Questions tagged [sample]

a sequence of objects or individuals collected from a larger (possibly infinite) population or process.

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76 views

What are the first four moments of a linear function of IID random variables?

Consider a sequence of IID random variables $X_1,X_2,X_3,...$ from a common distribution with mean $\mu$, variance $\sigma^2$, skewness $\gamma$ and kurtosis $\kappa$ (all finite). Given a sequence ...
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Calculating sample size for stratified sampling

I have an issue with determining sample sizes for a collection of strata. It regards comparing shares of a binary variable. I'm supposed to find the sample sizes for each strata using both ...
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Psychometric test validation question

We are trying to validate a test for young children using IRT analyses (rasch/2pl). Models do not converge due to a floor effect. Teachers also took this assessment. Would it skew results if i ...
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150 views

Finding the most equidistributed sample of a function's domain and the average of $f$ mapped on the sample?

Apologies if the notations aren't familiar. I don't have a statistics background and I hope that readers have a basic understanding of pure mathematics. ** Edit**: I want to find the sample of ...
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7 views

Mixed ANOVA sample size calculation

For my master's thesis I am planning an experiment in which a human participants interacts with a robot. The robot is multiple times cueing where a light might appear (in total 40 incorrect and 40 ...
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21 views

Question about sample normalization for distribution moments [duplicate]

I am having trouble understanding how the sample formulas for distribution moments are derived, for example, the third standardized central moment is: $$ \frac{1}{n}\frac{\sum{(x - \mu)^3}}{\sigma^3} $...
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11 views

Choosing a validation and test sample selection for a re-forecasting model

I'm currently testing improvements to an income re-forecasting model and am unsure on how to select a good validation and test sample to consider the time element of the model. The model takes ...
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1answer
25 views

Proper way to compute stats of multiple box plots

If I have 10 sample distributions that I've calculated the box plots for, what is the proper way to summarize that into a single box plot? I should add that the sample distributions are not drawn from ...
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1answer
27 views

Estimate population mean from sample with known distribution

My sample size is around 100k - should be enough for CLT to work. One intuitive approach is to estimate population mean by sample mean y. However, after plotting the sample data, I notice the ...
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Variance of CNR

So I have two ROI's in an image, let's say their pixels form two iid, Normally distributed random variables $ X $ and $ Y $ of size $ n_X $ and $ n_Y $. My question is concerning the variance of the ...
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What are the properties of the distribution of medians from samples of a set of integers?

Given a set of integers $S = \{1, 2, 3, ..., n\}$ I draw uniformly at random without repetition $m$ integers a large number of times ($1 \leq m \leq n$). For each of these samples (each of size $m$) I ...
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What are the skewness and kurtosis of the sample mean?

Consider a sequence of IID random variables $X_1,X_2,X_3,...$ from a common distribution with mean $\mu$, variance $\sigma^2$, skewness $\gamma$ and kurtosis $\kappa$ (all finite). The mean and ...
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Deriving quantity from two sets of data and do statistical analysis on it?

Say I have a factory that produces bottles of salt water, and there are two processes. One adds some water to a bottle and the other adds some salt. I have stats on each process. ie. a sample of how ...
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Method for calculating number of employees

I need to calculate the number of employees in a given number of organisations. I know how many organisations there are in total and I know the number of employees in 50% of those organisations. Some ...
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Consequences of paired healthy and diseased samples in machine learning

Consider a set-up in which we are using machine learning to classify between healthy and diseased samples. Obtaining the data requires some invasive procedure - therefore all the healthy samples come ...
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1answer
20 views

Data sample vs. groups/levels (and when testing for normality)

I have two questions that tie into one another (for context). I've been told to always check my data to see if it's normally distributed before doing any analysis, but if the data are associated with ...
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1answer
22 views

Confidence interval for the sample mean assuming Johnson SU distribution

I'm validating a machine learning model that outputs a certain sample of N>20000. After fitting the sample to multiple distributions, and then running the typical Anderson-Darling and Kolmogorov-...
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Statistics question: Why is the standard error, which is calculated from 1 sample, a good approximation for the spread of many hypothetical means?

