# Questions tagged [sample]

A sample is a subset of a population. Statistics, in general, is concerned with using samples to make inference about the parameters governing a larger (possibly infinite) population.

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### margin of error when proportioning sample space

I have the dataset that contains 10660 chess matches. 3000 of these matches start with the same opening. I want to proportionate this rate to 100000 matches, and when I did it, I got the result of ...
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### how to test auto-selected sample and modify it to represent population

Suppose you have responses from a survey on an entire population, i.e. an organization of 5000 people. All has been invited to respond. Only 65% of them did. Assume also you have the ground truth of ...
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### How to compare patient groups in cohorts containing different distributions and subtypes?

I have performed targeted sequencing on a panel of genes resulting in variant data for a cohort consisting of patients with different cancer diagnoses. These same genes have been analyzed in other ...
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### Calculate sample size (n) for 2 populations

We have a pre-study that gives us the amount of people voting for the left wing in one region (0,25%) with N = 123490 and (0,22%) N = 150578. We need to know how large sample sizes we need in order to,...
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### How to compare sample and population characteristics?

I have a sample $S1$ of 200 people, and I obtained a subsample $S2$ of 100 people by emailing a survey link to $S1$. So, $S2$ is a nonrandom subsample drawn without replacement. In the sample $S1$, I ...
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### Is this problem calculable only due to the parameter choices?

I am looking at a problem form Hogg, Tannis & Zimmerman (Ed. 10), and I am curious if the given problem is calculable (for an upper-level undergrad math/stats course) because of the choice of the ...
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### How to determine the most representative distribution of a small sample of size N?

Given a list of World Heritage sites by country of the top 5 countries + 5 other random countries: ...
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### Terminology - population and sample in repeated rolling dice experiments

The the law of large numbers wikipedia page has an example on fair, six-sided dice: According to the law of large numbers, if a large number of fair six-sided dice are rolled, the average of their ...
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### population size determination

I was studying statistics and came across a conducted survey; here are the elements of sample size determination. "We are now conducting the survey to see if beets are the best vegetable to ...
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### Making a continuous distribution from a discrete histogram

I was handed a discrete histogram of a random variable $x$. How do I generate 2,000 continuous samples from the histogram which represent the original random variable $x$? My first thought is to fit a ...
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### Bootstrap sample estimate vs estimate of the sample

See wubers excellent answer in Mean of the bootstrap sample vs statistic of the sample Can somebody elaborate on the part regarding "BCa" and ABC. Let say you want to estimate the standard ...
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### Calculate sample size from margin of error and confidence level

I need to calculate the sample size for the data I have. I am given a margin of error5% with a confidence level 95% . Which formula can I use to get the sample size value if the total population size ...
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### Estimating weights of known component distributions in a mixture distribution

Given $n$ probability density functions ($p_1$, ..., $p_n$) with known distributions, what are the ways of estimating the weights ($w_1$, ..., $w_n$) of these component distributions given a sample ...
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### GR&R when the samples are not stable over time

for air flow measurement, I'm testing some highly accurate MEMS pressure sensors, accurate to few 100s of pascals. For the test equipment, I want to perform a GR&R, but if my understanding is ...
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### How do I prove that the expectation of sample variance is equal to the population variance for any distribution? [duplicate]

In other words, is $S^2$ unbiased for $\sigma^2$ for any distribution? I know how to prove this for the normal distribution, but is it possible for me to prove this generally? Thank you
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### Determine item level variance of single test administrations as well as of an entire sample of administrations

I am decades out of school and need help determining the correct statistic / concept to use for my use case. My agency (human services) uses a specific functional test to determine how well clients ...
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### Why is the Hyndman and Fan 1996 recommendation for sample quantile definition to standardize on not more accepted? [closed]

The 1996 paper Sample quantiles in statistical packages is often cited as the comprehensive source of sample quantile definitions and many a software package refers to the paper in the description of ...
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### Calculating the expected value of the population and the sample experimentally

I am a little bit confused about calculating the Sample Mean vs the mean of the population and proving that the mean of the sample mean is $\mu$ experimentally. Say we have 1000 values of a certain ...
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### T-test for mean difference in one variable for data with lots of (potentially correlated) variables

I have a really basic question. I don't know how to formulate it correctly, so I did not find any helpful resources yet. Pointers to anything would be highly appreciated. So the issue is that I'd like ...
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### Assess timeseries sample representativeness

Problem I want to build a benchmark (for forecasting models/algorithms/auto model selection) that runs over a subset of all my timeseries (each timeseries is a different case/business). Question Is ...
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### Expectation of sample mean for a population group using simple random sampling

As we know, in case of simple random sampling the sample mean, $\bar{x}$, is an unbiased estimator of the population mean, $\mu$ (for a prove, see, for example, here). I assume a similar case can be ...
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### distribution of positive cases in random sample

If I know the true distribution of the number of people who are in each category in a population, how can I determine the probability that test on a random sample will have a certain range of positive ...
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### Is minimizing Koenker-Bassett error the only optimization problem that gives sample quantile? [duplicate]

Sample quantile can be estimated by solving $\min_\theta \sum_{x \in X}f_\alpha(x-\theta)$ $f_\alpha = \alpha |x|$ when $x>0$, $f_\alpha = (1-\alpha) |x|$ when $x\leq0$. Sample expectile can be ...
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### Implications for sample size of multilevel/mixed-effects model when level 1 units are participant decisions and level 2 units are participants

I am planning a study that will use a hierarchical design. The study has participants engage in a decision-making task, wherein they make 40-50 decisions between 'Choice A' and 'Choice B' (I won't ...
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### Implementing a sampling scheme that satisfies certain probabilities

Suppose we have two boxes of balls. Balls can be blu or red. In the first box: the probability of drawing (at random with replacement - this is assumed everywhere) a red ball is $p^1_R=0.4$ the ...