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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Can agresti-coull binomial confidence intervals be negative?
According to http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm
agresti-coull intervals cannot be negative, however using the formula from wikipedia as well as the binom.confint function ...
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How can one perform a two-group binomial power analysis without using normal approximations?
I would like to do power analyses for hypothesis tests of (non-)equality of proportions in which the proportions are very small. I would like to do so without using normal approximations of the ...
2
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1answer
46 views
Change in binomial proportion confidence interval
I'm having trouble calculating 95% confidence intervals for a change in binomial proportion. For example, in group $A$, there are $4$ successes out of $n =20$. In group $B$, there are $12$ successes ...
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Manipulating Binomial Distribution
Recently, I've been reading Yudi Pawitan's book, In All Likelihood.
In the book, there's a section on profile likelihood; the methods explored in this section are subsequently applied to some data on ...
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Exact version of Bowker's test?
I know there is an exact version of McNemar's test for symmetry, and am just wondering if there is an exact version for Bowker's test. From my understanding the exact version of McNemar's test uses ...
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51 views
Distribution of independent binomial variables conditional upon the sum
Suppose that we have independent binomial variates with differing sizes and probabilities $X_i \sim Binomial(n_i,p_i)$, and $Z = \sum_iX_i$ is the sum. I understand that $Z$ is distributed ...
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50 views
Fitting a Poisson distribution from missing observations
I am interested in fitting a Poisson/negative binomial distribution to estimate the number of times a phenomenon happens within a period, let's just say 10 years. I can count the events from monthly ...
2
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1answer
72 views
confidence interval for classification error---binomial assumption vs. bootsrap resampling
I am developing a classifier using a set of N patterns, where N~1000. I am using K-fold cross-validation (with K=5) and computing the probability of classification error p (typical value is p=0.03). ...
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1answer
41 views
MLE for simulated case of binomial p with constant labelling rate
I simulated the following example: 2000 binomial runs (p(Heads)=0.6). Each run has a sample size ranging from 500 to 300 0. (But that is not important: we have the same result if the sample size is ...
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1answer
19 views
Hypergeometric, binomial, or something else for enrichment analysis of potentially shared molecular barcodes between groups?
I need to analyze three samples of molecular barcodes, two from blood and one from tissue. My question is which of the two blood samples is more similar to the tissue in terms of molecular barcodes.
...
3
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1answer
32 views
chi-squared test for non-iid binomial data
Simple case: Suppose we have $N$ observations of $X_i$ that we believe are theoretically iid binomial random variable $\text{Binomial}(k, p)$. Well, one way we could test to see if this is true is ...
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29 views
How can I tell if modelling/testing with Binomial/Beta is correct?
My standard disclaimer: I'm a programmer, not a stats guy, mostly wanting to understand statistical tests for optimizing web apps.
Let's say I want to measure monetization rate of users. "How many ...
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2answers
138 views
Which test to use to compare proportions between 3 groups?
We are testing an e-mailing marketing campaign. On our initial test, we sent out two different e-mail types and had a third control group that did not receive an e-mail. Now we are getting back ...
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1answer
31 views
Finding the bionomial probability?
Ok so i have been taught this formula regarding binomial probability
Repeat an even n times
...
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26 views
non-parametric equivalence /non-inferiority for ratio variable?
I'm comparing subjects' success rates in two conditions A and B. All subjects run both conditions, so the data is paired. Each subject runs say 8 trials in both conditions, with 0 or 1 as output. The ...
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71 views
Determining if awards are fair
Imagine a population of people where $x\%$ have blue hats and $(100-x)\%$ have green hats where every year some people are awarded prizes. The rule is that everyone should have an equal chance of ...
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binomial test for testing significance of classification very sensitive to hits count
I'm doing a multi-class classification task and I wonder if I'm doing the binomial test correctly since it is very sensitive to the count of correctly classified trials (hits count).
Say, there are ...
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Binary outcome with categorical predictors - experiment control
I have a problem which I try to formalize/decompose/map to well-known cases, so this is more of a call for references/names/terms.
Description of the problem:
The system receives a stream of plant ...
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1answer
54 views
Hypothesis testing using different methods
I have a question related to hypothesis testing. I cannot seem to find error in my reasoning.
Initial question:
We have 230 pacients: 157 males and 73 females. 142 males are sick and 69 females are ...
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51 views
Pooling asymmetric confidence intervals for proportions?
I have several measurements of proportions (values in [0, 1]) $\theta_1,...,\theta_n$, each with an (asymmetric) 95% confidence interval. The $\theta$'s are repeated measurements of the same variable ...
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2answers
69 views
Normal approximation to binomial
What do I do when the normal approximation is not valid?
Here's the question I'm trying to answer:
A student guesses all 15 answers on a multiple-choice test. There are 5 choices for each of the ...
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1answer
73 views
Two independent random variables for Binomial distribution with different probabilities of success
Assuming that we have observed two independent random values $X \text{~} Bin(8; p)$ and
$Y \text{~}Bin(4; p^2)$.
Using the sample $(X; Y )$, I want to test the statistical hypothesis $H_0 : p \ge ...
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Mixture of binomial distributions
I am experimenting with a mixture of binomial models. Consider a binary variable $y_i$. Furthermore, there are two sub-groups in the population (not known a priori and not observable): $z_i=0$ or ...
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Hypothesis testing and a possibly incorrect glmm
I am new to the whole concept of generalized linear mixed models and have dug myself into a hole of confusion when it comes to the question (or hypothesis) I am posing and the construction of this ...
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59 views
Why may one use qbeta() to calculate CIs for binomial proportions that are actually based on the F-distribution?
