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.

learn more… | top users | synonyms

0
votes
0answers
32 views

what is the Probability of selecting 10 SNPs from a list of 5000 SNPs simply by chance

We conducted a study to predict deleterious mutations from a list of around 5000 mutations (which contains both neutral and deleterious mutations; the real state of each mutation is unknown), using ...
0
votes
0answers
13 views

logistic regression with plsRglm [migrated]

I am using plsRglm package to run logistic regression, and met two major problems as below. My $X$ variables includes factor variables, such as immigrant status ...
0
votes
0answers
10 views

Standard error for aggregated proportions

In order to obtain confidence intervals for proportions I'm trying to calculate the standard error, but I'm having difficulty working out what N should be in a case such as mine. My data is such that ...
3
votes
1answer
26 views

Confidence Intervals for a relative risk where i lack the underlying data

I have two estimated rates and their 95% confidence intervals but not the underlying data. I take the ratio of the two to get a relative risk, but how do I determine the 95% confidence intervals for ...
4
votes
1answer
44 views

Has the free kick spray in soccer an effect? Binomial Testing

In Germany a referee supported the use of the free kick spray introduced on the World Cup 2014. He reported some statistics. His data supported the assumption using the spray leads to more goals after ...
2
votes
2answers
46 views

What coefficients do I use for a binomial distribution problem?

I'm studying for an exam and my study guide explained combinations, permutations, and binomial distributions, but didn't cover much how to recognize where each comes into play in problems. I'm having ...
1
vote
1answer
32 views

Independent events in sequence

If I flip a fair coin twice, the probability of at least one Head is 0.75 (HH, HT, TH and TT). I flip the coin once and it lands Tails. In order to get at least one Head, the probability of the ...
9
votes
1answer
104 views

Show that if $X \sim Bin(n, p)$, then $E|X - np| \le \sqrt{npq}.$

Currently stuck on this, I know I should probably use the mean deviation of the binomial distribution but I can't figure it out.
3
votes
1answer
27 views

Residual variance for glmer

I am running a glmer model and I want to determine the total variance. My data is for survival and it is coded as 0 and 1, where 1 represents that the individual survived and 0 represents that the ...
1
vote
0answers
19 views

Mixed logistic model with complete separation

I want am trying to produce a mixed logistic model but certain explanatory variables suffer from complete separation. I am aware that I need to either use exact logistic regression or a firth ...
2
votes
2answers
48 views

Is it possible to model the conditional expectation of a binary outcome using an additively-separable link function?

Logit and probit link functions aren't additively separable. So, fitting a model using these link functions implies that the effect of one predictor in determining the outcome is not independent of ...
5
votes
1answer
31 views

multi stage binomial “process”

I wish to model the retransmission time of a file that divided into K blocks. I know the successful blocks of first transmission obey the binomial distribution $$ X_1 \sim \text B(K,p) $$ , p is the ...
2
votes
0answers
35 views

Put constraint on max (or min) predicted value (mgcv)

I want to fit my data using a logistic GAM model with cubic regression splines. I know for sure that in reality my estimated probability should not go above 0.5 (due to mislabeling). So I thought ...
1
vote
0answers
14 views

A binomial test with repeated measures?

I'm working on a study with a single trained animal (ie. our only participant). He is making a binary choice on a number of consecutive trials (we are essentially trying to teach him a rule -- if A, ...
1
vote
0answers
18 views

Test statistic and C.I. for population proportion

I'm doing a test statistic and C.I. for population proportion. Can someone explain to me what are assumptions coming from hypergeometrical distribution directly to normal distribution? As I ...
2
votes
1answer
14 views

Test equality of binomial variances across four groups

I have four 100x1 vectors of binary outcomes of a particular experiment. I want to test for equality in variance across all of the four different treatment groups. At the moment I have used the ...
1
vote
2answers
26 views

Determining unusual binomial results from a sub-population

If I have a population of 1948 students with a success rate of .154 (301 successes) and I break the 1948 students into their respective majors, how to I determine if the sub-population success rate is ...
-2
votes
1answer
28 views

