Questions tagged [population]

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

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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
70 views

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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3answers
74 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 ...
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1answer
45 views

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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0answers
9 views

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
15 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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0answers
16 views

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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0answers
23 views

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
131 views

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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0answers
50 views

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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0answers
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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
35 views

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
28 views

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
76 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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0answers
10 views

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
47 views

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
33 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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0answers
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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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0answers
50 views

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
11 views

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
28 views

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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0answers
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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
19 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
10 views

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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3answers
191 views

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
36 views

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
1k views

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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0answers
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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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0answers
40 views

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
40 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
27 views

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
42 views

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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0answers
13 views

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
60 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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0answers
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Another question regarding population proportion:

Here is the link to another question that I asked recently: The answer to my previous question very clearly proves that $\frac{P_sQ_s}{n-1}$ is the unbiased estimator of Var$\left(\frac{X}{n}\right)=$...
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1answer
41 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 $P_s=\frac{X}{n}$ ...
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0answers
15 views

Is my intuitive explanation of the premise for hypothesis testing correct?

They way I understand hypothesis testing is that there is some true data generating process out there, and that determines the 'population' distribution of variables, and then our sample is just one ...
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0answers
20 views

Confidence interval over estimated number of infected individuals in a population

I have built a machine learning binary classifier (using a Logistic Regression model) that outputs whether or not a person is infected with Covid-19, based on the symptoms that this person presents (...
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0answers
47 views

Statistical Test for Evolution of a Population Proportion?

The problem I am faced with is as follows - there is some population proportion $p$ of people with a certain characteristic that is evolving over time. We take new samples every day (without ...
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1answer
32 views

Do we consider the dataset to be sample even if the data we are given is complete data in analytics?

I was watching an online video on statistics and in the video we were making inferences on a real estate companies data, to predict our future customers. The instructor had all the previous data of ...
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0answers
8 views

Significance of single classification change across multiple time slices (archaeology)

I'm trying to determine if I'm correctly testing for significance of the change in artifact type presence across several time periods. In an archaeological survey, stone tool artifacts were cataloged ...
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2answers
50 views

Is a population parameter really a fixed quantity?

This might be a simple issue. I consistently come across internet sources that say that a population parameter is "fixed" and cannot change. However, if we define, for example, our parameter to be ...
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0answers
24 views

Testing similarity of proportions across groups of samples- is ANOVA the right method?

Generally, I'm looking for the correct way to test if samples of a certain population over time tend to have the same proportional distribution more or less e.g. if the amount of certain race in a ...
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1answer
34 views

Questions about Confidence Interval

could somebody please help me with this question. "What will happen to Confidence Interval if you change from using sample SD to population SD? Would the CI you calculated previously increase, ...
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2answers
41 views

Population vs Sample Space

In probability theory, it is my understanding that the sample space $\Omega$ is the set of all possible outcomes of an experiment. In my mind, I am thinking of it as a set of data points such as ...
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1answer
34 views

How to determine margin of error for a population size estimation using a size-biased sampling process?

I am trying to estimate the size of a discrete population $\Omega$. To do so, I draw independent samples $s_1\ldots s_n\in\Omega$ according to some distribution $p(s):\Omega\to(0,1)$. For each ...
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1answer
22 views

How to find confidence interval of expected sample results from true population proportion?

Let's say I know the true population proportion of a particular attribute, say 15% of people are left-handed. Imagine I perform a random sample of 1000 people around the world. How do I compute a 95% ...

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