''success'' probability $p$, the Bayesian inference on the parameter value $p$ is $$p|x\...
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1answer
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How to calculate the posterior probability with bayesian theory?

The Bayesian formula is given as the following simple way. $${\mathsf P}(a\mid x) ~=~ \dfrac{{\mathsf P}(x\mid a)~{\mathsf P}(a)}{{\mathsf P}(x)}$$ A factory makes pencils. prior probability: ...
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1answer
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How to “fit” the size of a binomial distribution

I'm solving a problem where I have 15 samples of a unknown distribution. They ask me to fit somehow the parameters of the Binomial, Poisson and Normal distributions. I could use the sample mean and ...
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1answer
26 views

binomial correlation?

I am interested in testing for a correlation between two variables, both of which are binomial. I guess this is equivalent to a Model II regression where both variables are binomial. Ideally I want ...
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9 views

Tuning the “strength” of updates to a posterior distribution for conjugates

I'm asking this question as a sanity check- I am not a statistician or research scientist, and just am doing a gut check on a model I am building. I want to quantify uncertainty of a specific metric ...
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1answer
211 views

Calculate the number of trials needed to achieve certain number of successes at a confidence level

If I know the probability of success for an event, the number of time that I want to observe the event at a certain confidence level how do I calculate the number of trials needed?
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25 views

Testing for extinction using the binomial distribution

I'm using quadrat sampling to determine whether a species of plant is present in a given area - my end goal is to work out how many quadrats need to be checked without finding anything before I can ...
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2answers
53 views

Covariance between two binomial random variables

Consider a binomial random variable $X$ with parameter $p$ and another binomial random variable $Y$ with parameter $q$. What is the covariance of $X$ and $Y$? How well does the proof generalize to $n$...
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Null hypothesis test for proportions without minimum requirements? [duplicate]

I have a typical dataset: sample A (method A) which has 200 samples and 25 failures. sample B (method B) which has 240 samples and 0-10 failures. Note that 0 failures is possible. Null hypothesis is ...
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1answer
65 views

How do you calculate an exact two-tailed P-value using binomial distribution? [closed]

First, I will preface this question with my ulterior motive: I would like more evidence that the use of 19th and 20th century approximations play little to no pedagogic advantage in modern intro stats ...
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20 views

flipping card with increasing probability

In an online game you can buy cards which has a 5% probability to be rare cards. If you don't have the rare card for more than 20 times, the chance of next purchase will increase by 5%, repeat until ...
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1answer
39 views

Why “sum of squared Pearson residuals” is around “number of dependent variables” in Binomial distribution?

A Pearson residual is defined as: $r_{i}(\theta)=\frac{y_{i}-E(y_{i}|\theta)}{\sqrt{Var(y_{i}|\theta)}}\tag{1}$ Sum of squared standard residuals $X^{2}$ is: $X^{2}=\sum_ir_i^2\tag{2}$ where $y_{i}$ ...
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1answer
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How can Bayes avoid Cromwell?

I'm studying widgets and their failures. Generally a widget will run for many years without trouble, but 1-2% of widgets will fail in a given year. I have a table which lists widget manufacturers (A, ...
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Does the number of trials and probability in binomial distribution should be independent variables?

Let's say that the number of trials and probability of success are a function of some variable t i.e, N(t) = f(t) and p(t)=g(t). Can we still use a binomial distribution in this case?
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Binomial Distribution variable classification

Situation: A coin has a probability for heads p=0.5 on any independent flip. After flipping the coin N=2,500 times, heads occurred G=53% of the flips. Question: The change in which parameter (only 1 ...
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1answer
18 views

Comparing proportions of two samples in time

I am trying to compare if the proportion of one bird subspecies in a roosting area is different now from over 20 years ago. My dataset looks like following: -In 1996 birds were counted at a ...
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GLMM analysis for multiple choice experiment

I’m a little bit desperate with this, so I really hope anybody can give me a hand. I did a multiple choice experiment, in which I had animals (n =6 per replicate) within an experimental arena, where ...
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21 views

Literature request: (in)appropriateness of negative binomial for count data with an upper bound

I conducted an analysis where I used binomial logistic regression to analyze x successes in n trials (where n varies between observations) in aggregate (using the R syntax ...
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1answer
46 views

Specification and Interpretation of Repeated Measures Binomial model in BRMS

I have two questions regarding specifying and interpreting Repeated Measures Binomial Models in BRMS We have a set of data in the following format: ...
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1answer
22 views

How do I calculate standard error for mortality experiment?

