Linked Questions
42 questions linked to/from Confidence interval around binomial estimate of 0 or 1
4
votes
2
answers
221
views
Confidence interval for proportion assuming binomial distribution when observed proportion is exactly 1 (or 0) [duplicate]
I have a simulation (a set of 200 iterations) which I used to compute a confidence interval for average statistical power. In binomial approximation, I know that the standard error is computed as $\...
1
vote
1
answer
329
views
Calculating Confidence Intervals when proportion is skewed [duplicate]
I have 15,000 address strings which I have written a piece of code which assigns them to broad geographic region e.g. American address assigned to North America. I would like to check the accuracy of ...
- 71
1
vote
2
answers
194
views
Confidence interval of the proportion in case of 0 [duplicate]
I am trying to estimate the (say 95%) confidence interval of a proportion.
For instance, I want to estimate how many students will take a particular course next year. There are N1 students in total. I ...
- 1,017
1
vote
0
answers
192
views
How to calculate a standard deviation given a sample proportion of 0? [duplicate]
I'm conducting a meta-analysis, and some of the studies that I have included only report the number of occurrences of the event of interest without an accompanying standard deviation. As such, I am ...
- 11
0
votes
0
answers
57
views
how to estimate confidence interval when p is close to 0 for binomial distribution? [duplicate]
I was trying to get confidence interval for $\hat{p}$. However, the estimated p in the population is close to zero. So I am wondering how I can calculate the confidence interval when p is that small? (...
- 133
0
votes
0
answers
29
views
Understanding the Coverage Probability of a Coin Toss [duplicate]
Suppose there is a coin where the probability of success if 0.63.
Let's say that I flip this coin 100 times and record the results (e.g. Mean, Standard Deviation and 95% Confidence Interval based on ...
0
votes
0
answers
15
views
Statistical question - conditional probability [duplicate]
I would like to ask below question:
i am trying to detect a kind of event by experiments, i repeat the experiment for 21 times, but no event of interest occurred.
My quesiton is based on current ...
- 75
1
vote
0
answers
14
views
Evaluate the probability of my experiment being deteministic AKA what tis the chance of something which has never happened happening? [duplicate]
Short version
Imagine I run the exact same experiment $n$ independent times and get $n$ times the same result. Can you put a lower bound on the probability of getting the same result the $n+1$ time I ...
- 111
58
votes
9
answers
33k
views
How to tell the probability of failure if there were no failures?
I was wondering if there is a way to tell the probability of something failing (a product) if we have 100,000 products in the field for 1 year and with no failures? What is the probability that one of ...
- 581
64
votes
4
answers
48k
views
Confidence interval for Bernoulli sampling
I have a random sample of Bernoulli random variables $X_1 ... X_N$, where $X_i$ are i.i.d. r.v. and $P(X_i = 1) = p$, and $p$ is an unknown parameter.
Obviously, one can find an estimate for $p$: $\...
Oleg
24
votes
7
answers
5k
views
Statistical fallacy from a Japanese light novel
The following is a snippet of dialogue from the first volume of the Japanese light novel series Combatants Will Be Dispatched:
"Listen here, number 6. This teleportation machine hasn't failed ...
- 243
24
votes
2
answers
4k
views
Mother milk of 6 Corona-positive (COVID-19) women does not contain the virus - can we make a confidence statement about this?
I am asking this question because I believe it would be great if the statistics community could make a contribution to solving this serious puzzle until more evidence is available.
The UK Royal ...
- 6,724
18
votes
1
answer
13k
views
ML estimate of exponential distribution (with censored data)
In Survival Analysis, you assume the survival time of a r.v. $X_i$ to be exponentially distributed. Considering now that I have $x_1,\dots,x_n$ "outcomes" of i.i.d r.v.'s $X_i$. Only some proportion ...
- 691
12
votes
4
answers
1k
views
Should point estimates for a parameter always be exactly in the middle of their 95% CI or does it depend on the distribution? [duplicate]
I'm modelling some count data using negative binomial regression with glm.nb in R. I've noticed that my point estimates are quite consistently not at the midpoint of the 95% CIs and wondering if this ...
9
votes
1
answer
8k
views
Calculating 95% CI of a proportion of 0%
I have a sample of 72 individuals. 0 of these had the trait I'm investigating. How do I calculate the 95% CI when the proportion is 0%?
- 91
7
votes
2
answers
17k
views
Chi-square test or Z-test for comparing two proportions?
On this website the appropriate statistical test for comparing two independent proportions is described as a $Z$-test (a normal distribution is used to obtain a $p$-value).
However, in R ...
- 4,056
4
votes
4
answers
1k
views
Use of Relative Likelihoods in Statistics?
I am reading this article here on Confidence Intervals for Binomial Proportions (https://www.scirp.org/pdf/ojs_2021101415023495.pdf).
In this article, the author lists several different methods (e.g. ...
6
votes
1
answer
10k
views
Are different p-values for chi-squared and z test expected for testing difference in proportions?
I'm trying to test the difference in proportions using the z test method and chi-squared method, but am getting very different answers. Is that normal?
My data:
...
- 1,821
8
votes
1
answer
2k
views
How to get the confidence interval of a Bernoulli trial if $\hat{p} = 0$?
I know the standard formula for the Bernoulli CI is:
$$\hat{p}\pm z_{1-\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$
If $\hat{p} = \frac{m}{n}$ how do I estimate the confidence interval when$\ n$ ...
- 183
7
votes
2
answers
3k
views
Confidence interval for mean of Poisson with only zero counts
I have 50 sample units in group A all with counts of zero. I have other groups that have some non-zero counts.
I would like to make a 95% confidence interval for the mean count per sample unit within ...
