# Questions tagged [binomial-distribution]

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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### Z-test for proportions with unequal variance and unequal sample sizes

I need to test a null hypothesis that two proportions are drawn from the same population. Data ...
1 vote
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### Difference between geometric distribution expectation and 1 - failure with Binomial

I'm trying to understand a simple problem: How many times you'd need to roll two dice to get two ones in a single roll. One way I see this is as a problem the geometric distribution describes. You ...
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### How can I determine which of two sequences of coin flips is real and which is fake?

This is an interesting problem I came across. I'm attempting to write a Python program to get a solution to it; however, I'm not sure how to proceed. So far, I know that I would expect the counts of ...
1 vote
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### Probability of outcomes from overlapping samples of a random variable

I have a feeling there is a straight forward answer to my question, but I'm not sure what the appropriate term to search for is. I'm trying to get a sense of what the probability is of finding some ...
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### Binomial mgcv::GAM with different behavioral states - how to interpret results

I'm trying to understand whether I have diel patterns of behavioral states of sampled animals. Per hour, each animal is assigned one of three states based on how much time it's spending in each state: ...
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### Find the probability of which sample comes from a "higher" distribution based on random sample from two distributions

I am trying to find the answer for the following question. I have two distributions of numbers between 1 and 8, as illustrated here: I draw random samples from each distribution, which we can call &...
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### Fisher's Exact Test for 4 subgroups

I have a question for using Fisher's exact test for subgroups. I have 39 subjects that was divided into 4 groups( n = 9, 5, 10, 15, respectively). There were 3 conditions dividing the groups. Table ...
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### Choosing statistical test for Preference-shift

I am having trouble choosing the proper method to support my hypothesis. I have conducted an animal study, where subjects chose A or B, 6 times a day for 3 days (day 1~3). At first, I divided the ...
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### Binomial test with Chance level prediction

Thanks for reading. I wanted to ask if my logic I used for my experiment makes any sense. My hypothesis is that watching Pepsi commercial increases Pepsi preference. My experiment has 2 steps. (1) ...
1 vote
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### Distribution for Fraction of Success in a Binomial Setting

So the actual original question I am trying to solve is a little bit different than the title: In a binomial setting with probability of success $p$, I keep examining observations until a fraction of ...
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### Setting null hypothesis for Binomial test

I have a question for setting null hypothesis in binomial test. More specifically, is there any way to assume chance level when it is unknown? For example, let's say that I have a slightly bent coin. ...
1 vote
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### binomial distribution with changing probability of success across samples

I've got a scenario question of: An economist interviews 75 students in a class of 100 to estimate the proportion of students who expect to obtain a ‘‘C’’ or better in the course. Is this a binomial ...
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### Expectation of indicator variable squared to compute variance of a binomial

$$X \tilde{} Bin(n,p)$$ I know that X can be written as the sum of indicator variables like this: $$Then ~ X = I_{1} + ...+ I_{n}, where,~ I_{i} = 1 ~ if~success,~0~ otherwise.$$ This is quite ...
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### If $X_1 \sim \text{binom}(p_1,n_1)$ and $X_2 \sim \text{binom}(p_2,n_2)$, how to prove that the MLE of $p = p_1 - p_2$ is $\hat{p}_1 - \hat{p}_2$?

Suppose $X_1 \sim \text{binom}(p_1,n_1)$ and $X_2 \sim \text{binom}(p_2,n_2)$, where $X_1$ and $X_2$ are independent, and let $p = p_1 - p_2$. How can I prove that $\hat{p} = \hat{p}_1 - \hat{p}_2$? (...
1 vote
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### Different types of residuals revealing different stories on model fit

I have a series of observations as y_actual and fit a glm model with binomial family using <...
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### How to test if watching a advertisement only 1 time is enough to change one's preference

I'm sort of having a trouble finding what statistical test to use in a specific project of mine. My experiment was as follows: I have 10 friends and they all prefer Coke cola then Pepsi. Each of them ...
1 vote
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### Cohens d in relation to a single case

Cohen's d in relation to a single case The average effect size (Cohens d) for insomnia-treatments ranges from about 0.3 to 0.4. If I had a patient that suffered from insomnia 4 out of 5 weekdays (...
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### Blocking Binomial Data (Bernoulli Trials)

Imagine you have a colony of roaches and you want to compare the efficacies of two insecticides. On one day you apply insecticide A to 50 insects and record your "outcome" as "1" (...
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### Convergence algorithm for power analysis?

I found this algorithm on a shared drive and I'm really curious how it works. From appearances, it's used to estimate the MDE in power analysis when the effect size (difference of proportion means) ...
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### Mean and Variance of an estimated squared proportion from a Binomial distributed random Variable

I want to make a confidence interval on the number of successes $K$, given a sample number $n_2$ and a proportion $h$, where the $K$ would be Binomial distributed. $$K \sim Bin(n_2, h)$$ However, ...
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### Probability distribution of binomial of binomial divided by same binomial

Let $Y \sim \mathrm{Bin}(n, q)$ and $X \sim \mathrm{Bin}(Y, p)$, is there an expression for the distribution of $X/Y$?