Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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.)

109 questions
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Explanation of finite population correction factor?

I understand that when sampling from a finite population and our sample size is more than 5% of the population, we need to make a correction on the sample's mean and standard error using this formula: $\hspace{10mm} FPC=\sqrt{\frac{N-n}{N-1}}$ Where…
Sara
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Why at all consider sampling without replacement in a practical application?

Sampling with replacement has two advantages over sampling without replacement as I see it: 1) You don't need to worry about the finite population correction. 2) There is a chance that elements from the population are drawn multiple times - then you…
Raffael
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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 estimating the cumulative distribution function by the…
James
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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 test statistic from a hypothesis test (and…
NickB2014
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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 population size is considered way larger than the…
Inox
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Sampling variance is reduced when removing duplicates -- why?

I have carried out a simulation experiment where $n$ out of $N$ items $x_i$ were drawn with replacement with unequal probabilities $z_i$ from a finite population. (If it matters: $z_i = 1/(Nx_i)$ in my case, but perhaps there are more general…
krlmlr
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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 large, the factor $1/N$ is approximately equal to…
user53064
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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 propensity scores to adjust a continuous outcome of…
Alex
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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} f(k,n)=P(Y=k|n)={n\choose…
Nicolle
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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 the population size is 60.
Ricardo UES
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When the population has a known fixed size, are tables for the t statistic wrong?

As I understand it, Student's t will asymptotically approximate the Z statistic at sample sizes approaching infinity (see the infinite degrees of freedom row for degrees of freedom in most introductory statistics books). However, Z tests are…
russellpierce
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Jensen-Shannon divergence for finite samples

I have two finite samples $s_1$ and $s_2$ and two distributions $p_1(s_1)$ and $p_2(s_2)$ that are associated to these samples. I'm essentially interested to measure the distance or similarity between these two distributions. I'm currently using the…
omidi
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Confidence of uniformity from a sample of a binary state collection

The system: I have a bag filled with 1,000 balls All of them are either red or blue I want to gain some amount of confidence that all the balls are blue, but I'm very lazy and I only want to examine a sample as small as possible. Question: How…
Stephen Crosby
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How to use finite population correction in multiple regression?

I have a small population of N=137 and a (presumably representative) sample of n=81. The corresponding Finite Population Correction (FPC) factor is FPC=SQRT {(N-n)/(N-1)}= 0.64. Can I apply this correction factor to the estimated standard error of…
user18368
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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 figure 10%, a widely recognized rule or an intuition,…
WXJ96163
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