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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128 views

Interaction plot between categorical and quadratic continuous variable

I ran a GLMM model with a binomial response to analyse bear presence at feeding sites (0 = absent, 1 = present) within two years. My code is: ...
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1answer
251 views

Are there better estimators of misclassification error than the fraction of misclassified test points?

Assume we train a binary classification model using the training set. Also assume that the model returns an estimate of the probability of success $\hat f(x)$ for every feature vector $x$ and was ...
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Linear mixed effect model with fractional/proportional outcome: choosing between binomial and beta

I'm looking to run a linear mixed effect model using lme4, where my dependent variable one_syllable_words / total_words_generated is a proportion and my random ...
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1k views

Use Chi-Squared or Binomial Test if Distribution is not Known?

Suppose you have a set of data (eg. [a, b, a, a, b, b, etc.]), and you have the suspicion that the set of data follows the binomial distribution. Your Null Hypothesis is: The probability of success ...
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472 views

Election fraud detection: the statistics of Quick Count

I’m reading the book Quick Count and Election Observation (chapter 5). I’m interested in understanding the statistics used in Quick Counts. Quick Counts is a methodology for verifying official ...
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433 views

Hypothesis testing for binomial distribution: a simple real-life case

I'm refreshing (or maybe just acquiring) some stats skills, and I have a real-life situation, probably very simple since it's quite close to a typical example from stats courses, that I would like to ...
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198 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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282 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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171 views

Simple $\chi^2$ test question

I have the following question which seems extremely easy, but the way the data are set up is causing me some uncertainty: I plan to solve this problem through finding the maximum likelihood estimate ...
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133 views

Joint distribution of column sums when row sums are fixed

Suppose I have an $m$ by $n$ table $X_{ij} \in \{0,1\}$, where in each row, $r$ randomly chosen entries are set to 1 (the rest are 0), i.e. $\sum_j X_{ij}=r$. I know that e.g. the column sum $\sum_i ...
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Binomial mid-p value

I've been under the impression that the mid-$p$ values generally control the Type I error, and consequently confidence intervals based on mid-$p$ values control the coverage. However I have checked ...
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2answers
560 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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30 views

Modeling binomial outcomes with repeated measures

I'm looking at patterns of a particular injury within individuals and how they vary by age and sex. For each of 1365 individuals I have four locations each of which may be positive for this injury. ...
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Beta-binomial distribution for scaled and translated Beta

Recall, that a binomial distribution in which the probability of success at each trial is randomly drawn from a beta distribution results in the so called beta-binomial distribution. One can calculate ...
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63 views

binomial glm where number of trials is also a predictor

I am modeling the probability of success $p_i$ under a binomial framework. In fact I am actually modeling $x_i \sim Bin\left( n_i, p_i\right)$ being the number of trial varying along each observation. ...
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2answers
217 views

What is the equivalent to a binomial test for more than two populations?

I have the minor allele frequencies for three populations for a given SNP (location in the genome). ...
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530 views

Multiple imputation of glm binomial size parameter

Suppose we have a generalized linear model with a binomial response $y_i\sim \mathrm{bin}(n_i,p_i)$ where $p_i$ is determined by the linear predictor in the usual way via some link function. Is there ...
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697 views

Including seasons and months into GLMM: should they be crossed or nested effects?

I have collected data from five consecutive fishing seasons (five factor levels). Each fishing season has five months within (five factor levels). Considering that I have a temporal correlation in my ...
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302 views

The marginals of a truncated multinomial are truncated binomials?

The multinomial distribution for a vector $\vec x$ of non-negative integers assigns a probability of: $$f(\vec x) = n!\prod_i p_i^{x_i}/x_i!$$ to every vector $\vec x$ of non-negative integers in ...
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1answer
90 views

Bayesian inference with unequal sampling

I have a "two-column" data set, with a multi-class categorical variable A, and two-class variable B. It is assumed that each observation is independent. For each category of variable $A$, I want to ...
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526 views

Theoretical justification of choice for confidence interval exact method for the success probability parameter of negative binomial variable?

I have a computer experiment that runs the Bernoulli series with unknown probability $p$ of success. The experiment terminates when $m$ failures are observed. So, the unknown parameter $p$ has the ...
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1k 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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1answer
11k views

How to analyse a continuous response having a bimodal distribution?

