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Questions tagged [finite-population]

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Estimating tail share of apparently subexponential distributions drawn from finite population, given a finite sample

Suppose I have data on a large sample of some units of observation, where the observed quantity has meaningful differences and ratios. The sample is much smaller than the population, but both are ...
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1answer
33 views

Why is the sample mean's variance smaller when we're sampling without replacement?

I know that we've to use the correction for finite population, but why do we have to use it? My lecturer said that "Sampling without replacement doesn’t waste information by the chance of finding the ...
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Unequal sample size for 2 proportion calculation group

I have a question. It’s about the uneven sample size between 2 groups. Let say I want to compare & analysis these 2 groups when 1 of them have small number of sample. To give you some light, here ...
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41 views

Calculating sample size for a stratified random sample

I have a total population of 4,000 farmers, divided into three unique regions. Approximately 50% of the farmers live in Region A (N=2,000), 27% in Region B (N=1,080), and 23% in Region C (N=920). I am ...
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Interpreting the margin of error when it is larger than the sampled proportion

Say that I have a population of $N=500$ individuals, and I'm sampling $n=60$ of them for a certain characteristic which is expected to be quite rare (say green eyes). In my sample I find out there are ...
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2answers
48 views

Simple random Sampling with replacement (SRSWR) [closed]

If a simple random sample (with replacement) of size $n$ is drawn from a population of size $N$, where $N \leq n$. Then what is the probability that all the population units (items) are present in the ...
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1answer
212 views

Unbiased estimator of binomial PMF

Is there an unbiased estimator of PMF of a random variable $Y=\sum_{i=1}^{n} X_n $ where $X_i$ are independent Bernoulli trials with probability $p$, that is, the estimator of: \begin{equation}\tag{1} ...
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1answer
86 views

Sampling from finite population with replacement

Suppose we have a population of size 10,000. We choose 1000 persons from the population, uniformly and independently, and ask them some question(s). The answers are random variables $X_i$. Since we ...
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Sampling without replacement - Normal sampling distribution [duplicate]

Most of the introductory stats textbooks, treat the sampling distribution of the mean as a normal distribution when sampling is done without replacement and n/N > 0.1. They just use of the finite ...
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Constructing an unbiased estimator

Suppose we have a finite population $I_N$ of size $N$ on which we define a variable $\mathcal{Y}$. We also have a generic sampling design $(\mathcal{S},p)$ with first and second order inclusion ...
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Distinct value estimate of a population from distinct value counts of two halves of it

A population $P$ is randomly divided into $A$ and $B$ (potentially differing in number of elements). I know how many distinct values are in $A$ and how many are in $B$, as well as the number of total ...
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1answer
116 views

How good an approximation is sampling with replacement to sampling without replacement?

I'm learning about probability with Feller's book and he states that, when the population size $n$ is big in comparison with the sample size $r$, then $n_r$, which is a shorthand for $\frac{ n!}{(n-r)!...
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1answer
1k views

When to use finite population correction?

I'm looking to understand where we would and would not use finite population corrections: at what point would you draw the line and say that fpc is not appropriate? I've read that it might not be ...
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1answer
955 views

What is the formula of the finite population correction factor? [duplicate]

Is it (N-n)/N or (N-n)/(N-1)? Provided that they can be used interchangeably, why would you use one instead of the other?
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statistical inference - what about population size?

I'll try to explain my question since it's very theoretical. In general, using statistical inference we try to estimate parameters of the population based on a sample. Several theorems show that as ...
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1answer
95 views

Gini coefficient finite sample correction

I wanted to compute some gini coefficients for different populations of differents sizes. In R I used the ineq package containing a Gini coefficient implementation. One of the paramater (i.e. corr) ...
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Does sampling fraction matter for McNemar's Test?

