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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Update to estimate of population mean based upon new sample

Suppose I sample some phenomenon with a potentially moving mean, let's say height of males on their 18th birthday, and I run this survey every year. Each year I produce a sample mean of height, which ...
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How do sample weights work in classification models?

What does it mean to provide weights to each sample in a classification algorithm? How does a classification algorithm (eg. Logistic regression, SVM) use weights to give more emphasis to certain ...
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Why don't we use the n-1 correction for standard error of sample proportion?

From my understanding, when we construct a confidence interval for a sample mean with a sample size of n, we try to estimate the standard deviation of the sampling distribution $$σ_{\overline{x}} = \...
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Is this conclusion drawn from sample or population?

"When asked what they would use if they were marooned on an island with only one choice for a pain reliever, more doctors chose A than B, C or D." Is this conclusion drawn from population or a sample?...
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Dilemma concerning prediction of user satisfaction

Imagine that you have data with information about users : Age, sex, location, etc ... with the answer to two additional questions : Q1 = Have you tried product P ? yes/no ; Q2 = Did you enjoy product ...
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What test to use to prove one sample is significantly different

I am studying performance of football teams. I want to prove one team is significantly more successful at home then other teams. I calculate the ratio between points per game at home and points per ...
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Implications of sample size increasing over time

I have apartment data on rents from 2000 to 2016 where the unit of observation is an individual property. The sampling methodology included more properties as time went on thereby expanding the ...
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119 views

Unbiased sampling and subsampling

Suppose I have a distribution $\mathbb{F}$ with mean $M$. Also, assume we have a set of i.i.d samples of size $n$ denoted by $X=\{x_1, x_2,..., x_n\}$ from $\mathbb{F}$. As a result, all $x_1, ..., ...
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Linear Regression & good sample [closed]

Edited: In relation with our research, the respondents were deaf employees but due to the difficulty to have a large sample size, we're hoping to target that the respondents will be n=40 to reasonably ...
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What the relation between a random variable and a sample (or dataset) in machine learning?

I'm having trouble with the machine learning vocabulary, especially with the concept of random variables. Given a sample $X$ (with features $x_1, x_2, \dots, x_n$) that you train your algorithm on (...
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Can we sample from a set of biased samples to get unbiased samples?

This is a follow-up question to How to uniformly sample vertices from a large graph with given distance from a fixed vertex?. Suppose I took a set $B$ of $n$ samples from a large but finite universe $...
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Survival model - sample with only censored observations

I have a question related to survival models: for instance, the survival probability of people that have a disease. In all examples I've seen so far, the data used to estimate those models sometimes ...
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34 views

How to find mean and variance of population of flat probabilistic distribution

I'm trying to understand the difference sample variance and population variance and how former converges to latter after ...
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48 views

How can I get a sample of a product of two independent random variables?

I have three random variables: $X_1$, $X_2$ and $Y$ such that $X_1$ and $X_2$ are independent and $Y = X_1 \times X_2$. I think that either this question is trivial or I'm making a rookie error, but I'...
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222 views

Strange results when applying Wilcoxon test in R

I am interested in whether the mean of one sample is statistically greater than the mean of the other one. The samples are not independent in that if the ith observation in sample A is positive, than ...
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Estimating the number of sources of population using sampling techniques

Background of the problem: There are about 500,000 uncatalogued specimen in a laboratory. These specimens are gathered from across the world. We want to answer two questions: How many different ...
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Is a kurtosis of 1 unique to a equiprobable two-point distribution?

This question came up while having a look for a CLT for the sample variance which I found under this link (Theorem 5.3.2) from another stackexchange question which I can't remember. The Theorem from ...
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How to calculate improved probability of getting a correct answer through replication

A mapping inspector checks a route to determine if it is a footpath (FP). Independently, another inspector checks the same route. And so on. The process is replicated N times. The results of all the ...
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Distribution of sample standard deviation [duplicate]

I understand that if $X \sim N(\mu, \sigma^{2}$), then the sample mean for a sample size of N is $\overline{x} \sim N(\mu, \frac{\sigma^{2}}{N})$ but I am not sure how was this derived $ \overline{\...
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Reducing variance of estimator using sample variance?

I want to estimate the mean of some distribution given some samples, but I would like to minimize some specific expected cost, where outputing a number higher than the true mean hurts me more than a ...
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1answer
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Making a random sample from data

I intend to use the following data of patients with liver/wo disease in my research: https://archive.ics.uci.edu/ml/datasets/ILPD+(Indian+Liver+Patient+Dataset)# But there wasn't any information on ...
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565 views

formula for sample covariance: Bessel's correction

Two options for the sample covariance between X and Y: 1)(with Bessel's) COV(X,Y) = $1/(n-1)$ * $\Sigma$ $(Xi - mean(X))$*$(Yi - mean(Y))$ 2)(without) COV(X,Y) = $1/n$ * $\Sigma$ $(Xi - mean(X))$*$(...
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Construction of i.i.d. sample

My task is to describe the construction of i.i.d. sample $\mathbf{X} = (X_1, \ldots, X_n)$ where random variables $X_1, \ldots, X_n$ should get the predefined univariate distribution $P$. Specifically,...
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Sample size calculation for safety trial

I need to know how to calculate the sample size for a safety trial of a combination of two drugs VS placebo. I have the proportions of event (AEs) for each drug: Drug A p1 = 0.12 Drug B p2 = 0.09 ...
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375 views

Getting the probability of a sample being between two values

I am learning on probabilities in populations and samples now but I'm stuck on this question. Suppose we have a sample with n=35 of a population with a mean of 80 and standard deviation of 5. ...
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If the parent distribution is skewed, but the sample size is greater than 30, is the distribution of the sample mean nearly Normal?