Reduce the polynomial terms in logistic regression (glm)

I've three categorical variables A, B and C with 5 levels each. The model I'm trying to fit is glm(Y~A+B+C, family=binomial()) How can I remove the higher order ...
2
votes
0answers
20 views

distribution of censored multinomial variable

Let $F$ be a multinomial random vector of $n$ trials in $k$ categories. Let the random vector $C$ be defined as \begin{equation}C_i \equiv \left\{\begin{aligned} 1 & \quad F_i>0 \\ 0 & ...
1
vote
1answer
36 views

Clarification on a paper regarding estimating N from a Binomial Distribution

I was wondering if someone could clarify the following for me. In the paper "Inference for the binomial $N$ parameter" by Adrian Raftery, his first example outlines the posterior of $N$ given $x$ as ...
1
vote
0answers
78 views

How to calculate confidence limits for various scenarios when drawing random cards from a pack?

I'm designing an experiment that involves a subject attempting to determine various attributes of a playing card drawn at random from a standard 52 card pack. The experiment is in four phases: ...
0
votes
0answers
15 views

Finding n and c in single sampling plan

I am learning a quality control course and in Single sampling scheme for attribute type inspection I don't understand the method used for calculating the values of $n$ and $c$. The method is as ...
5
votes
3answers
233 views

Logistic Regression - Error Term and its Distribution

On whether an error term exists in logistic regression (and its assumed distribution), I have read in various places that: no error term exists the error term has a binomial distribution (in ...
0
votes
0answers
20 views

What method to use in this cancer problem?

I am confused on what to do with this problem: "Suppose we identify fifty 50-to 54-year old women who have both a mother and sister with a history of breast cancer. Five of these women themselves ...
0
votes
0answers
17 views

Comparing the difference in proportions for 3 different groups

I conducted an experiment and just need some general guidance on where to go from here. I know I have to do some kind of binomial test on my data. Suppose I have the following data: ...
0
votes
1answer
106 views

Exact two sample proportions binomial test in R (and some strange p-values)

I am trying to solve the following question: Player A won 17 out of 25 games while player B won 8 out of 20 - is there a significant difference between both ratios? The thing to do in R that ...
0
votes
1answer
19 views

Computing mixture of Binomial distributions

I'm trying to model a simple Bayes net, with $n$ samples based on a (unobservable) Bernoulli parameter, representing a true state of the world. Let $T$ be a Bernoulli random variable, with ...
3
votes
0answers
140 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 ...
6
votes
1answer
191 views

Estimating parameters for a binomial

First of all I'd like to precise that I'm not an expert of the subject. Suppose to have two random variables $X$ and $Y$ that are binomial, respectively $X\sim B(n_1,p)$ and $Y\sim B(n_2,p),$ note ...
3
votes
1answer
79 views

Problem with urn

I'm reading Thinking fast and slow and there's this problem I cannot get a correct answer. Here it is: Half the marbles are red, half are white. Next imagine a very patient person (or a robot) ...
2
votes
1answer
79 views

How to compare the proportion female with the proportion male

I would like to know if it is correct to do the following statistical comparison: In a sample of $440$ patients, I have $241$ females ($54.8\%$) and $199$ males ($45.2\%$). Are these proportions ...
4
votes
1answer
67 views

Are these data underdispersed? If so, what mechanisms may explain this?

Say someone who is well practiced (appears to have reached a performance plateau) shoots 20 free throws on 15 different days and is successful the number of times shown in the upper histogram (...
3
votes
1answer
85 views

Can multinomial distribution be simulated by a sequence of binomial draws?