I am investigating unconscious racial prejudice as a predictor for guilty or not guilty judgements (Using SPSS). I have a continuous variable for unconscious racial prejudice (higher numbers equal ...
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Counter-intuitive result from Cochran Armitage trend test and glm binomial

My question is motivated by the Q&A at How to test the increase of proportions. The question is how to test for a trend in proportion between events and non-events given an ordinal risk of 3 ...
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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
30 views

Model/predict the number of malaria-infected cells

Background: In order to determine the severity of a Malaria infection, one takes a sample of red blood cells and determines, through a microscope, the number of cells infect by the malaria parasite. ...
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1answer
210 views

binomial responses in h2o gbm

I am modeling the probability of success in a dataset where I have a both the number of trials and the number of successes (and, obviously, I am modeling $p_i=\frac{total successes}{total trials}$). I ...
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110 views

Calculating a Confidence Interval for a Proportion for a Sample of Different Size

I'm interested in a (preferably analytic) solution or approximation to the following problem: Let $s_1$ be a sample from an unknown distribution of size $N_1$ and with proportion of successes $p_1$. ...
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164 views

What are models for count data where the variance is not related to the sample size?

For modeling count data that arises as the sum of Bernoulli random variables or according to an occurrence process with constant rate in some interval, there are many techniques, like using a Binomial ...
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88 views

Confidence interval of proportion of a proportion

Let's say we have $N$ users. Some of them could be hackers and some not. Only for a random $p_u$ percent (e.g. 1%) of users have we actually investigated manually to know which ones are hackers and ...
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43 views

Summation of combinations up to $r-1$ terms

I am trying to come up with a simplified expression for $$\sum_{k=r}^{n}\binom{n}{k}$$ Choosing $x=y=1$ in Binomial theorem, I have $$2^n = \sum_{k=0}^{n}\binom{n}{k}$$ $$2^n = \sum_{k=0}^{r-1}\binom{...
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284 views

How Negative Binomial Distribution and negative bionomial regression can be used to sales forecast?

My first question here. Due to the improper inventory management we seem to have dispersed sales, and the stores are unable to meet the demand because items are being out of stock. There are so much ...
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2k views

Detecting outliers in percentages

My dataset looks like below - Total Success Percentage 100 65 65% 50 25 50% 30 20 66.6% 50 40 80% Plot - Each row is ...
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1answer
14 views

sampling order sum from different order size and probabilities

I want to analyze the probable outcomes of an order pipeline for a business. Say we have ten potential orders, each (business) order has a different size (OS), say 1, 20, 3, 4, 5, 6, 6, 8, 8, 9 (mio) ...
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77 views

Differences from logistic regression and mixed effects logistic regression - rounding error or conceptual mistake?

I'm a bit confused. To my understanding, the standard logistic regression should be equivalent to a mixed effect logistic regression where the statistical unit is defined as random effect - but I ...
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210 views

Does clustering lead to overdispersion?

TL;DR Clustering is often cited as a source of overdispersion in count data. However, I seem to arrive at the conclusion that clustering actually reduces the dispersion. Could someone confirm this ...
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184 views

Residuals in Negative Binomial Data

I'm tackling the problem of Anomaly Detection in a dataset that's comprised of call counts to a call-centre. The data exhibits daily and weekly seasonality and is known to be over-dispersed. ...
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139 views

Probability of a Blizzard - Poisson vs Binomial vs Bayesian

My goal is to model data I have collected to compute the probability of a severe blizzard occurring in a given set of states (region). Assume the US is broken into 3 regions that categorize the ...
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261 views

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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167 views

Sample size formula for multiple regression between binomial variables?

Let's say we have k binomial variables, and a sample size of n observations per variable, where each variable occurs (positive case) at a given frequency/probability f. We would like to check if ...
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270 views

Pattern-mixture models

I am currently looking at pattern-mixture models but I don't seem to understand them and I wonder whether someone could help. I can see the model comes from the factorisation $ f(y,r;\phi, \theta)=...
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86 views

confidence interval for proportion

Suppose $k$ events were observed in $n$ trials. We then have $\hat{p} = k/n$ and the standard Wald confidence interval is $$\hat{p} \pm z_{\alpha/2}\sqrt{\hat{p}(1-\hat{p})/n}$$ I wonder why the ...
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69 views

Test of strict difference in independent binomial probabilities

Suppose $X,Y$ are two independent binomial random variables with parameters $n_1,p_1$ and $n_2,p_2$ respectively. Suppose one wanted to test the hypothesis $p_1>p_2$. Conditional on $X+Y=s$, ...
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337 views

Can I use Bayes Theorem to find a conditional distribution rather than conditional probability?

I might be going about this the wrong way, but I'm trying to develop an understanding of a particular conditional value, say $P(CustomerBuysFries | CustomerBuysHamburger) = P(F|H)$. Ultimately, I want ...
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204 views

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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1answer
71 views

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 effects that arise from a Run-to-Run variation. Example, case ...
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215 views

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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564 views

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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332 views

Correcting for multiple testing on non-independent sliding windows

Question Values taken from adjecent windows in a sliding windows are corrolated. If I calculate a p-value from each window, how can I correct for the fact I have tested many windows, given that the ...
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449 views

Should I use a beta-binomial or binomial glmm?

I have several data sets on wildlife disease incidence. One of the issues with my dependent variable is that it represents only current infection status, therefore 0 (no disease) can represent either ...

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