# 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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### 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 ...
11 views

### 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 ...
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 ...
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 ...
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 ...
33 views

### Generating statistical distributions and sorting them

I am creating two distributions as shown below. ...
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 ...
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 ...
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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### 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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### 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 $n$ ...
4k views

### 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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### 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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### 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, ...
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 ...
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 ...
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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### 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 ...
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 ...
28 views

### 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 ...
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,....
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 ...
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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### 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-...
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 ...
2k views

### 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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### 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 ...