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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5 views

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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18 views

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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17 views

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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39 views

Calculating variance of a random variable with different probability of occurring

I want to calculate the variance of sample mean of an iid random sample $X_{1}, X_{2}, \cdots X_{n}$ of the random variable $X$ which is distributed as $N(\mu, \sigma^{2})$ with probability $(1-\delta)...
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20 views

Duplication of data and effects on various statistics

I recently had a question about the following based on duplication of data: Say you have $x_1, x_2, x_3, ..., x_n$. The t-statistic calculated from this dataset is $t_1$. Now, assume the data was ...
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Consequence of a single replacement in a sample to the probability of the sample

Let $S=\{(x_i, y_i)^m\}$ be a sample with $m$ outcomes drawn from an unknown $p(x,y)$. Let $\hat{p}(x,y)$ be the empirical distribution of the sample. I am reading a proof based on the following ...
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Sampling distribution of Pearson correlation coefficient

Suppose I have draw a random sample of points $(x_i,y_i)$ iid from some distribution, then I compute the Pearson correlation coefficient $\overline{\rho}$ of the points in the sample. Is $\overline{\...
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28 views

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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37 views

are the variance of a sample and the variance of a sample mean the same thing?

Suppose we draw a sample $x$ from a population $X$, this sample has $n$ random variables $(x_1, x_2, x_3... x_n)$, the sample mean is $\bar{x}$, and it's variance is $v(x)$, the whole population is $...
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38 views

Confidence interval for the population mean

I learned that we can use $[\hat{\mu} - 1.96 \hat{\sigma}/\sqrt{n}, \hat{\mu} + 1.96 \hat{\sigma}/\sqrt{n}]$ as a confidence interval for the population mean, given a sample from the population, where ...
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How to calculate joint distribution probability samples from the probabilities of the two univariate distributions? [duplicate]

If random variables $x$ and $y$ have probability distributions $f(x)$ and $f(y)$ that each sum to 1, indexed by $i$, \begin{array} {|r|r|}\hline i & f(x) & f(y) & f(x,y) \\ \hline 1 & ...
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Is there a difference between a population and a set of realisations of a random variable?

Is there a difference between a population and a set of realisations of a random variable? I heard that a sample of a random variable is a set of iid duplicates of the random variable as a process, or ...
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Generating a min{p, 0.5} coin from a p-coin - Bernoulli factory type problem

Suppose we are given a coin with arbitrary (unknown) head probability $p$, I am wondering if there is an easy-to-implement algorithm for generating a $\min\{p, 0.5\}$ coin for any $p\in [0,1]$. ...
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How do I know which way this sample is skewed?

I have a sample where n = 15 and the median = mean but the mode is less. So I know to be: Positively skewed (mode<median<mean) Negatively skewed (mean<median<mode) Symmetric (mean=median=...
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141 views

Interesting question on confidence intervals

Say I conducted a sample and did the relevant processing to get a 95% confidence interval of a parameter to fall between a [10,14]. My friend did another sample, and got a x% confidence interval of a ...
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Does descriptive statistics only work with samples?

I was on wikipedia page acquiring knowledge on descriptive statistics: Descriptive statistics provide simple summaries about the sample and about the observations that have been made ... Later on, ...
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44 views

Order Statistics Question [closed]

A random sample of size 10 is drawn from a Uniform distribution on [0,1]. Calculate the probability that the third order statistic is greater than 0.50.
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How is regression estimate influenced by non-representative regressors?

I wonder, (1) how regression estimates are influenced by non-representative regressors and (2) what techniques exist to deal with this issue. I think a small example is helpful: Assume that we observe ...
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Finding the “most representative” variables of a population

Most polls use the so-called quotas method to obtain their sample. They draw candidates upon a large panel of people and add one-by-one each responding candidate to the sample unless a certain quota ...
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25 views

Sample log geometric distribution from log probability

I want to sample from the geometric distribution for a very small success rate. The success rate is so small that I represent it by its log. I want the result to also be represented by its log. Is ...
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root square vs log data transformation vs negative binomial model

I'm doing a statistical analysis on a survey based on a likert scale and I start by saying that I'm not an expert of statistics. What I want to understand is if there are significant differences in ...
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Meaning of sigma2 parameter in longpower package in R

I'm trying to perform a power calculation for a longitudinal study - 2 groups and 2 measurement time points that will be analyzed using GEE. I've been trying to run the 'longpower' package. However, I'...
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Probability that the sample comes from a certain distribution

Assume we have a data sample: $x_{1}, \dots, x_{n}$ from $n$ i.i.d. continuous random variables. Then, for simplicity, let us consider two distributions, $f(x)$ and $g(x)$. Is there any statistical ...
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1answer
50 views

Is it better to split sequences into overlapping or non-overlapping training samples?

I have $N$ (time) sequences of data with length $2048$. Each of these sequences correseponds to a different target output. However, I know that only a small part of the sequence is needed to predict ...
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21 views

One random sample Mean or 30 Random samples Mean

I have 30m records and i want to do a random stratified sample to estimate the mean based on predefined strata. Should i estimate the mean while taking 1 random (n=500) sample or to sample lets say 30 ...
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What is the probability that 80 out of 450 people would respond yes to a question by chance, if the true probability of such a response is 0.3?

I approached this question in R as follows: prop.test(80, 450, 0.3, correct = FALSE), however, am getting an incorrect answer. Does anyone know what I am inputting in R incorrectly?
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26 views

Normalize sample to match the mean and the standard deviation

There are two samples (sufficiently large and independent). One, size $n_1$ has the mean $m_1$ and the standard deviation $s_1$, the other, size $n_2$ with the mean $m_2$ and the standard deviation $...
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25 views

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 ...
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28 views

ANOVA with small sample (duplicate)

I have a study with only a duplicate sample. I would like to know if there are differences between the 5 averages, each group has two samples. In another case, I have 3 averages and each group has 3 ...
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Is it necessary for averaging amount of samples per class?

Say I have a mix of data from multiple sources, some classes have data up to around 200 whilst some have around 10~20 samples. (with negative samples ignored) Should I build my training, testing and ...

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