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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163 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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Matching a binomial Distribution to data

I've got inside my head a bit regarding matching my data to a binomial distribution. Say i have a sample of 200 people, with a measurement for blood sugar and a true false for each one indicating ...
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1answer
982 views

Binomial distribution for dependent trials?

Imagine a bag has some balls, some blue some red. Lets say there are 50 balls. 5 are red and 45 are blue. I have 4 bins, and am going to randomly pick balls out of the bag and put them into the bins ...
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1answer
336 views

Is Rule of Three inappropriate in some cases?

I'm building binomial proportion confidence intervals for a patient dataset containing the frequency of home nursing visits during the week prior to hospital admission. The freq. of home visit ...
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13 views

Calculating the number of excursions in a Gaussian

I've written an algorithm designed to solve the following problem: An m x n array, where m and ...
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2answers
33 views

Generating statistical distributions and sorting them

I am creating two distributions as shown below. ...
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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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2answers
34 views

How to model binomial data when the dependent variable is LITERALLY dependent on the independent variable

I am designing an experiment where a subject makes a choice between two options ("low value" (LV) and "high value" (HV)). The subject will experience both options during a trial ...
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Impact of Sampling from portion of Population

So here is a scenario that I am looking at. There is a population that has a binary variable of interest. This population was collected over a year. The population was sampled and mean of that ...
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3answers
76 views

Binomial and exponential distribution

If I am given $N$ is from a binomial distribution with the parameter $n,p$ and also $X$ is from exponential distribution with the parameter $\lambda$. Assume that $S_N=X_1+X_2+...+X_N$. How can I find ...
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1answer
102 views
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Test if two averages of two binomial distributions are statistically significant to one another

First, this may be a duplicate of: statistical significance I'm unsure if that post covers my exact situation. If so, just mark this as a duplicate. Let's say I have a list of 100k potential clients ...
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1answer
67 views

Bayes' theorem applied to a binomial variable

I just got an unexpected result, and wanted to check if I made any mistakes in my calculations, or if you can point me to posts/literature on the subject I describe below. Suppose you sample $n$ ...
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Why does the McNemar's test use $\chi^{2}$ and not the normal distribution?

I just noticed how the non exact McNemar's test uses the $\chi^{2}$ asymptotic distribution. But since the exact test (for the two case table) relies on the binomial distribution, how come it is not ...
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How to correctly use the binomial distribution for acceptance sampling?

I normaly use the hypergeometric distribution but when $n$ (sample size) is small in comparison to $N$ (batch size), I have been told by my lecturer that I need to use the binomial distribution ...
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Comparing win loss records or test results for statistical difference

I was reviewing some game statistics of wins and losses and was wondering what is the best approach to differentiate between how likely a person or team who had come in first is statistically that ...
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2answers
41 views

Test if the difference in sampled success rate of Bernoulli distributions are significant

I am drawing samples from two distinct Bernoulli distributions $Y_1$, $Y_2$. Suppose after $n$ trials each, I find values for $\check p_1$ and $\check p_2$, the sample success probabilities, for $Y_1$,...
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1answer
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Binomial data: Null Hypothesis $p = 0$ when all Sample Values are 0 - testing and power analysis

I am trying to investigate if the proportion of successes in my population can be shown to be larger than zero. Thus, $H_0: p = 0$ and $H_A: p>0$. Since $p=0$, the prop.test in R does not work, ...
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1answer
295 views

Compare species count data between sites

I'm comparing species counts between areas. My data is very similar to the below. ...
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If my data is overdispersed when binomial but not when Poisson does that alone mean I should use Poisson GLM?

Top is Poisson, bottom is Binomial Source of variation is different people observed over a week long period. 118 people to be exact. want to make predictions about the proportion of days/week one ...
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Binomial or Poisson? Binomial makes most sense but similar p values and Poisson has no overdispersion [duplicate]

I am modelling no. days exercised in a given week and so therefore I am using a binomial GLM. Yet the model is massively overdispersed (even as quasibinomial). When I model as poisson distributed ...
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1answer
557 views

When are real limits used for calculating z score?

I'm taking an introductory statistics course. At first, the textbook talks about real limits in the context of continuous variables and frequency distribution table, that is all clear. But on what ...
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1answer
20 views

Variance of Binomial distribution proof using Binomial Theorem

From Proof 1 why is $\sum_{j=1}^{m}{m-1\choose j-1} p^{j-1}q^{(m-1)-(j-1)} = (p+q)^{m-1}$ shouldn't it be $\sum_{j=1}^{m-1}{m-1\choose j-1} p^{j-1}q^{(m-1)-(j-1)} = (p+q)^{m-1}$
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30 views

What probability distribution would be look like this?

I was playing with R, I started with adding consecutive binomials (the n parameter of the second binomial variable depends of the result of the first binomial and so on...). After a few more ...
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1answer
300 views

Reporting binomial logistic regression

I want to report the results of a binomial logistic regression where I want to assess difference between the 3 levels of a factor (called System) on the dependent variable (called Response) taking two ...
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Why does using the pnorm function on the intercept estimate of a binomial regression recover the mean of the dependent variable?

I've fit a series of mixed effect models with the lme4 package in R on a set of binomial outcome variables (1: the event happened, 2: it did not). The fixed effect ...
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1answer
134 views

Appropriate estimation of standard deviation for a sample of proportions

I am working with some bird mortality data across 9 years of surveys and have run up against a problem estimating the standard deviation. Across the 9 years, survival estimates were .47,.60,.36,.58,....
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1answer
73 views

Using Chi-squared test when perfect separation in logistic model?