For McNemar's Test, does the sample need to be less than 1/20 of the population if the sample is without replacement? If so, can I correct for a sample that is larger than 1/20 of the population by ...
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Stopping outcome on reaching/crossing a target

I keep on throwing a fair die repeatedly till the cumulative sum reaches or crosses 100. What is the probability that the last throw was a six? This needs to be solved without asymptotic assumptions. ...
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1answer
98 views

Sample size with finite population and max error rate

I have a problem I need to solve. I have on average about 5,000 new documents that are created every month, and I need to determine what would be my optimal sample size so that I don't need to check ...
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1answer
82 views

Definition of the population of a discrete random variable

Consider the classical example of a random variable obtained by rolling two (fair) dice - the sum can take values between 2 and 12, where 2 and 12 have a probability of 1/36 and, for example, 7 has a ...
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108 views

Does this sampling without replacement have a name?

There can be many ways and ad hoc variants to perform sampling without replacement from a limited population. Consider we have $k$ categories (types of objects) and the k-length vector of their ...
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1answer
445 views

Difference in proportions with finite population

I'm looking for a suitable test for the difference in two proportions when dealing with finite populations. The standard z-test seems to only apply to infinite populations, so you lose some power. It ...
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What are the sample size confidence interval calculations for the Agresti-Coull and Wilson methods for finite populations?

There are formulations for the calculus of the sample size based on Agresti-Coull and Wilson confidence intervals for infinite population in some works (like Piegorsch - 2004). However, I didn´t find ...
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115 views

How calculate Gini coefficient (unbiased) and Lorenz Curve with stratified sample?

I'm working with a stratified sample by minimum variance method with 3 levels that becomes at 1176 stratum. The sample comes from finite population of income taxes data. I'm looking for how calculate ...
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1answer
200 views

Weak law of large numbers in finite populations [closed]

Background: The weak law of large numbers states that for a sequence $X_1,X_2,\ldots,X_n$ of iid RVs, with expectation $\mu$ and variance $\sigma^2$, the sample mean converges to $\mu$: $$\hat{X}=\...
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1answer
481 views

Bootstrapping a sample from a finite population

Can someone point me to some reference for theory on bootstrapping a sample took from a population of known size? I am used to use Bootstrap to calculate confidence intervals of a sample when the ...
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1answer
459 views

Variance of subsample from a distribution

I've simulated $N$ variables from a distribution $X_i \sim N(0,\sigma^2)$. I now take a subsample of size $n$ from this sample. Let the indices of this subsample be denoted $S_n$. I was wondering ...
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1answer
725 views

R survey package: finite population correction affects point estimate in addition to the variance estimate?

Forgive me if this is an idiot question, but I believed that including a finite population correction parameter in the R survey package should only impact my variance estimates in a stratified sample (...
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1answer
2k views

Derivation of formula for sample size of finite population

I found here the formula for computing the sample size $n$ of a finite population $N$ $$ n = \frac{n_\infty}{1 + \frac{n_\infty - 1}{N}} $$ where the sample size for an infinite population $n_\infty$ ...
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0answers
99 views

How to apply the finite correction error to adjust the required sample size

I am currently refreshing my stats knowledge where I came across the notion of the finite population correction. This notion appears when determining the sample size required to construct a confidence ...
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0answers
153 views

Sample size as proportion of population and statistical power?

I have done a study of information request response times in order to find out whether response time differs because of characteristics of the person doing the request. The studied unit is an ...
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0answers
154 views

Finite population correction, where does the square root come from?

The correction factor for finite populations is $\sqrt{1-\frac{n}{N}}$ (for known variance) where $n$ is the sample size and $N$ is the population size. I wonder where the square root comes from. ...
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1answer
122 views

Confidence interval for the odds ratio in a finite population

Does it make sense to estimate a confidence interval for the odds ratio / logistic regression model when the sample size is nearly equal to population size? For example, if the sample size is 50 and ...
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1answer
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Equality of two populations

Let's have two populations $A$ and $B$. Each population has $n$ integers, where $n>=1$. Can you claim that if means are the same, i.e. $\mu_A=\mu_B$ and so is the variance $\sigma^2_A=\sigma^2_B$ ...
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172 views

How to calculate stnd error for sample proportion with finite population correction when N is a random variable?

