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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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, ...
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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 ...
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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 ...
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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 ...
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How is the finite population of unequal sized clusters applied in one-stage sampling?
If clusters vary greatly in size, then it seems that the form $f = (1 - n/N)$ is not always a good choice. Usually in this form $n$ is the number of clusters sampled and $N$ is the pop cluster total.
...
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Appropriate means comparison test to detect fraud in population dataset by re-measuring outcome over a sample?
As part of a project, organization A contracted organization B to deliver an outcome $X$ across $N=500$ units. B compiled a dataset on $X$ which accounts for the entire population.
$X$ is a discrete ...
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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 ...
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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 ...
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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 ...
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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 $(...
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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 ...
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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, ...
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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 ...
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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)...
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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 ...
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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 ...
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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 (...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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:
...
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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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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-...
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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 ...
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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 ...
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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 ...
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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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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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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 $P_s=\frac{X}{n}$ ...
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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 ...
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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 ...
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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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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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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 ...
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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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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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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 ...
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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 ...
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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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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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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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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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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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