My dataset is similar to this; it describes the presence/absence of a parasite in six species of animal from two locations. Each row in the dataset represents a different individual animal. I would ...
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1answer
582 views

Exact binomial test using binom.test and qbinom, pbinom?

The below methodology is for a one-sided test.I am trying to use the two methods for obtaining the p-value where it should be the same in case of Binomial hypothesis testing. But I am receiving a ...
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5 views

Using average value of population instead of proportion value in p chart

I am trying to establish upper and lower limits for a population. In this apporach I cannot use samples. I want to use average of the values for the full population and use this average value in p-...
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1answer
25 views

Statistical test to justify looking at a subset of data or the entire data set

For a school project, we are asked to determine the expected pass rate of a driving test based on yearly data provided from 2010 to 2019. I am wondering if there is any statistical justification to ...
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Is it appropriate to treat n-point Likert scale data as n trials from a binomial process?

I've never liked how people typically analyze data from Likert scales as if error were continuous & Gaussian when there are reasonable expectations that these assumptions are violated at least at ...
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1answer
83 views

GLM interpretation

I have to use a GLM to interpret some data. Could anyone tell me whether this is correct just from looking at the output? I genuinely have no idea whether this is even correct! And if it is - is it ...
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1answer
56 views

Conditional expectaction with probabilities for a sum of independent random variable

I have a r.v $S_N$ built as a sum of Bernoulli with parameter $p$. So $S_N = X_1 + X_2 + \ldots + X_N$. There is a second variable N, such that $N \sim Poisson(\lambda) $. I have to compute: $P(S_N=0)...
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1answer
42 views

bernoulli distribution finding p from standard deviation

I have a binomial distribution and my n=20 and I am not give either p or q. I know that the standard deviation is 1/2 and I am asked the value of p. But after solving the equation of 1/2=sqrt(20p*(1-p)...
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1answer
58 views

Asymptotic distribution of “plug-in” variance estimator for Bernoulli data

I am stuck at the following exercise: Let $(X_k)_k$ be a sequence of i.i.d. Bernoulli$(p)$ distributed RVs with $p=1/2$. We want to estimate $Var(X_1) = p(1-p) = p^2 =: \tau_p^2$ by directly plugging ...
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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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4answers
716 views

Inequality of binomial probabilities

I need to show the following: I have two binomial random variables $X \sim BIN(m,p_1)$ and $Y \sim BIN(m,p_2)$, where $p_2 \geq p_1$. I want to show for any fixed constant $c \in \{0,...,m-1\}$ that ...
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14 views

Get the log likelihood from glmer with binomial data (and not only a proportional one)

The logLik.merMod manual page states that: logLik: Log-likelihood at the fitted value of the parameters. Note that for GLMMs, ...
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21 views

Issues with logistic regression using `glmnet` package

I'm trying to use the glmnet package to build a logistic regression model, but I keep getting sensitivity and specificity of 1.000. My data contains two factor ...
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25 views

Finding Unbiased Estimators for a Binomial Distribution

Let ${X_1},...,{X_n}$ be a random sample from a binomial distribution B(2,$\theta$). a) Use the test statistic $T(X)=\sum_{i=1}^{n}{X_i}$ to find unbiased parameters for $\theta$ and $\theta^2$ b) Use ...
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1answer
71 views

How to model errors around the estimation of proportions - with measurement error?

I have a situation I'm trying to model. I would appreciate any ideas on how to model this, or if there are known names for such a situation. Background: Let's assume we have a large number of movies (...
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1answer
35 views

How to find number of trials in Binomial Distribution?

Suppose we have a biased coin that we are testing that has a probability of getting a tail= 0.6. Say we test the coin. Using this information how do I find the number of trials P(X>=10)<=0.05?
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1answer
57 views

Difference between Variance $\sigma^2$ and variance in binomial distribution

I am reviewing some basic statistic concepts. Now I am not sure what 's the difference between variance $$\sigma^2=\frac{1}{N}\sum^N_{i=1}(x_i-\mu)^2.$$ and binomial distribution $$\mathrm {Var}(X)=np(...
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1answer
58 views

signed-rank test in R confused

I am self-studying a textbook, and I am confused with the below example. Could you explain to me how was the p-value calculate using R? I tried 1- pbinom(x ,y,.5) etc. I am confused we have one ( + ) ...
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1answer
33 views

How to calculate a confidence interval in R for a binomial mixed-effect model (which was fit using the R package glmmLasso)?

How does one calculate confidence intervals for a binomial mixed-effect model that was fit using the R package glmmLasso? I am interested in the 95% confidence intervals for the fixed effects. confint ...
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3answers
59 views

How to measure good or bad luck in roulette

I want to analyze and represent the performance of a bet (X numbers out of 37 total roulette numbers) for a series of spins (N spins). For example, let's say that I choose 5 numbers (my bet) and these ...
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Distribution of population size $n$ given binomial sampled quantity $k$ and selection probability $\pi$

Given a drawn (without replacement) sample size $k$ from a binomial distribution with known probability parameter $\pi$, is there a function which gives distribution of likely population size $n$ from ...
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27 views

Probability distribution with different probabilities and possible outcomes

I want to know how I can model a distribution that is basically n Bernoulli trials. However, these Bernoulli trials can have different probabilities and outcomes. It is basically the same question as ...
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657 views

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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21 views

Augmented binomial test where p is different for each trial

A have a model process whereby for each item, $i$, of $N$ total items I estimate a trial success probability $p_i$. I then have results for each individual process which has resulted in failure (0) or ...

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