Questions tagged [sample]
a sequence of objects or individuals collected from a larger (possibly infinite) population or process.
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What are the individual elements within the outcome of a sample space called?
What is each entry in an outcome of a sample space called?
For example, say our outcome is ${HHT}$, describing two heads and one tail.
What is each head ($H$) and tail ($T$) member of the outcome ...
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Closed form formula for distance of multinomial sample from underlying distribution
Suppose that I have a probability vector $p$ e.g. of size 10, and that I draw a multinomial sample of size $n$ from $p$. Does there exist a closed form formula to compute the expected total variation ...
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How can we use average total time if a job to determine time of components?
Imagine a scenario where there are tasks (called jobs) made of many smaller tasks (called assemblies). Each assembly has an average time to completion, and the job time to completion is a sum of the ...
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How to test that a sample of a discrete random variable is representative?
I am given a discrete random variable and several large samples from it. The methods how the samples are obtained are not truly random samples but are reasonable approximations to a random sample.
An ...
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Do I need a hypothesis test to compare two populations of complete annual count data?
I would like to compare the total number of public M&A transactions observed in two separate years (e.g. 2021 vs 2022). Given the data set for each year is complete (i.e. a population), can I ...
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Question about Analogy to Statistics
If anyone could help me verify if my analogy is correct, thanks so much!
Here is an analogy:
A population is like a pot of soup.
We stir the pot of soup with the ladle because naturally the contents ...
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Bayesian inference on model parameters from summary statistics alone
Consider quantities $y_1,y_2,\dots,y_p$, for the $j$th of which we have $n_j$ measurements $y_{1j},y_{2j},\dots,y_{n_jj}$. Unfortunately, I do not have access to the raw data $y_{ij}$ -- only to the ...
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What is the distribution of the sample (empirical) KL divergence and can we use bootstrapping to approximate it?
Let $p, q$ be two distributions, and suppose one can evaluate them pointwise.
Let $\{x_i \}_{i = 1}^n$ be an IID sample from $p$, and let $KL_n = \frac{1}{n}\sum_i \log\left[ \frac{p(x_i)}{q(x_i)} \...
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Bridging the gap from theory to implementation in "Conditional Distance Correlation" by Wang et al. 2015?
In an attempt to implement a form of conditional distance correlation for random variables represented as vectors of observations, I came upon this paper that nicely extends the notion of distance ...
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How to prove that if the bootstrapped sample means are approximately normal, then the sample mean is approximately normal?
I'm considering the scenario described in this question, namely:
we have IID $X_i, i = 1, ..., n$ sampled from a population with mean $\mu$, variance $\sigma^2$ unknown
the goal is to put a ...
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How to compare U.S. Census demographic data to a population-level dataset? E.g. how to approach a question like are women underrepresented on boards?
I have a population-level dataset of all people who testified on environmental legislation in a single year. I have data on all witness's ages, races, genders, and ethnicities. This dataset is not a ...
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Calculating sample size in a RCT with R vs G*Power - same method but, different sample sizes
I'm estimating the appropriate sample size for a RCT study, 3 groups, 3 measurements, power=90%, medium effect size (F=0.25), p=0.01 - anova repeated measures, within-between interaction.
When doing ...
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How to calculate confidence intervals in a subgroup of a weighted sample?
I have a weighted data sample (size : 20000) and I want to calculate a 95% confidence interval for the mean of a variable in the dataset, but only in a specific subgroup within this dataset (size of ...
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P value and sample size
Say for a 2x2 experiment, the power analysis said the sample size should be over 1000 to detect 0.1 effect size. Right now, with the sample size of below 100, the effect size of .12 is insignificant ...
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Regression with random vs uniform distribution of a covariate
Suppose we have some population of individuals, each having X and Y variable. I know that in the population, most individuals have low values of X, but I want to find regression formula for low as ...
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Does it make sense to do the power analysis if one of the sample proportions is 0%? [closed]
Can we have any sample size if one of the sample proportions is 0. I mean even the slightest difference detected between the two groups would be because of the treatment in this case, and hence I do ...
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Looking for a formula to determine accuracy of a sample
I am looking for a formula to help me determine the accuracy of a population.
Here is my business problem.
I have about 1 million scanned documents of many types that are currently unclassified ...
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Mixed effects model with data for whole population
I have a dataset about the whole population of interest, not just a sample of it.
I ran a mixed effect model where age and sex are fixed effects; urban area where individuals live and country of ...
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Sample size for a survey with randomly assigned questions
This may seen like a dumb question for someone familiar on how to structure survey sample sizes, but I have a hard time finding the literature to back this up.
I have a survey that cover's 3 countries,...
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Estimate potential distance from population mean given only sample size?
Let say I am sampling from a population with an unknown distribution to approximate the mean of the population.
I am trying to figure out how large my sample size n has to be in order to guarantee ...
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Sample size calculation in two different population for administration of a questionnaire
I need some help calculating a sample size.
I have two groups of people to whom I need to fill out a questionnaire. Group A consists of 45,000 people and group B consists of 3,000 people.
How do I ...
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Using t-test to check the difference between a sample and subsample? [duplicate]
I have a large dataset and I want to check if there is any difference between the whole sample and the subsample.
For example, I'm checking the difference in the age of patients in the whole sample ...
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How to determine sample size of rated objects for scale development
I am currently looking into developing a scale to measure a latent construct. I believe the latent construct is a property of conversation sequences. The scale I am developing has 4 a priori defined ...
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Estimand dependent on the sample
Suppose we have a sample $S$ of IID data and two different real-valued functions of $S$, say $\theta(S)$ and $f(S)$, and the latter is intended to estimate the value of the former. For example, the ...
