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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Is the difference between two samples of two distributions a sample of the difference of the distributions? [closed]

My question is as follows. Suppose you have two variables $X$, $Y$. If I pick a random sample $x$ from the distribution over $X$ that has probability density function $f_X$, and another random sample $...
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45 views

Distribution of the sample variance $S^2$ from a normal population

Let $X_1, X_2, X_3, ….., X_n$ be $N(\mu, \sigma^2)$ distributed. Then what is the distribution of $S^2$ I have already proven that if $X_i$ are $N(\mu, \sigma^2)$, then $\frac{(n-1)S^2}{\sigma^2}$ ...
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Weird sample variance when creating a lognromal sample with pre-defined mean and variance [duplicate]

I have been working with lognormal distributions as a proposal distribution for some MCMC routines which require the proposal distribution to have some pre-defined sample mean and variance, $m$ and $v$...
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1answer
32 views

Is this a valid way to get a simple random sample?

I have a data set of about 200,000 observations about establishments in my district and their operating time. I need to establish the correctness of my data. Consequently, I am trying to take a simple ...
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32 views

Probability and Normal Distribution

(sampling distribution) We randomly draw another sample of size $10$. What is the probability that the mean word count of these $10$ songs is greater than $436.531 = 374.9149 + \dfrac{2∗97.42498}{\...
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22 views

Probability of several consecutive drawn random samples of a standard normal distribution exceeding a certain value [closed]

I have trouble figuring out the following: I have a standard normal distribution (µ = 0, σ² = 1) and now draw n random independent samples. Lets assume the following: n = 3 What is the chance, that ...
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8 views

Logit regression (Panel data): resample?

I have a panel data (all listed companies in the US with quarterly data) in which the dependent variable is 1 if the company was recommended on a investment recommendations website, and 0 otherwise. ...
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1answer
27 views

Choosing the correct hypotheses [closed]

I was trying out some questions on hypothesis testing when some questions started challenging me. Here is an example: A lot of product X is to be rejected if the temperature of the lot is greater ...
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1answer
53 views

Determine sample size using reversed goodness of fit

I am asked to work on a specific problem in which I have to calculate certain expenditures for an industry, consisting of a population of about 400 companies. Although I already suggested to conduct a ...
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24 views

Proof that covariance of RV and group average is less than variance of RV

I have a random variable $X_i$ and a group of $N_j$ other random variables that includes $X_i$. Let's just call this group $J$. There are no distributional assumptions made on these RVs (other than ...
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31 views

Different sample size of control and test groups

Hope someone can help my question: I have a survey study with one control group and one test group. Each is set to have 500 completes. However, we are short in sample in one group: Test is 350 and ...
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39 views

Infering population from a sample?

I took a test in class and found it to be difficult. So I asked in my WhatsApp group if others felt the same. 4/36 people replied yes they felt it difficult. Others did not respond either in yes or no....
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18 views

How to calculate the Margin of Error in this specific scenario?

Assuming I have a population made of hotel bookings for a specific period and I need to send a survey questionnaire to each guest (guest=booking) by email. To simplify things, let us assume the ...
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21 views

Confidence Interval for the Difference Between Proportions in complex samples

I have two complex samples (with different sizes) from the same population in different times. I used the survey package to create designs for them: ...
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1answer
26 views

Calculate a Conditional Expectation via Samples

Consider a binary random variable $Y \sim p(Y)$, a random variable $X \sim p(X)$ (can be discrete or continuous) and a conditional distribution $p(X|Y)$. Suppose that I generate $N$ samples from $p(Y)$...
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intuition behind SD+

so i was reading statistics by Freedman and in the section where he describes the t-test he goes on to explain why we would use the SD+ instead of the regular SD to calculate the S.E with the sample ...
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How do I sample N items from a list ensuring the samples are as similar as possible to each other?

Is there anyway to sample 6 numbers without replacement this list of 12 numbers ...
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41 views

2x3 design, binary out come sample size calculation?

