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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What's the problem with my sports streaks problem solution?

The problem is from the book "Think stats". It's formulated as follows: If there are 10 players in a basketball game and each one takes 15 shots during the course of the game, and each shot has ...
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Unconditional distribution of conditional binomial

I have been trying to model a situation in which some observed values, denoted $y_{i}^{r}$, are bounded from above by unobserved values $y_{i}$. In my work, in order to demonstrate some impossibility, ...
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410 views

Why does the continuity correction (say, the normal approximation to the binomial distribution) work?

I wish to better understand how the continuity correction to the binomial distribution for the normal approximation was derived. What method was used to decide we should add 1/2 (why not another ...
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49 views

Some basic probability dilemma

So I started studying probability and while it seemed all ok I'm having trouble wrapping my head around this one. So the question is: We have 100 balls , 10 black and 90 white. In 50 tries what is the ...
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1answer
15 views

Test Retest of highly skewed dichotomous variables

Does anyone have recommendations on how to evaluate test retest reliability with 95% CI (individuals took the same survey 1 week apart) on data that is dichotomous (yes = 1; no = 0) where the data is ...
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1answer
43 views

Level of factor taken as intercept?

I am using a GLM to analyze binomial data from one factor (Group) with three levels: Control, Control Treatment and Treatment. ...
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14 views

Predicting viewer's cultural heritage from glmer and lmer versions of formula with different results?

I'm trying to understand why I'm getting different results when comparing anovas for glmer(binomial) and lmer versions of a formula. I am interested in whether a participant/viewer's cultural ...
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24 views

Diagnostic device hypothesis testing for superiority to a fixed value

I am designing a study to demonstrate that a diagnostic medical device is more sensitive than a fixed performance goal of 70%. Currently I am attempting to determine the appropriate sample size. My ...
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1answer
20 views

Determining coin biases, given some information

I have a real-life problem which essentialy boils down to the following: Given n biased coins, given to you ordered from highest to low bias, determine the last coin (by index) whose bias is still ...
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1answer
22 views

Can I use a binomial model with logit link function when dealing with continuous proportions?

I have continuous proportion data (i.e. ranges from 0 to 1). Or it could be percentage too if multiplied by 100. This is the proportion/percentage of overlap in home range between animals, therefore I ...
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1answer
64 views

Probability that two people get a certain number of heads on 100 coin tosses and all other outcomes with lower probability?

2 people flip a coin 100 times. The first person get 42 heads, the second person gets 58 heads. What is the probability of this outcome and all other possible outcomes that have an equal or lower ...
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Voting: probability of outcome flip

Assume you have a set of $N$ persons who should vote in a poll "for" or "against" an issue. The outcome of the poll is taken with simple majority. Each person's vote is independent of the rest and ...
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16 views

Estimating The Probability Of Success For Text Data

Imagine the phrase toy maker and by itself, it has 1 success and 887 trials for a success ...
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1answer
15 views

Test if two binomial distribution are significantly different from each other

I obtained two groups of data from my experiment and calculated the binomial distribution for each group, trying to see if they are significantly different from each other. However, the z sore I got ...
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should the product of 2 independent binomials converge to a normal distribution for large sample sizes?

I have been studying 2x2 contingency tables and specifically I have been looking at situations where the marginals are fixed by design for one categorical variable. As an example, suppose a ...
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31 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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1answer
62 views

log ratio of Poisson means versus logit of binomial probability

Assume that two observed counts C1 and C2 are independent realizations of two Poisson processes: ...
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1answer
12 views

Comparing large and small populations

Here is a hypothetical that mimics my actual data (sensitive so cannot post actual details). I have 149 students in a class. In preparation for the final exam (which is pass/fail, NOT ranked), I held ...
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1answer
46 views

Inverse Sampling according to Haldane (1945)

According to the inverse-sampling method (Haldane 1945) you continue sampling until m of the rare items have been found. Let p be the frequency of the rare item ...
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1answer
69 views

Learning how to compute confidence intervals

Say we have tossed a coin $n$ times and have counted $s$ times of heads (success). So our estimated success probability for this binomial model is $p=s/n$. Now we are interested to compute the ...
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17 views

Calculate false negative probability for "fair coin” type problem:

Imagine the problem of determining whether a new wine vintage is better than one offered to customers in the past. Our null hypothesis is that both wines are equally good, i.e., 50% would rank it ...
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analyzing binary mortality data collected at different remeasurement intervals. Bonus for R implementation

I am replicating an analysis that models tree mortality data. Data are structured such that forest sites are revisted at some random interval, which is recorded. It is then determined if a tree lived ...
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1answer
16 views

Why is multinomial variance different from covariance between the same two random variables?

We know that if $\big(X_1,X_2...X_k) \sim multinomial(n;p_1,p_2...p_k)$ then $X_i \sim bin(n;p_i) $ Then, $var(X_i) = np_i(1-p_i)$. But we have $cov(X_i,X_j) = -np_ip_j$. So doesnt that imply ...
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How many boxes have balls?

I have N boxes, each of which may or may not contain a ball. I want to know how many boxes have balls by sampling the boxes in the following way. For each box in the N boxes: I open this box with ...
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31 views

Nonlinear regression vs. GLMs for estimating ED50

Are binomial GLMs better than nonlinear regression for model-fitting, and predicting ED50s and other effective dose point intercepts? In toxicology it is typical to run an experiment with a ...
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Strange predictions from binomial glmm?

I am analysing the dominance of a Species, i.e. its relative abundance in a community. Since these data are proportions I use binomial models. However, the predictions from these models are ...
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52 views

What transformation should I use for a bimodal distribution?

