Questions tagged [population]

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

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37 views

Does it make sense to use a population parameter like $\sigma$ (population standard deviation) in the formula for SE?

Correct me if I am wrong but in the formula for SE $\text{SE} = \sigma/\sqrt{n}$, the numerator refers to population parameter. But in practical life, we resort to sampling because we don't know much ...
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What would be the gender ratio? [duplicate]

Suppose, families in a particular locality decide to have children only until a baby boy is born if their first two children are girls. The probability for a child being a girl or boy is 50%. Will ...
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Comparing populations of greatly different size

I'm reading an analysis someone gave me comparing two different populations of loans. One has about 3,000,000 loans and the other has about 6,000. The analysis compares the percentage of defaults in ...
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How to determine “per” population size for incidence rate

I am reading notes for a given assignment and incidence rate is defined as $$ \frac{new cases}{observed population} x 10^n $$ The only thing that is confusing me is that what to use for ...
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How to test if the subset is representative to whole dataset

I would like to ask how to test if the subset is representative to the whole dataset. I have for example 150 values in whole "population" and I selected (not randomly) 30 of them. I would ...
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how to test auto-selected sample and modify it to represent population

Suppose you have responses from a survey on an entire population, i.e. an organization of 5000 people. All has been invited to respond. Only 65% of them did. Assume also you have the ground truth of ...
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How to compare sample and population characteristics?

I have a sample $S1$ of 200 people, and I obtained a subsample $S2$ of 100 people by emailing a survey link to $S1$. So, $S2$ is a nonrandom subsample drawn without replacement. In the sample $S1$, I ...
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1answer
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Terminology - population and sample in repeated rolling dice experiments

The the law of large numbers wikipedia page has an example on fair, six-sided dice: According to the law of large numbers, if a large number of fair six-sided dice are rolled, the average of their ...
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Determine item level variance of single test administrations as well as of an entire sample of administrations

I am decades out of school and need help determining the correct statistic / concept to use for my use case. My agency (human services) uses a specific functional test to determine how well clients ...
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1answer
35 views

How statistically relevant are COVID information about the number of infections per day?

I am French and the restrictions in place in my country are driven by several indicators, including "the total number of infections per day". For reference, it is currently given as about ...
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Is “$\mu_{\bar{x}} = \mu$” the same thing as saying the mean of the population is the same as the mean of the sample?

My e-textbook is telling me that, when finding a sample from a population using a normal probability distribution $\mu_{\bar{x}}$ is roughly equal to $\mu$. It then gives me a problem asking me to ...
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How to forecast temporal series and have them match with external values?

I have a hierarchical population dataset with 3 grouping variables (Age, Gender and Urban/Rural Setting). I would like to generate predictions at the bottom-level (i.e. disaggregated at Age * Gender * ...
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1answer
31 views

Is there a difference between a population and a set of realisations of a random variable?

Is there a difference between a population and a set of realisations of a random variable? I heard that a sample of a random variable is a set of iid duplicates of the random variable as a process, or ...
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How do we decide when a small sample is statistically significant or not?

Sorry if the title isn't clear, I'm not a statistician, and am not sure how to phrase this. I was looking at the global coronavirus statistics on worldometers, and sorted the table by cases per ...
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2answers
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statistical method for finding significant numbers in a set [closed]

Suppose that we have a population of $N= 1000$ people and they want to select 5 items (for simplicity) $\{A, B, C, D, E\}$ (but actually number of items is in the order of thousands). Number of ...
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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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1answer
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Population vs. Data-Generating Process

A lot of elementary statistical and econometric literature bases on so called "population models". An example is econometric handbook "Introductory Econometrics: A Modern Approach" ...
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Re-calibrate interaction matrix in population sample

Let's say I have a population {$(G, p)$} where $G$ is a group within the population, and $p$ is their proportion distributed as such: ...
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1answer
18 views

Sub-population analysis

I'm facing a statistical issue. I'm analysing a medical dataset, in which I have a full population. I know if they have a certain disease or not. Let's say I have 100 000 people on this, 20% having ...
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Why is minimum sample size not based on proportion?

In different situations there are many tests or general agreements for a minimum sample size, which are usually some fixed number that is not that high, capping at <400. Common numbers include 100, ...
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Confidence intervals: What does the histogram of sample means have to do with the true population mean?

I believe the interpretation of a 95% confidence interval is the following: in 95% of random samples, the true population mean is within 2 standard errors of the sample mean. The 95% number comes from ...
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2answers
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How to calculate the range from mean and SD?

Is is possible to calculate or estimate the range of a population if I know the mean, population size and standard deviation? I am doing a research and the mean age of the population is 29.9 +/- 5.3 ...
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Does the 'no serial correlation' condition for regression only make sense with respect to a sample and not the population?

In this post, one of the answers provides the following information about the assumptions of linear regression in the case of random design (as opposed to fixed design): The usual regression model is $...
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Concurrent validity when the sample size of two populations differs much

I have two measures, the first scale was validated succesfully. Now, I want to validate the second measure by using concurrent validity. However, the first measure has the sample size of 300; on the ...
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1answer
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I need to find the Z-score of a population to use as a cutoff point in order to reduce the value sum of numbers to a new sum [closed]

This may be tough to describe, but I'll give it a shot. I am setting up an analysis that produces a large set of numbers. Let's call this Analysis 1 (A1). If I run A1 and return 60 numbers with a ...
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1answer
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Interpretation of confidence intervals for population data?