A coworker in the health insurance field is pulling a random sample of patient charts who have attempted suicide for a standard government report. Every random sample requires manual chart review, ...
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1answer
762 views

What role does the sampling fraction play in the simple random sample variance formula?

Consider a survey where the population being estimated is finite. Using a simple random sample, you draw $n<N$ data. The sampling fraction is $f=\frac{n}{N}$. The variance will be $(1-f)\frac{s^...
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1answer
2k views

Justifying the use of finite population correction

Given the fact the finite population correction effectively reduces the standard error of the sampling distribution, which (compared with the lack of a finite population correction) will increase the ...
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71 views

linearization of an estiamtor

Suppose we have two variables $x$ and $y$ defined in some population, with all values of $x$ known. A Poisson sample is drawn, with corresponding inclusion probabilities $\pi_k$ that are proportional ...
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1answer
221 views

variance of the variance for finite population for normal distribution

I am interested in calculating the variance of the sample variance for a finite population...of course in the limit of sampling the entire population, this will be zero. There seems to be one author ...
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2answers
385 views

Finite Population Variance for a Changing Population

How does the addition of one unit affect the population variance of a finite population if everything else remains unchanged? What are the conditions such that the new unit leaves the variance ...
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3answers
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Bootstrap: the issue of overfitting

Suppose one performs the so-called non-parametric bootstrap by drawing $B$ samples of size $n$ each from the original $n$ observations with replacement. I believe this procedure is equivalent to ...
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0answers
75 views

Interpreting coefficient errors in regression from uncertain population

I'm working on some regressions for UK cities and have a question about how to interpret regression coefficients. In a typical regression, one would be working with data from a sample and so the ...
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2answers
2k views

Standard error of the sampling distribution of the mean

I found an equation that says the standard error of the sampling distribution of the mean is: $$\sigma_{\bar{X}} = \sigma \cdot \sqrt{\frac{1}{n}-\frac{1}{N}}$$ And when the population size is very ...
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1answer
275 views

Margin of error (questionnaire response)

I sent a postal questionnaire to 1618 schools. In total, 220 responded (13.6% response rate). For one question, which had Yes, No and Don't know response options, 217 schools responded (Yes=85, No=127,...
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183 views

Origin of the finite population correction (FPC) factor?

I'm trying to figure out the origin of the finite population correction (FPC) factor. That is, who developed it as a concept and theory, and when was it first documented. I realize this is a tricky ...
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2answers
894 views

How can any statistics be calculated from a infinite population.

My understanding of some statistics: For a given experiment a finite number of samples can be taken, defining the sample size. However this experiment may have an infinity large population size. ...
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1answer
115 views

How to find the probability that a random sample of 10 points out of 52 points of data will have a mean close to the total mean?

I have a data set that consists of 52 weeks of data. I want to find the probability that any 10 weeks of data within the set of 52 weeks is close to the mean of the total 52 weeks. Close meaning ...
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1answer
56 views

What benefit can be gained from finding total population size

I would imagine this has been asked before but I can't find it so feel free to link if you can! Lets say I have a sample size of 100 and an unknown population size. There's a great deal I can learn ...
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1answer
424 views

Ratio estimation model in 2-stage cluster sampling

I've been reading about stratified sampling, 2-stage SRS sampling, and ratio estimation in finite populations and I have a question. When the ratio estimator is introduced, it seems that in order for ...
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2answers
1k views

Adjusting any power analysis with FPC?

Is it correct (perhaps at least as a good approximation) to determine sample size via a power analysis that assumes an infinite population and then to adjust the required sample size by a finite ...