I'm designing an experiment as part of a marketing assignment. I'm planning on running a 2*3 between-subjects design (6 conditions comprised of two factors, one with 2 levels and one with 3 levels). ...
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38 views

How can we write the sample variance's formal definition of a continuous random variable considering Bessel's correction? [closed]

I am trying to find the formal way of writing the sample variance of a continuous random variable considering Bessel's correction. I ask because the sample variance is usually written this way: $$ ...
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16 views

When to use a certain sampling technique

I'm taking a class where we learn about different sampling techniques. For the most part it has come down to SRS, Ratio/Regression/Difference estimation, Stratified random sampling, Systematic ...
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Smaller dataset or bigger but risking ovb?

I am testing whether financial access is correlated with the education of young individuals using a longitudinal panel. Among the controls I am using there is parents' education that is a determinant ...
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21 views

Does reliability of measurement affect the minimal sample size required?

The following calculator (like many of its kind) uses a number of variables to determine an adequate (and importantly, representative) sample size: https://www.calculator.net/sample-size-calculator....
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1answer
52 views

Sample size prediction in multivariate A-B testing

I need to run an A-B testing with one control group (40%) and 3 variants (20%) each. Base line = 0.65 Target lift = 0.25 Power =0.8 Confidence = 95% I found following R code to find minimum ...
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Test whether multiple (>2) sets of samples should be combined into one set

I have a set of problem instances of some type, and a set of algorithms which all solve that type of problem. The problems come in m different sizes and for each size I have the same number of ...
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25 views

How does the nth sample impact Mean and Variance? [duplicate]

Given the Mean and Variance of $n$ samples $x_i$: $$M_n=\frac {1}{n}\sum_{1}^{n} x_i$$ $$V_n=\frac {1}{n}\sum_{1}^{n}(x_i-μ_n)^2$$ How do Mean and Variance change, when we take into account one ...
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Calculating change in mean and standard deviation of Sample X due to replacing p% of X with data from another distribution

Suppose we have two independent normal distributions $A \sim \mathcal{N}(\mu_a, {\sigma_a}^2)$ and $B \sim \mathcal{N}(\mu_b, {\sigma_b}^2)$. Suppose that we have a sample $X$, which is drawn from $A$...
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Dealing with self-selection in the treatment group

I wanted to do a Randomized Controlled Trial for a new curriculum that was announced in my area. The issue is, certain teachers, under the organisation that I'm working with, have selected to teach ...
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Weighting Survey data - Achieved sample, Survey sample, population

I have designed a small survey for my work place of 2000 people. 200 people were selected based on gender (Male female), age group (4 25-year age groups) and working grade (a,b,c). Out of my sample ...
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Find number of elements to check for finding false negative rate

I have 3500 pictures that were classified in four different possibilities of match: very low (16%), low (1%), high (30%), very high (53%) All labels are not known, i.e., I don't know if they were ...
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1answer
64 views

Multiple linear regression: am I interpreting the methodology right?

This is a follow-up question to 1 and 2. So we have the normal linear model \begin{align*} \textbf{Y} = \textbf{X}\beta + \epsilon \end{align*} where $\epsilon\sim\mathcal{N}(\textbf{0},\sigma^{2}\...
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2answers
34 views

What exactly is the sample size of an investigation?

My understanding of sample size is that it is a portion of the population that serves to represent the population. However, I'm not sure if the sample size of an investigation to investigate how X ...
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27 views

What is the sample size formula which i could possibly get minimum value in-vivo studies?

I am an undergraduate students who is struggling on how to do in vivo studies with my low budget. Therefore, I ask some help of you just in case you know about what sample size formula that I could ...
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How to infer the distribution of a statistic (Bayesian inference?)