Suppose that I have access to the observations from the entire population $x_1,...,x_N$. If I fit a distribution to this population $x_i\sim F(\cdot ; \theta)$, and I calculate confidence intervals/...
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1answer
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I want to get a statistic for the number of cases per person living in urbanised areas

I have the number of cases by country since the beginning of covid. It is simple to plot this against the population to get the cases per capita. But I also have the population density per square ...
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1answer
556 views

Confused when to use Population vs Sample standard deviation in engineering testing

When I run an test for something (say 10 trials) and want to find the standard deviation of all 10 trials, I am getting confused if I should use the sample or population standard deviation. My initial ...
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Modelling uncertainty at both the individual and population level with beta-distributions

I want to measure the distribution of a population's performance on a test. Each person takes a version of the test with a random selection of N questions from a large pool of possible questions. ...
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2answers
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Summary statistics for two populations

I have two populations: part-time worker in the health industry (IND=17) and part-time worker in the financial industry (IND=12) For those two populations I have several variables (demographic ...
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2answers
43 views

Hypothesis testing: Significant difference between multiple iid samples?

I have four samples x1 = [1,1,2,5] x2 = [1,1,1,2] x3 = [1,5,5,5] x4 = [1,1,2,2] I am looking for a way to test whether the four populations are siginificantly ...
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Comparing percentages with different denominators to derive metric

I have read similar question posted here but could not find an answer to match my specific problem. So I have a list of countries and number of POI in each country. For eg. Austria (Total POI) : 100 ...
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Explain the descriptive statistics notion of population (distribution) to a measure theorist

My understanding of probability theory is a rigorous measure-theoretic one and I know almost nothing about descriptive statistics. However, I need to understand some of the commonly used notions in ...
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1answer
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Confidence in determining proportion of population with a given characteristic

Say I have discipline incident data from a total population (not a sample) of students in a school district. If I split the students into groups by some demographic marker (such as race), then I will ...
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1answer
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Proportionality of discipline incidents between student groups

My goal is to see if one student group has a disproportionate number of discipline incidents relative to the another group/s, to what degree, and with what margin of error. I will be speaking mostly ...
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1answer
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Regression Analysis with a Census or All Observations (Not a Sample)?

I have data that I've collected from every element in my population of study (a census), and not a sample. I am hoping to use the data to develop a regression model to answer questions like for a one ...
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Splitting a single large data set that contains two populations into two data sets

I have a single data set that contains two populations(This is a fact.) The means are different. It's obvious when charting the data, but not obvious to me how to split them. Is there a method or ...
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1answer
24 views

How can I calculate sample size for case control study?" [closed]

Please, I want to understand how to calculate the sample size the formula for the project entiled, "Evaluation of renal function in type2 diabetes mellitus patients attending federal medical Like&...
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0answers
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Can population have anything to do with calculating the growth of a function?

I'll explain. I'm trying to calculate "how fast" the virus is spreading, trying to "score" this growth. This could be done by: $rate = \frac{newValue + oldValue}{oldValue}$ What I'...
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Clarification on the definition of “population”

In stats classes, I've always learned that a population is always a very broad, almost unquantifiable group (e.g., all voters in a country, all consumers of a company, all viewers of a TV channel), ...
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2answers
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Discrete Random Variable vs Population Variance - Why Is Only The Latter Normalized?

The formula for the variance of a discrete random variable $X$ with values $\{x_1,x_2, ...,x_n\}$ and probabilities $\{p_1,p_2,...,p_n\}$ is given as $\sum_{i=1}^{n}(x_i - \mu)^2p_i$ where $\mu = \...
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4answers
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Detect if there is actually two populations in a sample

I have been counting stomata on fossil leaf material to apply a known relationship between stomatal index and CO2. I thought that the material was all from one population (one species at a given site)....
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What does replication mean for a mixed model?

I'm struggling to figure out how to test fixed effects appropriately in a mixed model, because of the concept of pseudoreplication (I have only seen this term in the fields of ecology and psychology). ...
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Additivity of sample (rather than population) variances

I'm trying to use the fact that variances are additive to derive the variance of an unknown random variable. Say that A and B are both independent normally distributed random variables. A third ...
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1answer
90 views

Use standard deviation of sample or population in z test

I am reading the book Statistics by Witte & Witte. Some questions puzzle me. Question 10.9: The normal range for a widely accepted measure of body size, the body mass index (BMI), ranges ...
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Rubin Causal Inference Book Study Question on Subsample and Subpopulation

Page 259 of the book writes: Suppose we look at the subpopulation of all units with $X_{i}=x ;$ within this subpopulation the difference in the distributions of the observed outcomes, between ...
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1answer
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Truncated CEF of normally distributed RV. Is sample analogue a consistent estimator of the 'population' truncated CEF?

If I have a random variable that is normally distributed, and truncated such that I only see $y$ if $y\geq 0$, and I want to do some calculations with the truncated Conditional Expectation Function in ...
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2answers
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How to sample when the size of the two populations differ greatly

I have to compare the distributions (means, variance, ratio of specific features, etc.) of two populations. However, the sizes of the two populations differ a lot, one with only 30,000 observations, ...
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Testing Multivariate Group Homogeneity

I have a multivariate dataset with data from several groups. I'm interested in determining at what point are two groups similar enough such that they can be treated as a single group for sampling ...
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1answer
265 views

It is possible to find point estimate of population mean and population variance when confidence interval of population mean is given?

Let's say that somehow $100(1-\alpha)\%$ confidence interval of population mean $\mu$ is known as $(a,b)$ and the number of samples is $n$. Is it possible to infer point estimates of population mean ...

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