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Null hypothesis significance testing when values are known
I'm looking at the association between two categorical variables in a genus of birds. The variables are 'Conservation Concern' (Yes/No) and another binary variable (Yes/No) and I have these for every ...
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Which test to use for small and unequal samples
I have a sample of stroke patients and I want to find the education effect on their performance in a neuropsychological tool. The total sample is n=19. I have divided the sample into 3 groups ...
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Regression Coefficients
I am performing regression analysis based on a full sample and two sub samples from the full sample. Is it always the case that the coefficient of the full sample lies between the coefficients of the ...
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How to account for difference in group sizes for logistic regression
Using this study as an example, I am wondering if the size of different study groups run in the same models impacts the conclusions we can draw from statistical tests.
In this study, the researchers ...
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Why does one interested in modelling the distribution of median of random samples?
I was reading this article which introduce the families of distribution for the median of an random sample. However, the writer did not state the reason why one is interested in modelling the ...
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Bessel correction for the variance of dependent sample
Assuming a sample $X_1, X_2, ..., X_n$, the sample variance is calculated as
$s^2 = \frac{1}{n-1} \sum (X_i-\bar{X})^2$
The fact that there is $n-1$ in the denominator instead of $n$ is called the ...
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Should I use null hypothesis significance testing when I have the full population? [duplicate]
I have data on every species in a genus, and am interested in how two factors relate to each other specifically within that genus. Should I use a statistical test to do this or does it not make sense? ...
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When the sample sizes of two datasets are greatly different, is the result of non-parametric testing still reliable?
I want to investigate whether there is a significant difference in the centrality of eigenvectors between two groups. The sample sizes of the two groups are over 9000 and 300, respectively, with a ...
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Tools for reporting sample size that contains the percentage of the population
If we have a recorded percentage (statistic) on a population, if we take random samples we might not encounter the percentage till e.g. even we exhaust the population.
E.g. a box with $500000$ balls ...
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Estimate how many wrong measures there is in a sample
This study shows that the average penis mean is 13.24cm and the standard deviation is 1.89cm. Let's suppose we have a population with this mean and standard deviation for penis length.
Suppose we ask ...
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Distributions of random (partial) correlations drawn from a given data matrix
Background: Let $X=[x_{j,k}]_{j=1,\ldots,p, k=1,\ldots,n}$ be a $p\times n$ data matrix. Each column is an i.i.d. $p$-dimensional centred random vector. One can compute the sample covariance matrix
$$...
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Can I use the chi squared test to check a sample is representative of my population across multiple categories?
I was wondering if I could use the chi square test to see if my sample % split size is representative of all the splits.
I know I need to use integers and not %. So, could I multiply my split % by my ...
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The standard deviation of the mean of the means
I have 8 means referring to 8 groups. Since I have the numerosity of each group, I can calculate the mean of the means. How can I calculate the standard deviation of the mean of the means?
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Is Kendall's tau uniquely determined by Pearson rho?
I know that two data sets can have the same Kendall's $\tau$ but different Pearson's $\rho$.
What about the opposite? Can two different data sets have the same Pearson's $\rho$, but different Kendall'...
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Comparing two binomials with with partially matched sample
Imagine a scenario where I want to understand a population's support for a political candidate. I sample n=500 people randomly with replacement and ask them if they want to vote for candidate A or B. ...
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When monitoring a sample, how to gauge when a substratum significantly exceeds sample size estimates and should therefore have its rates adjusted?
I'm in charge of a year-long, stratified sample where the population is estimated based on previous years but which is also quite dynamic, changing in unpredicted ways every year (furthermore, past ...
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Sample variance of a normal distribution
If my sample variance of a random sample from a $\mathop{\mathcal N}\left(\mu,\sigma^2\right)$ distribution is
$$S_2^2=\frac{1}{n}\sum_{i=1}^n{\left(X_i-\bar{X}\right)}^2,$$
then
$$Q \mathrel {:=}\...
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How to combine standard deviations from independent samples?
I have a population of 7954 subjects and multiple random samples from it:
1st sample size 2,665 with a standard deviation 1.386 and mean -7.45
2nd sample size 2,399 with std dev 1.53 and mean -7.33
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Distribution of the point estimator of a sample
We know that point estimator is defined over a sample and is said to be unbiased if its expectation value is same as that of some parametric function $g(\theta)$ where $\theta$ is a parameter for the ...
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Doubt in empirical distribution, sample and random variable
I have a basic doubt in sample and random variables. I have read related posts on this site but still some doubt is still left.
Suppose we have a population and we are drawing some entries from it ...
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Why sample size calculation for ratio-based metric doesn't consider the standard deviation of the ratio
When calculating sample size for ratio-based metrics like CTR or Purchase Rate, it appears that one doesn't need to consider the standard deviation of the ratio metrics.
I tried calculators like https:...
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Association preserved under sampling
Suppose I have two columns of data as follows:
X
Y
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I am interested in the entries where X and Y are 1, suppose in this case 50% of the records have 1 , now let's say, I ...
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A question about the variance of sample variance? [duplicate]
if I have negative kurtosis in my distribution (meaning negative exceeded kurtosis) - which indicates that the tails are lighter than normal distribution tails.
Does it also mean that I have more ...
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Survey with two simple random samples without repetition
I have an particular exercise of sampling survey, or sampling theory, which I report below.
One is interested in knowing the price per gram of gold produced by 100 companies. A monthly survey of a ...
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Definition - Simple random sample
In a textbook of mine I detected the follow definition of a random sample:
"Every possible sample of size n has the same probability of being selected"
However, I also already saw some ...
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Comparison of two histogram with increasing range scale
I have a requirement of comparing two histograms. It is a distribution of buckets of time frames and each bucket has finite no. of entries.
An example of the histogram:
buckets - [2, 4, 8, 16, 32, 64, ...