I'm re-learning statistics and got confused by the idea of taking the standard error from 1 sample's worth of data (standard deviation of sample divided by the square root of sample size, i.e. $\frac{...
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1answer
30 views

Pooling Two Samples to a Single Sample

Let us say we draw 10 sample values from a given (continuous) population. However, the values tend to be very different than expected, so that we suspect that there might have been an error with the ...
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1answer
58 views

Calculating Sample Size For Multiple Groups (in R)

I am working with the R programming language. Suppose I have 1000 patients in a medical study, and I want to take measurements on these 1000 patients. 500 patients in Group A 250 patients in Group B ...
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558 views

Estimating the Population Mean with the Sample Mean

I am trying to better understand how the sample mean can be used to estimate the population mean. Using the R language, suppose I have the following population: ...
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Are inferences made on a set of samples (from the population) ONLY intended to describe that set of samples?

Are inferences made on a set of samples (from the population) ONLY intended to describe that set of samples? Suppose you have measurements on the height of 1000 giraffes from zoos across the world. ...
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Are unpaired samples always generated by independent random variables?

I am confused by the terminology because the term "independent samples" is usually used as a synonym for "unpaired samples". Does this fact mean that unpaired samples are always ...
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Population size determination in a dataframe

I am running into the following problem and I was wondering if there is any easy way to solve it. Suppose I have a Dataframe with a large number of records, let's call this number $N$. In the ...
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Sample of a sample

Also posted in http://www.talkstats.com/threads/sample-from-a-sample.77658/ If we were to carry out a survey on say, workers in a chemical industry asking for responses such as: Are you a smoker? Y/N ...
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"Relative" Vaccine Efficacy

Merck just released data on their covid-$19$ antiviral medication. In the medicated group there were $28$ unfavorable outcomes in $385$ cases. Or ~$7$% In the placebo group, $53$ negative outcomes in $...
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Find the distribution of a statistic [duplicate]

I'm trying to solve the next excercise. Let $X_1,...,X_n$ iid random variables with pdf $$f(x,\theta)=\frac{\theta}{(x+1)^{\theta+1}}, x>0$$ with a parameter $\theta>0.$ Find the distribution ...
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Is there a specific term for denoting samples that are used in a test of independence?

I know that there are independent samples and paired samples (paired samples is a special case of dependent samples of equal size). In any test of independence we have a pair of random variables $(X,Y)...
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Alternative definition of a sample?

From my little knowledge of statistics, a sample is a subset of a population. Now I am reading a textbook on mathematical statistics. In the introductory section of the chapter on sampling ...
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When calculating proportion, is the total that I'm using to calculate it also the sample size?

This probably has a very simple answer and I'm just overthinking it. I have a very large dataset (~30,000 individuals), that contains data on casualties seen at a wildlife rehabilitation hospital. I'm ...
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What is target and sample population? the portion of population for whom we have received data or those who were invited to participate

I am new to statistics and I am trying to understand target population and sample data. Suppose a company wants to know the level of satisfaction of all their customers. To this end, it has sent a ...
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How to simulate two datasets that satisfy specific constraints such as having specific mean , standard deviation, and correlation coefficient? [duplicate]

I know that generating different random datasets having certain standard deviation and mean values are possible. However, I'm just wondering if it's also possible to generate, let's say 2 datasets, ...
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How to calculate the distribution of the sample mean of uniform distribution? [duplicate]

I am working on the following question but I'm not sure if my approach is correct. Given that X~U(4,8), I need to find the distribution of the sample mean for a sample size 30. My approach is that ...
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Can/How you run correlations with weighted data (csvplan data file in SPSS)?

