# Questions tagged [population]

A population is the entire set of units from which a sample may be drawn.

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### How to interpret below, which formular is meant to be used [closed]

A study shows that 70% of consumers believe cheaper supermarket brands are just as good as national name brands. In response to these findings, the manufacturer of a national brand asked a sample of ...
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### Appropriate statistic for comparing Population Matrix Model predicted values to observed values

I have 2 different hindcast population matrix models (left and right) that predict annual nest numbers (median black line, 50 and 95 CI blue ribbons). These models are completely independent of any ...
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### Sample vs Population variance

I understand that sample variance is $$\bar X= \frac{1}{N} \Sigma _i^N X_i$$ whereas population variance (for a continuous variable) is $$E[X]= \int f(X)\cdot X \:dx$$ I do not see how these relate. ...
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### Standardization in cross-country time-series: using population or sample?

I have a dataset with countries, years and different measurements. If I would like to transform measurements in a standard score would I use the whole dataset as reference or only the countries and ...
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### Can Positive Values of Observations imply Population Positive Mean?

Suppose that we have N-observations for a random variable $V$ from a population: $$\{v_1,\;\ldots,\;v_N\}$$ , and all of the observations is positive: $v_i>0\quad \forall i=1,\;\ldots,\;N$. Here, ...
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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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### Like a census...but we sample with replacement until we have the same number of observations as are in the population (even if we miss some)

(Inspired by this recent post) In a census, we have a population with $N$ members, and we draw $n=N$ observations without replacement. This assures that we observe each population member exactly once, ...
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### How to infer unknown cell frequencies (effect of a variable) if table marginals are known and cell frequencies for another population is known?

I want to infer cell frequencies (or conditional probabilities) for a population table where: I know the marginal totals but not the cell frequencies, and I know the cell frequencies for a table of a ...
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### Z score across averages ? Or better anomaly detection

Currently having trouble finding the best way to compute a z score between “averages” Let’s say I have 1 group, that contains N patients. Each patient has a list of features corresponding to a ...
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### Does the population mean differ significantly in calculation from the sample mean after multiplying by 1/n?

The expectation of a binomial distribution is given by E(X) = np, where n is the number of trials and p is the probability of each trial. When using a normal distribution to approximate the binomial ...
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### comparison of a sample to another sample described by a histogram

I want to compare two groups -- a population and my sample. I need to find out if the sample is a representative sample of the population. Normally, I would use the Welch t-test to find out if the ...
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### Population studies - interpreting confidence intervals, should they even be included?

I work with administrative ('routinely collected') data in situations where the data capture the entire population, e.g. hospital records, prison records, etc. When reporting statistics the question ...
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### How to sample for compliance when a portion of the population is already known to be non-compliant?

Say I wanted a representative sample to estimate the portion of a population that is compliant on "doing their taxes correctly". Normally, I'd do a random sample of that population to make ...
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### Why is standard error of the mean always calculated from the population variance?

The standard error of the mean is often calculated with the formula $\sqrt{\sigma^2 / n}$, which uses population variance (or an estimate of it). However, standard error of the mean is defined as the ...
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### Why don’t we calculate the average of an entire given population instead of computing confidence interval to estimate the population mean?

We compute confidence intervals to estimate the true population mean of either a sample (when population standard deviation is unknown) or an entire population (when population standard deviation is ...
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### Can spurious correlations exist in the (theoretical) population?

Is it possible that spurious correlations exist between two random variables X and Y in the (theoretical) population (here I mean purely by chance, not due to missing confounders in a model, etc.)?
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### Comparing the Change in Size between Three Populations at Two Points in Time

I'm trying to measure the efficacy of a program that serves people experiencing poverty. We have data for the region that received the intervention, and data for two comparable regions that did not ...
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### Adjust a Sample Mean towards the Population Mean

This feels incredibly basic but I can't seem to find the answer! Let's say I knew the pass rate for an exam in a huge population of students is 50% (let's say millions of students). A new class of N=...
1 vote
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### Estimating a population total from a stratified simple random sample

I have a stratified population. I want to estimate a population total $T$ from a stratified simple random sample. I have two strategies: I compute $\displaystyle T=\sum_h N_h\bar x_h$ where $x_h$ is ...
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1 vote
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### question of a Poisson random effect model

Assume a Poisson random effect model (with a random intercept) $$\log E(Y_{it}|b_i,x_i)=\beta_0+\beta_1x_i+b_i$$ $$b_i \sim N(0,\tau^2)$$ How to derive the population-averaged effect of one unit ...
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### When I have population data do I need probability and can I infere? [duplicate]

Say I have data about a population and I want to analyze them, then in my understanding the "sample" is the population. And then do I need probability, like p-values, confident intervalls ...
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### Measuring variability of log in hours

I'm working on measuring the usage patterns of an app for a population of users. I want to find out if they usually log in at the same hours or if their usage times vary a lot. The variance of the ...
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### Combining results of 2 survey sources

In my study, I have data from 2 survey sources (from 2 groups of people). They are very different from each others. A few major differences: First group did not get paid to answer the survey while ...
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### Another question on population vs. sample

The problem that bugs me can be boiled down to: "What is population? (Really)." This is my thought experiment I've dealing with for a few days. There is a researcher A, who gathers data from ...
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### How to compare trend of two different datasets?

