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Questions tagged [finite-population]

Use this tag to refer to situations when the population of interest is not infinite. (Much of statistics, estimation & inference, relies on the assumption that the population is infinite.)

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Comparing distribution of continuous data and binned data that are compositional

The Data I have a list of N ∼ 6700 population members who have a condition and are labeled with age in whole years and biological sex. For the parent population, I have The total number of each sex (∼...
abalter's user avatar
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Does it make sense to use a hypothesis test with population data rather than a sample? [duplicate]

I have recently been learning statistics from the ground up (for context I am an engineer by training with no formal education in statistics/probability). I have seen various hypothesis tests: z-test, ...
ac19's user avatar
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1 answer
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Does the Central Limit Theorem Apply to All Finite Samples Even If They Come From Distributions That Don't Have a Finite Variance?

Some distributions, like the Cauchy distribution, don't have a finite variance, and therefore the central limit theorem does not apply to them. If I have a thousand randomly selected observations from ...
David Moore's user avatar
1 vote
1 answer
115 views

bootstrap resampling technique when comparing medians with finite population size

When comparing differences in samples (e.g., difference in medians) between two groups, I am adjusting group size to account for finite populations of the groups, pooling all of the samples together ...
Docuemada's user avatar
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4 votes
1 answer
180 views

bootstrap confidence interval and p-value calculations for finite population sizes

I am comparing the difference of medians between two groups of sample sizes $n1$ and $n2$. I would like to confirm that my boostrap approach for finite population size without pooling sample data ...
Docuemada's user avatar
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Non-parametric test for separating samples from two populations

I have samples $\mathcal{Z} = \{Z_1,\ldots,Z_n\}$. These samples either come from the unknown distribution $\mathcal{D}_1$ or $\mathcal{D}_2$. (Note: I can't make any assumptions about these ...
Deep Patel's user avatar
1 vote
1 answer
23 views

Can I use polling techniques in card games?

In a 50 card deck where 4 copies of a card are allowed at maximum,there are around 2 million possible starting hands. My question is: If I take a random sample of the 300-350 and analyze it. Can I ...
Alyosha OL's user avatar
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171 views

Binomial Proportions when sampling without replacement not studied?

Question When doing surveys with a population, we obviously don't replace by design. Why is it then that the mathematics and statistics described in textbooks seems to be veering more on the side of ...
user3659451's user avatar
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1k views

Why does the finite population variance requires the (N-1) factor in the literature?

Recently I've encountered the formula for finite population variance in Davison's and Hinkley's book "Bootstrap Methods and their Application" (see screenshot below). The formula includes $(...
itdxer's user avatar
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Confusion regarding proof that the variance estimator is unbiased for finite population

Going through Sharon L. Lohr's Sampling design book (2nd Edition), I have no issues with the content all the way until it goes into the proof in chapter 2 on SRSWOR that $E[s^2] = S^2$, where $S^2$ is ...
philiptomk's user avatar
3 votes
2 answers
286 views

Why do two different population sizes result in nearly equal sample sizes?

I have calculated the sample size for two different populations, N1= 29414 and N2= 625 (see code below). Why do I almost get the same sample size n1= 380 and n2= 239. There is not much difference, ...
Unknownuser's user avatar
5 votes
2 answers
197 views

Finite population correction for the variance

Just when I thought I was starting to understand Bessel's correction, I noticed that it is not valid when the sample size equals the population size and so likely not valid for sample sizes close to ...
Zaz's user avatar
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2 votes
1 answer
141 views

Is there a standard error of the mean for when population size is known?

Background Let us suppose that we are sampling from a finite population which is itself drawn from a univariate normal distribution. This accomplishes (1) having an underlying probability model and (2)...
Galen's user avatar
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1 vote
1 answer
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Estimate sample size from a variable population

Context: I want to measure accuracy, precision, and recall for individual raters. Each rater completes a variable amount of labels, for ex. rater A may complete 500 in a given time period while rater ...
acrobaticrock's user avatar
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1 answer
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Population overlap of random distributions of binary choices

I’m trying to figure out how to calculate the overlap (concurrence) of certain building features, for example: high-efficiency windows, thick insulation, efficient lights, etc. I know the probability ...
Determinant's user avatar
3 votes
0 answers
103 views

How do I calculate a finite-population correction for a weighted sample?

I have a weighted sample from a population. These are probability weights (as samples are taken with unequal probability). What's the variance in the estimated total? All samples are exchangeable (...
Closed Limelike Curves's user avatar
2 votes
1 answer
232 views

Finding percentiles without complete data set

I have a set of incomplete data for wealth of a given population. Whilst I have the wealth of these individuals (around 27% of the population), I do not have the wealth of every individual. I do have ...
twelfth's user avatar
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Estimate the sample size in cross sectional study when the required sample size larger than the population in a small city

I would like to know how to estimate the sample size in the cross-sectional study when the required sample size is larger than the population on Prevalence of vitamin Deficiency in multiple sclerosis ...
Rani's user avatar
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7 votes
1 answer
715 views

What is the *finite-population correction* for the Wilson score interval (for a binary proportion)?

