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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“… because sample mean gets different values from sample to sample and it is a random variable with mean $\mu$ and variance $\frac{\sigma^2}{n}$.”

This answer by user "sevenkul" says the following: The sample mean $\overline{X}$ also deviates from $\mu$ with variance $\frac{\sigma^2}{n}$ because sample mean gets different values from ...
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Proof that the sample mean is normally distributed [duplicate]

I am studying the book of Larsen and Marx and stumbled upon I can prove that $\bar{Y}=\frac{1}{n} \sum_{i=1}^{n} Y_{i}$ and $Var(\bar{Y})=\frac{\sigma ^{2}}{n}$ but how would I go to show that $\bar{...
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+50

Representativeness test: how?

A survey to a representative sample of the population has been submitted. This sample is composed by 4.400 individuals. However, only 2003 individuals have completed to survey. I want to verify if ...
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Calculating Sample Size for Confidence Interval of Given Level and Margin of Error

I would like to calculate my ideal sample using the Qualtrics calculator: https://www.qualtrics.com/de/erlebnismanagement/marktforschung/stichprobenrechner/ For this, I need a confidence level and a ...
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1answer
40 views

Power of two-sample test of binomial proportions

Suppose that I have info about a sample, and In one University, we have 70% females in the population and 30% males. In another University, the numbers are interchanged and 30% are females and 70% are ...
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1answer
42 views

Identify a contaminated distribution

I have a patchy time series of means, medians and sample sizes (n) that occasionally appears to be "contaminated" (either by bad or atypical data). For example: ...
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Are there convenient methods/tricks to make calculations with non-independent terms? (two examples here in particular)

In a recent question it came out that I needed to calculate the sample distribution of $\dfrac{Cov(XY,X)}{Var(X)}$ where the distributions of $X$ and $Y$ are known. By this, I mean the law of $$\dfrac{...
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Do we need hypothesis testing when we have all the population?

From what I understand hypothesis testing is done to identify if a finding in the sample population is statistically significant. But if I have a census data, do we really need hypothesis testings? I ...
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Independence Between sample mean and Any element in sample

Suppose we have i.i.d. observations X_1,..., X_n drawn from a population. we calculate the sample mean, Is X_1 Independent from Sample mean??
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1answer
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Stratified Sampling - Confim usage and sample size

I want to conduct a survey on a population of college students to run models on. My hope is that it will accurately represent the population. I am concerned about the sample not giving a close ...
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Diary study: Should I model time with very unbalanced time-points? (Multilevel analysis)

I have a data set from a diary study in which daily stress during the current pandemic was assessed for 30 days. However, participants began their diary period at different time points, leading to an ...
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Which kind of sampling is it?

What kind of sampling it would be if I leave a notice on the board of some university departments to test individuals who call me?
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What is the actual infection rate (per 100,000) of Covid-19 in my area (I'm in the UK)?

I think I'm misunderstanding some basic data given by the UK Government. https://www.bbc.co.uk/news/uk-51768274 On the above page, about three fifths of the way down, there is a table entitled, "...
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1answer
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Is a sample i.i.d or is a collection of random variables i.i.d.?

Basic terminology question. I hear “let the sample be i.i.d.“ and “let these random variables be i.i.d.” being used interchangeably. Even Wikipedia uses both: A collection of random variables is ...
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sample without replacement

A population contains 10 units, labelled U1, U2, U3,.......U10. The value of a character Y under study, for Ui is Yi(1<=i<=10). In order to estimate the population mean, Y*, a sample of size 4 ...
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Explain the descriptive statistics notion of population (distribution) to a measure theorist

My understanding of probability theory is a rigorous measure-theoretic one and I know almost nothing about descriptive statistics. However, I need to understand some of the commonly used notions in ...
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1answer
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Can I use a chi-square test to determine whether my samples are independent or paired?

I am conducting statistical tests for my current research project. Within the scope of this research project, I have two samples (divided by country clusters). The samples contain approximately 1500 ...
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ANOVA with groups having different sample sizes

I have 3 groups Group 1 with sample size ($n_1$) = 54 Group 2 with sample size ($n_2$)= 87 Group 3 with sample size ($n_3$) = 409 Can I carry one way group ANOVA? Also, can I include this ...
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variance of sample mean using srswor

while deriving variance of sample mean in case of SRSWOR, i came through this. how did the highlighted term came there. while solving it, there should be 2Cov(yi,yj) but that term is not there. in ...
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Regression Analysis with a Census or All Observations (Not a Sample)?

I have data that I've collected from every element in my population of study (a census), and not a sample. I am hoping to use the data to develop a regression model to answer questions like for a one ...
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Assessing the change in a single variable, in two distinct groups each made up of multiple population samples. What significance test should I use?

I have 2 high schools, School A and School B. For the first school, I have 5 classes of students; for the second, I have 3 classes (so 8 classes in total). Within each class, I have different ...
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How can I estimate a percentage in a two-stage sample design?

I'm trying to solve a exercise that I have to do. In this, there is a two-stage sampling design. The first stage is a Poisson design and in the second stage is an IS. The problem that proposes the ...
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Should independent variables measured only once per set of replcations be duplicated in the data?