I have two different datasets (ID 1 and 2) which show the number of animals per hectare for each year. I need to know if the trend for the first periode is different then the trend for the second ...
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### Analysing PSI for much smaller sample size

I would like to analyse if data of my customers have changed recently, hence wanna check Population Stability Index. However, number of my customers have decreased recently, hence number of samples ...
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### Sample Bias in Study

I have following Study statement: A council wishes to study the digital awareness of its resident senior population (over 65 years), so it questioned in person 50 residents randomly chosen from a ...
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### What actually is Population of Data?

I have just started my statistics journey and as part of assignment I was given one statement and had to deduce population, sample etc from it. The statement is as follows: A council wishes to study ...
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### Effect size calculation?

We are currently analyzing medical records data. During the study period, we have a minimum of 60,000 population patients in group ...
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### Does it make sense to have error bars if there is no uncertainty in calculating the percentage?

I know a couple questions have been asked on this site that are similar, but they were slightly different from mine, and the answers don't seem to apply to me directly. I have the following simple ...
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### What sort of statistical test should I use to determine significance between independent groups in my (kind of unprecedented and strange) study?

I have designed a study where I am collecting price data from a particular niche of businesses in my state. Some of these businesses are owned by a conglomerate, and others are not. I want to know ...
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### Do I know the population or just a sample?

I have to analyze an artifact (a pencil), more specifically I need to analyze the production of the last semester of 2021 (during 2022 the artifact is still being produced but in my analysis I'm not ...
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### non-parametric inference assumption

This may be somewhat of a philosophical or foundational question. In parametric inference, we make a distribution assumption to relate sample to population. Even in a non-parametric technique such ...
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### What's population, what's sample, in a website conversion hypothesis test?

Context I am a marketer; and I run marketing campaigns and website design tests a lot. There are many tools - such as online A/B testing calculators - out there to help me test the statistical ...
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### Sample size of population to be representative of all names

Im not a mathematician but need some help trying to calculate the sample size of a population needed to be indicative of the whole population with respect to the prevalence of names. Assuming sample ...
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### Can I use an I-MR chart for a process in which the sampling time is random, or not regular?

I am currently studying a process which produces one sample for testing at one time. Not only that, the time at which the sample is taken for inspection is also not fixed but it varies. The process ...
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### Comparing capture efficiencies of sampling gear?

I have capture data for a fisheries population assessment. Two different crews were used that did surveys separately, each with variations in specifications of the gear that they used (same gear type/...
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### When calculating Horwitz-Thompson estimator, is it correct to multiply the pairwise terms of the calculation by two?

I'm currently trying to learn how to calculate the Horwitz - Thompson estimator for population variances. Using this formula  \hat{V}ar(\hat{\tau}_\pi)=\sum\limits_{i=1}^v \left( \dfrac{1-\pi_i}{\pi^...
1 vote
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### Representation of population data mean/median (similar to BMI/age curve)

I want to represent my data (n=150 samples with a curve of value over time, similar to BMI representations in figure). Possibilities are either mean/std and median/percentiles. The question are: Can ...
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### Can the sample equal the population?

I came across this test question from an introductory statistics course for undergraduates in biology. The solutions are in square brackets. Which cases are possible? The sample is larger than the ...
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### How to confirm population distribution type in industries

Studying some basic distribution problems that always start with "assuming this or that is a normal/exponential distribution", got me curious - how do people even arrive at these assumptions ...
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### Is it appropriate to put "error bars" on data when you have the full population?

I have data on the large number of people who were applying to receive an award. Everyone who applied must fill out a survey and specify their gender (although they can choose "prefer not to say&...
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### Which test to use when I have population data?

Population Data I have a large dataset of government funds to all the training schools in London. It's a complete dataset i.e. it represents the population I am studying. I only want to know about the ...
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### Fitting a von Mises Distribution over the Global Population

For a statistics course I'm taking this semester, we decided to conduct a worldwide survey. One of our questions, is an approximate coordinate of where the respondent lives. Our instructor recently ...
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### Why is the expected value of any data point in the sample equal to population mean?

Suppose we have a distribution of heights of all males in a country. Let population size = N. Now, I take a sample of 100 males = {h1,h2,h3,....h100} How is the expected value of any data point, i.e., ...
1 vote
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### Problem with weigts in survey analysis of GSS cross-sectional data

I have a dataset made from https://gss.norc.org/get-the-data There is a description from the codebook how to use weights: ...
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### Method for calculating number of employees

I need to calculate the number of employees in a given number of organisations. I know how many organisations there are in total and I know the number of employees in 50% of those organisations. Some ...
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### How to interpret big data models with poor local prediction

Dear big data experts, I’ve been confused with how to think about machine learning models trained through population-level big data that could not make good predictions at the individual level. I ...
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