Questions tagged [finite-population]

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1answer
26 views

Sample confidence interval

I am observing a 1/3 of a large (1 000 000) population (e.g. university students). I know that 10 000 students from my observed sample opted for a extra test. I estimate that 30 000 in total opted for ...
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0answers
22 views

Adjusting mean for very small population size

I have survey data from 8 respondents out of a population of 10 (very small I know). I know that FPC applies as we have more than 5% of the population in the sample. I can calculate the mean for a 0-...
3
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1answer
23 views

Problems with central limit theorem and bigger SE with bigger samples [duplicate]

It is said that “the finite population correction factor is used when you sample without replacement from more than 5% of a finite population. It’s needed because under these circumstances, the ...
2
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0answers
19 views

Adjusting for non-response bias in a survey

Say I have a target population of 10,000 for a survey, and only 2,000 respond, because they likely feel strongly about the survey topic (either happy or angry). I have clear, abundant non-response ...
3
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1answer
31 views

choosing sample size in prevalence study with a finite population

I am looking to conduct an epidemiological study on a population of 1000 individuals and need to find the appropriate sample size. So far, I have the parameters to calculate my sample size but I am a ...
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0answers
17 views

Is the sum of the medians of two sequential events a meaningful statistic?

Say I have two types of events $A$ and $B$ which happen to an individual entity, where $A$ is necessary for $B$ to occur, and $B$ starts right away after $A$. Also say we can split up the entities ...
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0answers
12 views

Another question regarding population proportion:

Here is the link to another question that I asked recently: The answer to my previous question very clearly proves that $\frac{P_sQ_s}{n-1}$ is the unbiased estimator of Var$\left(\frac{X}{n}\right)=$...
2
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1answer
38 views

An unbiased estimate for population variance

Specifically, my notes claim that when calculating confidence intervals for population proportion $p$, the estimator for the population variance is given by $\frac{P_sQ_s}{n}$, where $P_s=\frac{X}{n}$ ...
4
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1answer
36 views

Estimate number of pairs in population of known size from sample

I'm trying to estimate the number of pairs that exist in my data (specifically, these are identical, or near-identical, images). Checking for pairs is expensive and time consuming. My population size ...
1
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2answers
44 views

Why does the standard deviation of the sampling distribution of the sample mean needs N >= 20n

I keep seeing sources stating, without proof, that the standard deviation of the sampling distribution of the sample mean: $$\sigma/\sqrt{n}$$ is an approximate formula that only holds if the ...
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0answers
9 views

Bayesian estimation of number of cases given country data with variable coverage

I have a database with the number of cases for a specific disease for a number of countries. For each country I have case coverage estimates provided by the country itself, so for certain countries ...
1
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1answer
256 views

Cochran's sample size formula p variable meaning and intuition

I want to calculate a sample size for a large population of about 50 million. I came across Cochran's formula and the finite population correction. In short, Cochran's formula is the following: $$ n_\...
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0answers
20 views

Minimum sample size for estimating proportion of finite set of binary values

I have a finite set of data points where the number of data points has a known size $N$. The data points are binary and independent of each other, they are observations where we have either observed a ...
1
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1answer
71 views

How can I estimate a population size from the probability of randomly drawn members?

I have a finite set $X$ of unknown size. From that I independently draw a multiset of samples $S\subset X$. For each sample $s\in S$ I can give the exact probability $p(s)$ with which it has been ...
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0answers
48 views

Correction for sampling from infinite population?

I am currently creating a procedure to simulate the generation of data from an unknown, finite population (size $N$). Let's say data generation for a sample of $n = 100$ is done by drawing from a ...
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0answers
21 views

How well does population data fit a model?

Say I have a model that predicts hair color in a population: $X_1\%$ is brown, $X_2\%$ is black, $X_3\%$ is blonde, and in general color $i$ occurs $X_i \%$ of the time. Now, I go out and measure the ...
2
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1answer
180 views

Confidence interval for a proportion when sample = entire population?

I calculated the proportion ($\approx$0.12) of people who had a binary variable = true at a specific calendar date in a large geographically-defined population (N $\approx$ 2,000,000). I used data ...
0
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1answer
131 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 ...
2
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0answers
115 views

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 ...
3
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2answers
163 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 ...
6
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1answer
289 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} ...
2
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1answer
296 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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0answers
76 views

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 ...
3
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0answers
225 views

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 ...
2
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0answers
81 views

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 ...
5
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1answer
221 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)!...
4
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1answer
3k 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 ...
0
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1answer
2k 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?
2
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0answers
62 views

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 ...
1
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1answer
144 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) ...
3
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0answers
38 views

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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0answers
20 views

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. ...
0
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1answer
115 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 ...
1
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1answer
99 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 ...
4
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0answers
133 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 ...
1
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1answer
578 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 ...
2
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0answers
132 views

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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0answers
120 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 ...
3
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1answer
270 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}=\...
8
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1answer
660 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 ...
0
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1answer
572 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 ...
3
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1answer
1k 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 (...
1
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1answer
3k 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
116 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
157 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 ...
0
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0answers
210 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. ...
5
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1answer
142 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 ...
1
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1answer
40 views

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 $\sigma^2_A=\sigma^2_B$ ...
3
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0answers
197 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, ...
2
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1answer
1k 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^...