I have a dataset from an experiment on soil erosion, where soil samples a, b and c where ...
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Clarification on the definition of “population”

In stats classes, I've always learned that a population is always a very broad, almost unquantifiable group (e.g., all voters in a country, all consumers of a company, all viewers of a TV channel), ...
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Confirm that an eventual over-representation in a sample is statistical significant

I need opinions on this one, so any thought you can contribute will be highly appreciated. My population is an entire set of customers, my sample is all the customers to whom something specific, which ...
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1answer
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Parameter estimation of a transformation

imagine you have a sample $X_1, X_2, \ldots, X_n$ from a random variable $X$, and another sample $Y_1, Y_2, \ldots, Y_m$ from a random variable $Y$. You know that $Y = \phi(X)$. For concreteness, say $...
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Detect if there is actually two populations in a sample

I have been counting stomata on fossil leaf material to apply a known relationship between stomatal index and CO2. I thought that the material was all from one population (one species at a given site)....
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The quantile of prob=0.05 and mean

What is the meaning of the difference between the quantile of prob=0.05 and mean for a sample form a specific distribution? In other words, I would like to understand the relationship between ...
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1answer
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How do I select participants in study results analysis? All participants or only the ones who have answered all questionnaires?

I have data on a student training for my master thesis. Variables were measured across 3 time points (before, directly after and 1 year after the training). Some students have filled out all 3 ...
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1answer
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Algorithm to get representative sample

For a dataset I wanted to pick-out some most representative points from it. Lets say the first point could be centroid, next could be the one farthest from it in the data-set(To get variance in data) &...
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Do correlated training examples matter?

Suppose I have three features, $a, b, c$, that I take measurements of at each time $t$ for every day $i$, and each day has a corresponding measurement $y_i$. So I have a data set that looks like $((...
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1answer
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Use standard deviation of sample or population in z test

I am reading the book Statistics by Witte & Witte. Some questions puzzle me. Question 10.9: The normal range for a widely accepted measure of body size, the body mass index (BMI), ranges ...
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Which test to use for non-normal paired data, with different sample sizes?

I posted a similar question yesterday, but was brought to my attention that I may need to consider the variance of my samples. I swabbed 9 rooms (3 cold/6 hot) for bacteria. The bacteria was counted ...
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1answer
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Which test to use for paired samples with different sizes and only 1 categorical variable?

I am testing 9 rooms for bacteria growth, and want to see affects of heat. Assume Blue Room is colder, Red room is warmer. I am not sure how to approach this because samples are too small (so can't ...
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Large sample size creating significant variables

I'm currently working with a large sample size (around 400,000 observations) where I did a t-test and the p-value turned out to be less than 0.001 for all variables. This ofcourse is not something ...
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Using Random forest and keeping sample independence when having multiple observations for each sample

I have a real estate property dataset with the property attributes as independent variables and the asking price at which the property was valuated by a real estate agent as a dependent variable. For ...
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1answer
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Sample size and number of Samples?

I have come across two major problems recently, and couldn't solve them. Imagine we have measured an independent variable 2000 times and I'm interested to talk about the mean of the population: So as ...
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Sampling distribution from a parametric curve?

I'm not sure if this question is well-founded, given that it seems to be mixing random and deterministic processes, but I'm wondering if there's a meaningful answer. Suppose we have a parametric curve ...
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2answers
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How to sample when the size of the two populations differ greatly

I have to compare the distributions (means, variance, ratio of specific features, etc.) of two populations. However, the sizes of the two populations differ a lot, one with only 30,000 observations, ...
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1answer
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Given we observe $x$ successes in sample of $n$, what is the probability that $p>0.5$

I flip a coin $n$ times, and I find that for $x$ of these it lands on heads. Let $p$ be the true probability of the coin landing on heads, though this is currently unknown. I am interested in $P(p>...
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3answers
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Connection between uniform distribution on a set and uniform sampling from a set - intuitive pictures and necessary mathematical formulas

What's the connection between uniform distribution and uniform sampling from a set $S$? Are these two terms synonymous: "uniform sampling from a set" and "sampling from a set according to a uniform ...
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Cross validation on unbalanced datasets using a simulation approach on a subset of data

Within my field I often end up using linear regression to look at two variables, normally how some factor (e.g. size) changes through time. I'm increasingly coming across datasets that are unbalanced ...
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1answer
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Variance of Sample Mean for a Positively Correlated Sample

Suppose we have a sample of n observations which are positively correlated with correlation matrix given by $\sigma^2$ as diagonal entries and $a\sigma^2$ as off-diagonal entries. Then we should get ...
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1answer
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How can I compare a not-continuous metric from two samples?

Let's say I have a store and I want to know which people buy the most. I decide to divide my customers between young people (under 40) and old people (above 40). I have a data frame and in each of its ...
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Combining two datasets into one for classification purposes

I am currently working on a research project and my goal is to analyze reviews on both Play Store and Appstore. I have two datasets for the same five apps, 50,000 for Android, and 5,000 for iOS. I ...
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AI algorithm blind test - sample size

My company works in healthcare consulting, and are working with medical practitioners to explore how AI might be able to assist the remote, early diagnosis of central nervous system disorders such as ...
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Minimum subgroup sample size

I have a population-level data set of continuous data, where a column represents a single individual and a row represents the measurement of the variable in question. Given the scope of the data, I ...
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Is my intuitive explanation of the premise for hypothesis testing correct?

They way I understand hypothesis testing is that there is some true data generating process out there, and that determines the 'population' distribution of variables, and then our sample is just one ...
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1answer
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Distribution of urns for non-uniform distribution

Let $X_1,\dots, X_n$ be i.i.d. random variables on a set $X$. Let $j$ be a uniformly random number from $1$ to $n$; define a new random variable $$ Y(j) = \frac{\left\vert \{i: X_i=X_j\}\right\vert}{...
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Is the mean of samples still a valid sample?

Suppose I sample $n$ times from a distribution $$ x_1, \ldots, x_n \sim p_\theta(x) $$ is the mean of the samples always a valid sample from the target distribution? I.e. is $\overline{x}$ a valid ...

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