I wonder if single multinomial distribution (I will use the notation from JAGS/WinBUGS, but in fact, this is principial thing rather than of particular language) ...
1
vote
1answer
30 views

Testing for samples being drawn from identical Bernoulli r.v.'s

Suppose that I have a sequence of size $n$: $x_1,\ldots,x_n$, $x_i\in\{0,1\}$. My null hypothesis is that all $n$ members of the sequence are drawn independently from an identical Bernoulli ...
-1
votes
1answer
49 views

75% success, ranges for given sample sizes with 95% confidence

A given task has a 75% chance of success. With 90% confidence, what would be expected ranges of success for - 10 attempts - 50 attempts - 100 attempts - 1,000 attempts - 10,000 attempts very many ...
2
votes
1answer
20 views

Confidence Interval for the average of a set of proportions

If I have a dataset of 500+ observations (people in this case) that has the % of allotted dollars that were spent for each person (so, I have each persons allotted dollars and their dollars spent), ...
3
votes
0answers
42 views

Sum of Bernoulli random variables

I need some help with a homework assignment. The question I'm given is: "Suppose that $X_1, X_2,..., X_n, W$ are independent random variables such that $X_i\sim Bin(1,0.4)$ and $P(W=i)=1/n$ for $i=1, ...
1
vote
1answer
47 views

Power analyses of 5 populations of infection data (binomial data) [duplicate]

I am PhD Biologist. I have 5 populations of infected moth larvae (3 inbred, and 2 outbred). The infection in this case is spread vertically (from mother or father to offspring). Normally the virus is ...
1
vote
1answer
40 views

Statistical measure of international diversity

I've got a large collection of geotagged tweets, each linking to an article from a given author. For each author, I'd like to derive a number that describes how diverse is their list of tweeting ...
4
votes
1answer
33 views

Distribution of random sample of confidence intervals containing the true mean

Given 50 random samples, each of size 25, from a normal distribution with mean 20 and standard deviation 5. From each of the 50 samples, you can find a 90% confidence interval for the mean. Let Y be a ...
1
vote
1answer
36 views

Questions about non-standard test statistic for difference of two population proportions

Background I'm considering the number of observed 'successes' $x_1$ and $x_2$ from $n_1$ and $n_2$ independent trials respectively. These counts can be considered realisations of random variables ...
0
votes
1answer
72 views

Bootstrapping probability of success: what is wrong with my method?

I have a dataset where each row represents the outcome of individual bets placed by a population of players; each row has two fields: a player identifier and the outcome of the bet (1 if the player ...
0
votes
3answers
62 views

For Y~B(11, 0.3) what is P(|Y-5| >= 3)?

I feel this is a simple problem, yet I cannot seem to solve it. Any help is greatly appreciated.
0
votes
0answers
9 views

Scaling Specificity to larger data set

Suppose I have the following 2x2 table ...
0
votes
1answer
49 views

Binomial Probability (Dice)

The throwing of a one or two is called a success. The six dice are thrown together 64 times and the frequencies of the throws with 0, 1, 2,..., 6 successes are summed over all six pairs are as ...
0
votes
1answer
16 views

Combining two estimates of p in a binomial estimation

I have an estimation problem for a binomial data. I got a sample and from that I can get an estimation. But I also have a kind of prior information about the p. But mind it, this prior is just a ...
0
votes
0answers
17 views

Binomial distribution - one-tailed

I am still struggling with a few questions regarding binomial distribution. Any help or ideas on how to solve them, would be very much appreciated!! Regards Ida N = 20. Determine the critical number ...
0
votes
1answer
36 views

Binomial distribution - coin toss

I would be really happy, if someone would explain how I solve this; Let p denote the probability for “head” in a coin toss, p = 0.5. The coin is thrown N times. What is the probability of the ...
1
vote
1answer
49 views

Evaluating a binomial (success vs. failure) glm

I'm familiar with (some) approaches to evaluating the fit (or accuracy) of a binary (logistic) model (e.g. AUC). Are there methods/approaches that are particularly well-suited for a binomial (success ...
0
votes
0answers
16 views

Binomial Distribution's Syntax in R

About The Binomial Distribution and statistics R. dbinom(1:6, 7, 0.8) What is number 7? Is it population?