I ran an experiment looking if injuries affect the mortality of crabs over 50 days. How do I calculate the standard error for days when crabs died in relation to the percent mortality? Say I start ...
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24 views

Binomial distribution - Variance (Experimental vs theoretical)

Just been experimenting with creating a simulation for the binomial distribution. I've made an applet in Geogebra that generates the histogram, mean of the experimental data, the variance of the ...
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6 views

Number of trials needed in a 2AFC to test for significant difference from chance

I am running a two-alternative force choice task (2AFC) in which subjects indicate which of two intervals they believe a stimulus was present in. Some subjects will be blind and as such, we would ...
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26 views

Binomial regression check

I have run a simple binomial regression using the rethinking package in R, but I just want to double check that my interpretation is correct. Here is my model: ...
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1answer
20 views

binomial distibution in r, cannot replicate correct answer

I'm given a problem: An event occurs with probability 0.7. Over the course of 10,000 events the event occurred only 55 times. Verbatim question What is the probability that you would observe at ...
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2answers
23 views

What is the proper test for sparse binomial data?

I'd like to preface this by saying I am a statistics newbie. I have a single sample from a binomial distribution of some experiment. The exact numbers are: Yes: 1 No: 45 I'd like to determine (1) ...
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1answer
40 views

Computing the number of trials required in the binomial distribution

I want to know how I would go about computing how many times I would need to flip a coin where $P(H) = 4/5$ to make sure that the proportion of heads that shows up is in between $75$ and $85$ percent ...
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17 views

Total variance on binomial statistic with uncertain probability

Consider an experiment to measure a random occurrence with a probability $p$ to pass some selection criteria. If I have $N$ independent trials and $p$ is known, this is a standard Binomial ...
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9 views

Power analysis for assessing performance of a binomial classification model [duplicate]

I'm looking to perform third-party assessment of the false-positive rate of a video classification algorithm. I am feeding unlabeled video through a given classification algorithm and need to assess ...
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39 views

Distribution to model Binomial distribution with parameter p in trial n dependent on result from trial n-1?

I'm wondering how one can model a Binomial distribution as described in question. E.g., p = 0.5 for trial n = 0; p(n+1) = p(n) + 0.01 if for trial n Bernoulli(p(n)) samples to 1, else p(n+1) = p(n) - ...
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1answer
47 views

Interpretation Confidence interval including zero

I'm performing a negative binomial regression (xtnbreg in Stata). However, I found that the confidence interval of my regression includes zero. I have no clue how ...
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52 views

Likelihood Ratio Test for Equality of two proportions

Suppose we have two i.i.d samples from $X_1,...,X_n$ and $Y_1,...,Y_n$ where $$X_1,...,X_n \sim B(n,p_0)$$ $$Y_1,...,Y_n \sim B(n,p_1)$$ I want to show that we get the familiar test of equality of ...
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30 views

How to test if 2 binomial samples are equivalent?

Problem: Let $X_1,..., X_{n_1} \stackrel{iid}{\sim} \text{Binomial}(n, p_1)$ and $Y_1,..., Y_{n_2} \stackrel{iid}{\sim} \text{Binomial}(n, p_2)$. I want to test the following hypotheses: $$ H_0: p_1 ...
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Is my overdispersion too large in this quasibinomial model?

I have used a quasibinomial model on my data, but my overdispersion coefficient seems to be too large with a value of 40.78776. ...
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28 views

How do power calculations for binomial distribution work?

I'll use R for the example calculations. I want do design a controlled study. A usual one-tailed A/B test on the web. So, let's say we have a base conversion rate of 10% and we want to determine our ...
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36 views

MCMC Metropolis-Hasting with binomial distribution

For some time I have struggled with understanding MCMC Metropolis-Hasting application. Especially the terms in the acceptance ratio. I understand this is the correct form \begin{align} \alpha=min\...
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0answers
34 views

Should I use Poisson or Binomial distribution to solve this question? [closed]

My question goes as below: A major warehouse facility has 10 semi-trailer loading bays, which can all be used simultaneously. On average only 7 bays are in use. a. What is the probability that all ...
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2answers
90 views

How do I carry out a significance test with Tarone's Z-statistic?

Context In this blog the author suggests using Tarone's Z-statistic to test for overdispersion in a binomial model to determine whether or not it is necessary to use a beta-binomial model instead. In ...
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1answer
66 views

How to prove or disprove that $T(X_{1},X_{2}) = X_{1} + X_{2}$ is a sufficient statistic

Let $X_{1},X_{2},\ldots,X_{n}$ be random sample from a population whose distribution is given by $X\sim\text{Bernoulli}(\theta)$, $0 < \theta < 1$. a. Show that $T(x) = \displaystyle\sum_{i=1}^{...