I would like to run correlation analysis in SPSS using data from a national dataset that uses stratified random sampling. The dataset came with a csvplan datafile to be used when running weighted data ...
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1answer
76 views

testing whether a sample of the population has a different mean than the population mean

I have a short question regarding testing whether multiple subsample means are different from the population mean. To be specific, I have the full population of the energy consumption per square ...
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1answer
102 views

How to check if a sample is representative of a population if I know the population’s parameters in advance

I have a dataset with the real height of an entire generation of high school students. Since I have the height of literally every student in the generation, I know the population’s mean, $\mu$, as ...
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2answers
131 views

Calculating the confidence interval for the mean value from a sample

The central limit theorem states that the means of many different samples with n>30 from a population that follows an arbitrary distribution are normally distributed. If you now have the ...
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1answer
266 views

Compare two fractions from two populations for statistical significance

I am trying to determine if what I am trying to do makes any sense: basically, I have two populations of patients, one being roughly 12 million people, the other one being 30 individuals. Now, from ...
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testing equality of estimated coefficients generated from same regression models but different samples

I use a regression model ($Y = X*\beta_1 + Ylag*\beta_2 + \epsilon$) to compare the profitability ($Y$) of companies with high corporate social responsibility index ($X=1$) versus a matched control ...
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How to construct the confidence band for a timebased sample of n individuals

Let $X^{(i)}(t)$ be some measurement at time $t$ for individual $i$. Let $\bar{X}(t) = \frac{1}{n} \sum_{i=1}^n X^{(i)}(t)$ be the mean of the individuals at time $t$. Let $\bar{X}_{t_0} = \frac{1}{T}\...
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1answer
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Sample three Bernoulli variables given the 2 by 2 by 2 table

I want to sample three Bernoulli variables given their 2 by 2 by 2 table: where the last column is the probabilities with sum being equal to 1. What I am thinking now is to use a multivariate normal ...
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Weight for Samples on SVM (Support Vector Machine)

there is a option sample_weight in fit(X[, y, sample_weight]) function (OneClassSVM, sklearn library). If I use the option ...
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Should I use sample weights when doing regression(e.g. glm) with a subset from the whole survey samples?

My dataset is from a national survey with a complex sampling design, and it has 50,000 samples in total. (Target population : working people in the age of 19-59) Thus, it has a sampling weight in the ...
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I am trying the determine the relation between the pdf of the sample mean and the pdf of the sample total (T_0= X1+X2...+Xn)

I know that the sample mean (X bar) = (X1+X2+...+Xn)/n and so the sample total = n(X bar). I am not sure how this relates their pdfs and also how to prove that relation.
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113 views

Kurtosis and Skewness for 2 or more samples' combination [duplicate]

Question: Can we calculate kurtosis and skewness of 2 or more combined samples, given each samples' mean, std, sample size and kurtosis/skewness? Let's say we have sample size, sample mean, sample ...
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Inference about a Population(Theoretical)

I have this theory question about inference: Why can't the answer be "All female students across all universities"? Wouldn't it be more reasonable to apply the generalization to the biggest ...
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1answer
34 views

Samples from a black box

Say I have a black-box that contains a lot of numbers (integer numbers). The quantity is very very large and the range of the numbers is finite but unknown (the numbers can be repetitive). I want to ...
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Is sampling by even/odd serial numbers a simple random sample?

I'm working on a project where each member of the population has a serial number. Each serial number is issued sequentially, so smaller serial numbers reflect older records. I'm drawing a sample of ...
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1answer
159 views

Asking about clustering condition following Abadie, Wooldridge 2017

Abadie, 2017 have a paper about when we should cluster. And this paper has been summarized by McKenzie here. I used the paper of Dasgupta,2019 to link to the summarized work of McKenzie. So, in ...
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1answer
83 views

Why a variance of a sample mean is the population variance divided by a sample size?

On the wikipedia page about variance I have found the following equality $$ Var(\overline{X})=Var(\frac{1}{n}\sum_{i=1}^{n}X_{i})=\frac{1}{n^{2}}\sum_{i=1}^{n}Var(X_{i})=\frac{1}{n^{2}}n\sigma^{2}=\...

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