# Tagged Questions

A sample is a subset of a population. Statistics, in general, is concerned with using samples to make inference about the parameters governing a larger (possibly infinite) population.

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### Is sample variance an unbiased estimator of population variance? [on hold]

Population has 3 values 2,3,4 A sample of size 2 is drawn sample : 2,3 2,4 3,4 Population mean = 3 Population variance= 0.6667 mean of sample means = 9/3 = 3 . Therefore, sample ...
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### Evaluate “sampling error” due to lack of data

I'm working on a problem of evaluating the long term success of some investments in some companies around Europe. My problem is that I have the information, before the investment was done, of say 100 ...
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### Systematic sampling and informed consent: Does the requirement for informed consent introduce sampling bias into randomly selected samples

Probability sampling methods help reduce sampling bias. In clinical research, simple random sampling methods works well for randomised control trials, and systematic sampling methods are easy to ...
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### Lee (1983) sample selection correction with accelerated failure time model (in Stata)

I am trying to replicate the selection control used by Henderson et al. (2006), which is derived from Lee (1983). Henderson et al study CEOs over time and try to control for the likelihood that a CEO ...
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### Grouped monthly sample sizes

This will be really simple, but I'm having a hard time figuring out how to Google this. Let's say we have 12 months of trailing data on something like "Calls per month," and that data is on the low ...
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### Make inference on overall density of duplicate records from a sample

I have a file, typically of several million records, for which I need to make an inference on the percent of duplicates (perhaps testing for whether the rate exceeds a certain percent, or just coming ...
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### The practical use of the lower/upper semivariance adaptation of Chebyshev's inequality for sampled data

The wikipedia article about Chebyshev's inequality also lists a one-sided sharpened variant, based on upper/lower semivariances. It is additionally mentioned there there that "The inequality with the ...
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### Selecting Subsets with Linear Correlation

I'm looking for a method of grouping 200+ samples with 30+ features into groups which share linear correlations among a subset of the features. I've found Ransac to sometimes return a good ...
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### Calculating power of a sample (need a layman's/beginner's definition)?

We have a bi-annual survey and an intended sample size of 1,300. This sample size was determined using Krejcie's means formula for finite populations, and we drew the sample using 2-stage clustering. ...
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### What is the effect of using survey sample weights for a sub-sample?

If a sub-sample of the survey sample, selected based on certain demographic characteristics of the data (e.g. age, race etc.), is used, which means the sub-sample might not be representative of the ...
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### Sample from a multivariate distribution with contraints (Sand +Silt + Clay = 100 %)

I need to generate a sample from three distributions (I assume them Gaussian), respectively sand, silt, and clay. Actually, these variables are found in three soil maps. For each of them we have the ...
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### Comparability of the data from two samples

I have a data sample with 600 units, this data sample is representative. From these 600 units I compute economic sentiment indicator on monthly base in period 2006-2010. From 2011 I want to change (...
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### Should there be some changes on SE after an intervention?

I found this quite confusing from a Udacity course and also got a problem open the course forum. On the following figure, the red curve represented the sample distribution before intervention. After ...
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### Standard Errors for 2X2 Regression

If we have two dichotomous variables variables and run an interaction constructing the means for each cell seems straight forward, but not the standard errors. I would like to use these standard ...
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### Which Statistical Significance test for two samples of different sizes?

I would like to compare the statistical significance of a key difference in my population: 25% of my population have attribute B (let's say B is red trousers) 75% of my population don't have ...
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### How can I calculate ± estimate based on sample set?

Say I have a completely random sample of 25M weights of a population of 100M. Say the average weight of the 25M random sample is 150lbs with a standard deviation of 45lbs. How can I be more precise in ...
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### How to determine if sampling is representative/similiar to my population

Let say for whatever reason I have obtained a sample of an initial population. (ie. we have paired case:controls on a set of confounders). I wish to compare how representative my sampled (or let me ...
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### Proving a property of $(n-1)s^2$

I would appreciate your help as I climb the stats learning curve! I want to prove the following: "Let $x_1, x_2, ... , x_n$ be any numbers and let $\overline x = (x_1 + x_2 + ... + x_n)/n$ Then ...
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### Splitting an i.i.d. sample in two by criterion - what survives of independence and population representation?