I have a list of approximately 30,000 venues in a major US city. These venues hold all kinds of events, sports, conferences, concerts etc. I want to know the distribution of the 'capacity' of these ...
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Estimate frequency based on given sample

I have a list of users (~25 million) and a dataset containing events created by the users in a specific time window (eg all tweets of all Twitter users that happened in a month - on avg I have 100K ...
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Using mean length and mean weight to calculate mean BMI?

Is it valid to use mean length ($h$) and mean weight ($w$)) from a given population to calculate mean Body Mass Index ($BMI = \frac{w}{h^2}$) for that population?
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A question about power for a cohort study

In short, we are planing a cohort study, were we want to investigate the occurrence and the importance of a given event on response of a treatment. We expect the event to occur in about 2% of all the ...
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29 views

Is there any way to resample in order to change the distribution of a sample?

I ran an experiment that involved an independent variable which is known to have a right skewed distribution. However, in the experiment, the independent variable was distributed differently between ...
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3answers
350 views

How to figure out whether the data is sample data or population data apart from the client's information?

What are the ways available to figure out whether the data is sample data or population data apart from the client's information?
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1answer
49 views

Calculating required sample size for estimate lower bound on 95% of the population

I'm interested into sampling from a population, with a long time to get a sample (O(1), usually 1/2 mins), with lots of candidate populations to sample from (running a metaheuristic optimization). I ...
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1answer
32 views

Testing whether two timeseries samples are from the same population

I would like to test if different timeseries samples (over the same period of time) are plausibly from the same population. e.g. popularity of movie Avengers over time from different websites. The ...
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168 views

Calculating a sample size based on the target width of a confidence interval with stratification

I am reviewing a sampling design devised by a colleague and completely fail to understand it, although I am not a novice in statistics (but not a huge expert either). The said colleague is no longer ...
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29 views

Sample from a distribution constructed by Dirac measures

I am reading the paper in the following link https://link.springer.com/article/10.1007/s11203-009-9037-8 In the page 19, the author suggests to sample $\eta_i$ from the following distribution $P^{\...
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Unbiased Estimator of the Standard Deviation of the Sample Standard Deviation

I'm looking for an unbiased estimator of the standard deviation $\text{SD}(s)$ of the sample standard deviation $s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \overline{x})^2}$. I have found this ...
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A question about the definition of sample

Let $(\Omega,\Sigma,\mu)$ be a measure space. The definition of a sample is that it is a sequence of iid random variables $X_1,\ldots,X_n$. Usually random variables are real valued and the ...
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1answer
36 views

How exactly can I get sampling distribution of means for calculation of standard error?

Let's denote population by $ N $ and sample with which I want to make inference about $ N $ denote by $ n $. Let's assume I have already collected $ n $. Now I want to get means for sampling ...
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1answer
35 views

Probability density of the product of independent identically distributed random variables

Let $X_1, X_2, \dots , X_n$ be a random sample from the PDF $$f(x;\theta)=\theta x^{\theta -1},\;\; 0<x<1,\;\; \theta > 0$$ What is the probabilty that $\prod_{i=1}^n X_i > t$? The joint ...
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1answer
44 views

Standard error of sample variance

We know that an unbiased estimator of the variance is: $$ \hat{\sigma}^2_{unbiased} = \frac{1}{n-1}\sum_{i=1}^n (x_i - \bar{x})^2$$ I was wondering, does it have the smallest possible standard error? ...
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1answer
44 views

Sample is almost the same as the population

I'm interested in a situation where I have a small list of events, somewhere in the range ten to a few hundred. Each event can be a 1 or 0 outcome. I have a good reason to believe that the factors ...
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1answer
20 views

What distance function to use for matching observations on a mix of ordinal, nominal and numeric variables?

I'm trying to match potential respondents to a random sample from the target population, and not sure whether any of the usual methods available out-of-the-box in e.g. R are right for the job. ...
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1answer
28 views

Problem on conducting a hypothesis test with sample data

I'm trying to perform a statistical tests for the sample data(n=63) which is the effect of smoking for time(measured in minute) to fall asleep. First, I set a null hypothesis, there's no effect of ...