I just barely grasped why large-sample confidence limits that assume approximately normal distributions are not the best approach when relative frequencies approach either one or zero - so that in ...
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Homework: Bayesian Data Analysis: Priors on both binomial parameters
The following is a problem from Bayesian Data Analysis 2nd ed, p. 97. Andrew Gelman has not included its solution in the guide on his website and it has been driving me crazy all day. Literally all ...
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1answer
40 views
Binomial probability function
What is the probability of rolling exactly two sixes in 6 rolls of a die?
Solution by the Binomial Probability formula is
$$\binom{6}{2} \left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right)^4 = ...
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Distribution help
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.
It is known that 85% ...
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2answers
167 views
Binomial GLM and different sample sizes
I have a data set which consists of binomial proportions, let's say the success rate of converting a customer depending on the advertisement, the customer age, and various other factors.
For some ...
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1answer
34 views
How to find the distribution of the result of a compound experiment
I'm trying to find the distribution of data collected from a die-roll and coin-toss experiment. The experiment is as follows:
1)Roll a fair die so that you get a number $D \in (1,...,6)$
2)Flip a ...
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1answer
29 views
How many measurements (10 million molecules each time) are needed to analyze 15 million unique molecues in a 20 million pool?
This is my homework: There are 20 million DNA molecules in a library for high throughput DNA sequencing, each sequencing run can generate 10 million reads (i.e., analyze 10 millions of DNA molecules), ...
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1answer
234 views
Finding the z score and p-value of a binomial distribution
Emily is a big fan of lady gaga, and 20% of the songs on her ipod are lady gaga songs. Suppose Emily has her ipod on shuffle and repeat mode, which can be assumed to mean that each song to be played ...
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Why doesn't this represent a normal approximation to the binomial?
Suppose the registrar's office at a college reports 58% of the students live on campus. An intern working in the administration building is unaware of this 58% parameter value. He designs a study in ...
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combining binomial and normal values into one significance test
I have conducted an experiment in which a participant completes memory tasks (3 levels, within) while exploring a virtual environment (2 levels, within). The performance on these memory tasks is ...
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Plot the binomial distribution
How to plot the binomial distribution for p = 0.3, p = 0.5 and p = 0.7 and the total number of trials n = 60 as a function of k the number of successful trials. For each value of p, determine 1st ...
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1answer
44 views
How do you test for independence of k binomial variables?
I am analyzing some orthopedic data and our outcome is union vs. non-union of a fracture. One of our independent variables is whether or not the initial fracture was closed (skin intact) vs. open. ...
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Likelihood of events coinciding at random
I have what is probably a very naive question, but I've been unable to find a suitable explanation elsewhere. I am trying to calculate the likelihood of two errors occurring at the same position if ...
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Matched binomial pairs
I am trying to analyse the following table:
5 5 5 5 4 5 5 5 5
3 4 3 3 4 4 3 5 5
Each number is a success score out of 5 attempts, so we can assume binomial (p, 5), for unknown p. ...
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1answer
91 views
Finding parameter $p$ of the Bernouilli distribution which is exactly 99% significant
I ran some experiments first. Afterwards, I looked for the parameter $p_{max}$ for which I can claim the chance a matrix has the ESP-property is $p_{max}$ or lower to a significance of exactly 99%. Is ...
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2answers
108 views
Binomial distribution where probability of success is dependent on another binomial distribution
How does one model the Binomial distribution where the probability of success is the result of another Binomial distribution.
For example, say I make 10 coin tosses many times and record the number ...
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2answers
51 views
Which test should I use?
I have a set of probabilities that an event will occur (yes/no). E.g. [0.87, 0.56, 0.97], and I need to know "What is that probability that at least X of these events occurs?". I've been looking into ...
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Approximating binomial distribution by normal distribution
I got a very small probability in my homework so are there any mistakes?
Benford's law says that if we have a collection of numbers, the first digit has the distribution ...
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CDF and confidence interval on non-parametric binomial data
I am having trouble with a series of system tests in which each test is assumed to be a normal approximations of binomial distribution. Each test sample, n, is a Bernoulli ("success", "failure") trial ...
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Determine likelihood that a list of N items contains no negative results after examining X items
I have a large (N) list of results from a process that is either positive or negative. After examining X of them and receiving only positive results, how certain can I be that the list only contains ...
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2answers
338 views
What is the difference between logit-transformed linear regression, logistic regression, and a logistic mixed model?
Suppose I have 10 students, who each attempt to solve 20 math problems. The problems are scored correct or incorrect (in longdata) and each student's performance can be summarized by an accuracy ...
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1answer
36 views
Confidence intervals for count data of a categorical
I'm trying to analyze the results of a survey question. The question is multiple choice (but each respondent can only select one answer) and I want to calculate 95% confidence intervals for their ...
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2answers
378 views
Testing equality of two binomial proportions proportion (one near 100 %)
I am testing equality of two binomial proportions 87/88 and 48/60. I use
this online calculator and it noted that the Standard Normal approximation is not valid in this case. It seem quite strange to ...
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Non-parametric confidence interval for a small sample
I have a question about measuring a confidence interval for a binomial success rate using from a "small" universe. I should say that I don't think that the underlying distribution is binomial for ...
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Non-inferiority testing without normal approximation
I am performing a non-inferiority test on two binomial trials. I want to determine if my test proportion, pT, is not worse than my control, pC, by more than an amount d. Assuming nT trials of my test ...
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Estimating population size and a proportion
I am interested in the following sampling problem, which I will try to describe by a motivating example.
Suppose we want to estimate how many people in a certain area, has blue eyes, how many have ...