I have some bimodal data like the one generated down (R language), and I don't know how to transform it to have a normal distribution or homoscedasticity. I'm running a linear discriminant analysis ...
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1answer
27 views

Generating Random Variable from Binomial Distribution [closed]

I am using r for generating random numbers from Binomial distribution using the following code: ...
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100 views

Probability of a claim being rejected or accepted using binomial distribution

I am self-learning statistics. I was going through Probability and Statistics For Engineering and the Sciences by Jay L. Devore and stumbled upon the following example: An electronics manufacturer ...
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30 views

68–95–99.7 rule for binomial distribution?

What I want to calculate is the probability that the size $k'$ of an intersection of two subgroups with sizes $n$ and $K$ that have been randomly selected from a group with size $N$ that is smaller ...
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How to derive bernoulli deviance

I found the deviance definition in https://en.wikipedia.org/wiki/Deviance_(statistics) and the one-observation bernoulli deviance in Scikit Binomial Deviance Loss Function. $$ ...
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1answer
56 views

Beta approaching Binomial

If we have a Beta likelihood and a binomial prior, we get a beta posterior. Can someone please explain why this approaches a binomial as $n\rightarrow\infty$. I plotted it and this appears to be the ...
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8 views

Estimated values for Chi-square

To test if my point pattern is random, I am going to conduct a Chi square test. The data has 40 points divided to 3 by 3 tiles. Should I use Binomial or Poisson probability to calculate expected ...
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1answer
41 views

normal approximation to the binomial distribution: why np>5?

Nearly every text book which discusses the normal approximation to the binomial distribution mentions the rule of thumb that the approximation can be used if $np\geq5$ and $n(1-p)\geq 5$. Some books ...
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Looking for derivation of Shannon entropy of binomial distribution

According to Wikipedia, the Shannon entropy of a binomial distribution is $\frac{1}{2}log_2 (2\pi*e* np(1-p)) + O(1/n)$ Does anyone know where I can find a derivation?
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Exact binomial test. Directional hypotheses - how to explain differences in results?

Let's assume the following problem: A sample of 30 subjects has been drawn from a specific population. It has been proved that the expected rate of some negative events among the subjects in ...
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21 views

How to interpret glmer results based on a bootstrap dataset?

I have bird nesting data and I am trying to see whether the nest treatment has any significant effects on the survival of the nestling. My original data set is relatively small (n=101). The response ...
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25 views

Comparing binomial outcomes from prediction algorithms in R

I've written a simple model to predict the outcome of soccer games based on some input. The outcome is either "H","D",or "A", short for home team, away team, or draw. I'm comparing the results of this ...
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20 views

How to deal with 2 response variable model?

given, for example, a glm model: fitglm <- glm (formula = cbind(Successes, Failures) ~ other variables, family = binomial) How would you interpret the ...
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24 views

Confidence interval for estimator of the mean of different binomial distributions

I have a dataset that is a series of binary matrices like so: 00000 01110 00110 00000 Each matrix is sampling from the same distribution. I'm aggregating the 2D ...
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GLM model specification in distribution and link function for fractional (percentage) response data

I have some aggregated data. Indep. Dep. N 1.3 78% 23 1.2 67% 20 Note that both the independent and dependent variables are aggregated by ...
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1answer
57 views

Standard Error differences Binomial Regression vs Poisson Regression

I'm running three different models on a dataset found in table 9.1 of Dobson's Introduction to Generalized Linear Models textbook. Model 1 is a poisson regression, Model 2 is a binomial regression ...
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Offset instead of percent data?

In R I want to build a GLM explaining the fraction of a coral perimeter that is covered by different algae. I measured the perimeter of the coral (in cm, integer values) and fraction that is contacted ...
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1answer
35 views

Can there be overdispersion in a logistic regression model where each observation represents a single Bernoulli trial?

A friend and I are having a dis-agreement about over-dispersion in binomial/logistic regression glm modelling. We have structured our data so that each observation represents 1 Bernoulli trial (so the ...
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15 views

Compare two distributions with varying focus on different regions

I have been trying to find if my problem matches has been discussed in prior research and if any technique exists to solve it. Here's the problem: Given two distributions (pdf) D1 and D2 over a ...
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1answer
43 views

Basic Binomial distribution computation

first post on this website. I have a very basic question on computing a somewhat large computation. The equation to be solved is as follows: $$P(X<262) = \sum_{x=0}^{261} {5236 \choose ...
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3answers
64 views

Why doesn't multiplication by constant affect MLE? [duplicate]

I have an example that derives the MLE for Binomial. Since there's that factorial term $n_i \choose x_i$ in front of the Binomial p.d.f. and it's a constant, the example claims that one can merely ...
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1answer
29 views

Expectation of a function of a binomial distribution

I have a question that is: Given n iid Bernoulli(p) distributions: $X_1, X_2, \ldots, X_n$ and $S_n=\sum X_i$. Find $E[(S_n-np)^3]$. Hint: $S_n-np= \sum (X_i-p)$. So far, I have gotten that $S_n$ is ...
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Best sample size formula and continuity correction for tiny proportions?

I have found the following formulae (from http://www.itl.nist.gov/div898/handbook/prc/section2/prc242.htm) to estimate the sample size required to test the binomial proportion in a single sample. I ...
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What is the best test to measure deviations from tiny proportions?

What is the best (most reliable and robust) test to measure deviations from tiny expected proportions (e.g., p0 < 10^-6) in a huge sample? Binomial? Poisson? Negative binomial? Something else? ...