- 579
2
votes
1
answer
5k
views
How much sense does median of one number make?
Median of one number = the number itself.
I am calculating the median price sq ft of properties of different areas based on the different data entries I have got that include their ID, area and ...
6
votes
2
answers
2k
views
Uncertainty in a fractional count
What is the uncertainty (68% confidence level) of $N/M$, where $N$ is the number of entries that pass a cut and $M$ is the total number of entries? ($N$ and $M$ are both integers, and I'm interested ...
- 211
1
vote
1
answer
2k
views
How to calculate confidence interval of an MLE estimate for a Bernouli random variable
Let's say a coin has a probability of P=2/3 of landing on heads on any independent flip. After flipping the coin N=10000 times, you observe heads on F=60% of the flips.
Suppose the width of the 95% ...
- 153
4
votes
2
answers
1k
views
Is it reasonable to expect any process to have a zero error rate ?
I am interested in the philosophical answer to the question: can any complex process with a measurable outcome of success or failure truly have a zero error rate (ie 100% success and 0% failure). I ...
7
votes
1
answer
214
views
Which binomial prediction interval works well for tail probabilities, i.e. $\hat{p}=1/n$ for large $n$
I'm working on a problem which has the following qualities.
The available data $x$ is numerous - on the order of $10^6$
The CDF $F_X$ has support over nonnegative real numbers.
I don't know $F_X$.
We ...
- 94.1k
1
vote
1
answer
2k
views
Estimation of the variance of MLE with small sample size and binomial distribution
Let $x$ be an observation from $X\sim Bin(n,p)$. I want to estimate $p$ and use ML estimator, $\widehat{p}=\frac{x}{n}$. I also want to estimate the variance of the estimator $\widehat{p}$. It equals: ...
- 461
1
vote
2
answers
900
views
Determining the significance of rare events
We have been having a discussion about the significance of 2 accidents.
If I have 2 groups:
Group 1 is a baseline where an accident has occurred 70 times in
3,500,000 and
Group 2 where an accident ...
- 13
7
votes
2
answers
469
views
Which binomial confidence interval is correct?
Background: I am working with a data set that requires a transformation. It's prevalence data so I have proportions to deal with, and as the proportions are quite low, I'm using the Freeman-Tukey ...
- 111
0
votes
1
answer
849
views
Bootstrapping if the estimate of interest equal to zero in the available data?
Let's assume I have a small sample (say 20 data points) and I'm interested in estimating the true proportion of the population based on this sample. My data looks as below (assume 20 Orange balls and ...
- 103
6
votes
1
answer
329
views
Using Rule of Three to obtain confidence interval for a binomial population
I have a large population of data instances (say, 1000 instances) that are either of class1 or of class2. I would like to obtain ...
- 171
4
votes
1
answer
511
views
minimum number of rolls necessary to determine how many sides a die has
For example, say you have a black box that has a number of n-sided dice in it. You have 4-sided dice, 6-sided, 8, 10, 12, 20 and so on. The die sides are all A except for one side that says B, e.g.
...
- 78
1
vote
2
answers
601
views
Confidence Intervals of the Positive Predictive Value: Adjusting my Bootstrap
I have two data sets, A and B, and I have linked them together using automatic, probabilistic methods to create a set of linked records (L). For example, my code could have predicted that record 1 in ...
- 179
1
vote
1
answer
436
views
Computing sample size for a sample to estimate binomial distribution when point estimate of proportion is 0
For example, I have a estimate of p = 0 (95% CI: 0, 0.01), and I want to know the sample size for this sample.
For $p\not =0$, I can compute the s.e. by $\sqrt(p(1-p)/n)$ to get the $n$, but not sure ...
- 151
2
votes
1
answer
121
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 ...
- 251
2
votes
1
answer
272
views
What is the proper way to estimate the probability (proportion of time) a rare event occurs?
Often, I need to estimate the probability (proportion of time) a rare event occurs. The standard MLE estimate often gives me extreme estimates since the denominator is usually 1, and the numerator is ...
- 21
2
votes
1
answer
254
views
0
votes
1
answer
233
views
Interval Estimation for a Binomial Proportion Given a Specific Test Outcome
Imagine that I had a coin, I tossed it 10 times (n) and it came up heads each time (x). What proportion heads I would get if I tossed it infinity times? A point estimate is 100%.
I can get the ...
- 179
3
votes
1
answer
81
views
Abnormally large confidence interval with binomial gam when p->1 at max of predictor range
I am running a gam (mgcv in R) to model a non-linear effect of time on a binomial reponse (positive or negative sample). This is a minimal example of such a model:
...
2
votes
0
answers
176
views
Estimating probabilities for binary data with only '1s'
I am working on a project with a set of data where people have a certain quality of interest, say "red hair." My goal is to estimate the probability that an individual has red hair. Normally, we'd use ...
- 2,941
2
votes
1
answer
52
views
Limit Case (1.0 prob) in Binomial Distribution Hypothesis Testing
I am trying to figure out a way to run a hypothesis test based on binomially distributed random variable, using R.
I have a control sample with size 1000. Random variable is binary. The probability ...
- 3,049
1
vote
2
answers
56
views
Compare multiple means and finding which one is the biggest and which one is the smallest
Is there a statistical test I can apply to compare multiple rates and get which one is the biggest and which one is the smallest?
Example:
1 person converted out of 2 for page A. conversion 1/2
10 ...
- 11
2
votes
0
answers
38
views
How much confidence to have data is correct based on checking N samples
If I have a dataset of size $N$, and choose $n$ samples, where $k$ of the samples are OK, how confident can I be that the dataset is OK?
To make it more concrete, suppose I have a dataset D1 with 5,...
- 936