The Wilson score interval is an approximate confidence interval for an unknown binary proportion for IID binary data. The interval is based on the central limit theorem like the Wald interval, but it ...
Ben's user avatar
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133 views

How do I use finite population correction in SPSS?

in our study, we have 80% of Norway's living brain cancer survivors. As we almost have sampled the entire population, we need to make a finite population correction. As this influences standard error, ...
Emilie Smith's user avatar
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212 views

Finite population correction for Binomial distribution without Normal approximation

I would like to evaluate the quantile function for a binomially-distributed random variable $X\sim Bin(n,p)$, where $n\ge 1000$. There are a couple of problems: The number of trials $n$ is very close ...
demim00nde's user avatar
3 votes
1 answer
75 views

What are the terms involving the mode's frequency?

Suppose I have a finite multiset of $n$ elements (a "population" I guess we can call it). Suppose this set has a proper mode, appearing m out of $n$ times. What term(s) do statisticians use: ...
einpoklum's user avatar
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4 votes
3 answers
411 views

Population covariance, are these two formulas equivalent?

For the population covariance, you can write it as: $$\sigma_{x,y} = \frac{\sum_i(x_i-\bar{x})(y_i-\bar{y})}{N},$$ where $N$ is the population size. I think you can also write it in terms of expected ...
Steve's user avatar
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7 votes
1 answer
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How can I use Propensity Scores to adjust for survey non-response bias?

Say I estimate the probability that each member of my target population responds to a survey using propensity scores. I am having a hard time finding a clear explanation of how I can use the ...
Alex's user avatar
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1 vote
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Bounding error of percentage estimation on binary data for small populations

Let's say you have a set $X$ with $N$ elements belonging to one of two categories. So, $x \in X$ can be of type A or B (these categories are mutually exclusive). The elements, however, are not ...
Ezequiel's user avatar
  • 111
1 vote
3 answers
2k views

Is heights of humans actually a discrete random variable? [duplicate]

Suppose the human population consisted of $N = 3$ people, each with a specific height. Let $X^N$ be the random variable representing the heights of this population of $N$ people. Since $X^N$ can only ...
Bertus101's user avatar
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19 views

i have likert data (1 to 5). 50 responses from 150 target population, not a random sample

Is there a statistical significance test i should use to get a p value that relates to the chances of my data being a true reflection of the population?
Gale's user avatar
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3 votes
2 answers
86 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 ...
Filip's user avatar
  • 31
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0 answers
79 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-...
DrPaulVella's user avatar
3 votes
1 answer
100 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 ...
Zhaleh's user avatar
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0 answers
524 views

Covariance between sample mean of two simple random samples

Suppose that we have two simple random samples without replacement $A$ and $B$ from a population $P$ of size $N$ such that $B = P-A$ where $n$ is the size of $A$ and $m$ is the size of $B$. I want to ...
Ana Pau De la Fuente's user avatar
3 votes
0 answers
85 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 ...
Alex's user avatar
  • 497
3 votes
1 answer
321 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 ...
P.Weyh's user avatar
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1 vote
0 answers
209 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 ...
Ryan1729's user avatar
  • 111
5 votes
2 answers
1k 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 $P_s=\frac{X}{n}$ ...
Hello's user avatar
  • 153
4 votes
1 answer
127 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 ...
Jeremy Miles's user avatar
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5 votes
3 answers
860 views

the rules of "approximately independent"

A tutorial says when the sample size is much smaller than the population, like 10%, we can assume that the element in sample approximately independent. I can imagine 2 possibilities about the ...
WXJ96163's user avatar
  • 297
2 votes
2 answers
3k 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 ...
StatsSorceress's user avatar
1 vote
1 answer
10k 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_\...
Darkov's user avatar
  • 113
1 vote
0 answers
43 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 ...
thomasvakili's user avatar
2 votes
1 answer
88 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 ...
fuz's user avatar
  • 221
1 vote
0 answers
151 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 ...
Waldir Leoncio's user avatar
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0 answers
23 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 ...
qgp07's user avatar
  • 101
4 votes
1 answer
2k 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 ...
Orion's user avatar
  • 214
0 votes
1 answer
1k 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 ...
Lailaps Fuentes's user avatar
2 votes
0 answers
454 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 ...
st1led's user avatar
  • 242
3 votes
2 answers
384 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 ...
Ashok Jaiswal's user avatar
6 votes
1 answer
504 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} ...
Nicolle's user avatar
  • 63
2 votes
1 answer
1k 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 ...
kludg's user avatar
  • 235
1 vote
0 answers
153 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 ...
Manos's user avatar
  • 91