I have my AP Stats exam tomorrow and had this question. I apologize if it is too simplistic for this forum. I'm pretty sure the sample's distribution is nearly normal, but not 100%, can someone ...
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How would one obtain a random sample of pennies (from the U.S)?

I am doing a project for my Statistics class to answer the question: "Is there a relationship between the year and the number of pennies minted that year?". I need a random sample of pennies, but don'...
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How to deal with few subjects leaving the study in the sample?

I am having moving population. As in everyday new subscribers are getting added in the population and few are leaving my subscription service. Sample I take on starting period of the study, from that ...
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134 views

What is „sample space“?

Analogous to the question: What is "feature space"? What is the mathematical definition used in the field of machine learning for sample space? For example, correlations can exist in ...
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Law of large numbers with population data

The LLN refers to the convergence of the sample average to the population mean when the sample is iid. This is, for a random variable $X$ with $E(X)=\mu$, we know that in a sample of size N, and with ...
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2k views

Power calculation and sample size for retrospective cohort study

Forgive me if this is a very straight forward question but I could use some advice! I am a veterinarian designing a retrospective cohort study to investigate whether there is an increased risk of ...
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What is the effect of more than one chance of selection when sampling?

I am designing a clustered sample. Within each cluster there are 3 groups that will be sampled from - two at a higher rate than the other. The two subgroups that will be sampled at a higher rate are ...
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How can the central limit theorem hold for distributions which have limits on the random variable?

I've always taken issue with, and never been given a good answer, for how it is possible that the central limit theorem - the classical version where the distribution of sample means approaches ...
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Compare maxima of two Bernouilli experiments

I am looking at the following question -- which has already been solved for the case of Gaussian samples Compare maxima of two Gaussian samples but I am unable to find a similar answer for the ...
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1answer
965 views

How to check if a sample is representative of a population, across several criteria.

I have a total population of several hundred houses, which have different sizes, prices, and ages. I want to be able to select a random sample, of a few dozen or so houses, and test how ...
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Chi Square Test of Homogeneity [closed]

I'm trying to answer a question about whether there are any significant group differences (between subjects design) on one independent variable with three levels (three different interventions). Some ...
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1answer
468 views

How to generate randomness using a biased coin? [closed]

Imagine we have three people and we want to select one of them at random. If we had a fair coin we could have tossed the coin twice to get one of the 4 outcomes and could have related the occurrence ...
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Sample size re-estimation in an adaptive seamless phase II/III trial with interim analysis

I have an adaptive clinical trial that includes these elements: Seamless phase II/III: phase III follows immediately after phase II ends. Phase II has a different endpoint than phase III's endpoints. ...
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Sample size human sciences [closed]

I will apply a questionnaire with 90 questions about the possible requests: very bad, bad, neutral, good and very good, the answers will be categorized into 8 different groups. Subsequently the data ...
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113 views

Non-parametric test for difference in parameter with unequal sample size and different variance [duplicate]

I would be thankful for some advise on this issue: I want to test whether the skewness for two distributions is significantly different from each other. (I know that skewness is often not the best ...
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1answer
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How to determine if sample with standard deviation is normally distributed?

I am currently making my way through a textbook called "Modern Statistics: A Graphical Introduction". (I'm not currently taking a related course through university or school.) I came across a question ...
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33 views

Check for randomization

I have a fairly large data set with 500000 observations for 100 variables. Observations are randomly assigned to treatment and control group. How do I infer that treatment has indeed been randomized ...
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105 views

Inferring a distribution from a sample [closed]

I would like to know more about the general process of finding an approximate distribution to fit a given sample. Or, more accurately, given a random variable $X$ with unknown distribution, and a ...
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Comparing two samples

A hospital I work for has implemented a new method of segregating patients into wards based on the complexity of their needs at the end of 2016. We are now wondering if there is a measurable ...
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3k views

When do we use S.E.M. and when do we use S.D.?

Put simply, the standard error of the sample mean is an estimate of how far the sample mean is likely to be from the population mean, whereas the standard deviation of the sample is the degree to ...
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Is working with all customers a sample or population?

A company wants to run a promotional campaign to encourage usage of a credit card that the customer already has. The company wants to send this promotion to all credit card customers. It wants to ...
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133 views

Which is the relation between population/probability space/sampling?

I am trying to understand the relation between population/probability space/sampling. My arguments are divided in 3 sub-questions which trace my attempt to link in a logical way the three concepts. I ...
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Commenting on wider population from survey sample

I am conducting a survey in 9 restaurants, hoping to gather data on our customer demographic profile. The population is equal to the number of covers the restaurant had over the corresponding period ...
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Let $X$ and $Y$ random variables, $\{X_{i}\}_{i=1}^{n}$, and $\{Y_{i}\}_{i=1}^{n}$ samples. Is $\{(X_{1},Y_{1})\}_{i=1}^{n}$ a sample of $Z=(X,Y)$? [closed]

Let $X$ and $Y$ two random variables with dnsity distribution function $f_{X}$ and $f_{Y}$ respectivelly. We assume that $(X,Y)$ is a random variable on $\mathbb{R}^{2}$ where $$\mathbb{P}((X,Y)\in ...
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Stratified Random Sampling

I have a made up scenario that involves sampling from a factory that makes foot-long hot dogs. The 3 teams that make the hot dogs are graded on their ability to make foot-long hot dogs. A previous ...

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