Assume that I have available a $k$-dimensional i.i.d. sample of size $n$, collected in the $n \times k$ matrix $\mathbf X$. Each column represents a series of realizations from a random variable. ...
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### Independent or Dependent Samples

I want to perform a statistical test: Wilcoxon Signed Rank Test to test if there is a significant difference between them, but I don't know if the two samples are dependent or not? Context: I have a ...
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### Independent or dependent sample in content analysis

I am conducting a quantitative content analysis on specific crime news reports and want to explore difference in the quantitative amounts of coverage depending on whether the victim was male or female....
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### Are the Observations in A Random Sample Independent?

guys. I am learning the t-test on my own. The assumptions of t-test have been confusing to me. The assumptions included "A random sample is used" and "The random sample is made up of independent ...
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### Compare scores calculated for two groups who overlap?

I have three groups of ten children (A, B and C). They are each have different treatments (the treatments are to do with how they are taught about a certain biological feature). Two scores are ...
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### Algorithm for ranking population elements based on occurrences and sample ranks

I have a finite pool (population) of about 10000 elements. Samples of 100 elements are randomly chosen, and each sample is then ranked based on random element attributes. The 100 elements are then ...
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### Stratified sampling when creating a test/training set

I am creating a dataset that I am going to use as the training/test sets for a supervised classification problem. The problem is to identify quotations in a large corpus. I have randomly sampled the ...
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### How well does sample average range estimates sigma?

Suppose there are m subgroups of n items each. The following practice is described by Montgomery in the construction of a $\bar{X}-R$ chart: Let $\bar{R}$ be the average range of the m subgroups. ...
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### Proportion Sample Size Estimation? Cluster Sampling

I was asked by someone running a food drive to help with the following problem: Food is being collected in bins, which hold about 1,500 lbs of food each. They are looking to collect about 500-600 ...
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### Determining the required sample size to meet a bound

A company produces a special kind of utility terminals. It has N = 26016 such terminals out in the field in some city for many years. Over time these utility terminals go bad. The company decides to ...
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### Estimating Distributions of Weighted Data

I'm trying to build a bivariate copula-based model of income and wealth in Italy and I'm having trouble handling weighted data. I have access to micro data, a survey of about 10,000 households that ...
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### Sampling size question [closed]

I wanted to know the sampling size of a population where size is low and moreover it doesn't follow a normal curve. Moreover I wanted to roll out quality numbers at monthly level as the weekly level ...
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### biological sample size when instrument accuracy is weak?

I'm using a porometer to measure the transpiration of grape leaves. Unfortunately, the instrument's accuracy is 10% and it has a relatively slow (60 seconds) round trip time to produce readings when ...
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### Good algorithm to compute the sample mean and variance [duplicate]

I am looking for good (fast, memory efficient, ideally one-pass) algorithms to compute the sample mean and variance. I have found a technical report by Chan, Golub, and LeVeque from 1983 with ...
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### Pool data from two different points of time with different attendants

I have two samples (each nurses) one from 2008 and the other drawn 2013. Both got the same questionaire to fill out. Now I would like to pool the data but do not know if I just can do it. My idea was ...
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### Overview of predictive modelling, machine learning, etc.

My text Intuitive Biostatistics is a nonmathematical explanation of conventional statistics. Chapter 3 explains the basic mindset of statistics as analyzing a sample to make inferences from a ...
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### Sample size choice with binary outcome

Our civic association is planning to implement a survey asking our neighborhood one true false question. I would like to make sure that we obtain an adequate sample size. Let's assume N = 2500 ...
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### Census Data for Regression model: American Community Survey or 2010 Decennial?

I have a data set that contains electricity use for 2012 aggregated to the city level for a number of cities in the United States. I was interested in doing some analysis to see the relationship of ...
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### Parametric Bootstrap to determine sample size capabilities

I'm pretty new to the world of Statistics, so perhaps my understanding is lacking, but I'm interested in testing the capabilities of a smaller sample size in resolving a population mean. My thinking ...
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### How to determine if sampling is representative to population

Is there any coefficient or some metric that will tell how well sample reflect the population?
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### How to estimate the reliability of an exhaustive list of data?

I have a purported exhaustive list of beneficiaries under a social security scheme. My question is how large must be the sample of this population must be tested to check for fraud etc to derive an ...
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### Is sample standard deviation a valid approximation of population standard deviation for z-scores?

Given a Normal distributions for the population and my sample, a population mean of mu, and a sample standard deviation of s, if I want to find the area under the population curve from x to infinity, ...
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### Compare standard devation between different samples?

I am calculating standard deviations $\hat\sigma_i$ from many samples from distributions with mean equal to zero but different variances $N(0, \sigma_i^2)$. Each sample has different size $N$. When ...
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### R how to get same sample size from different categorical values [closed]

I have an unbalanced set of records for different values of a categorical variable as shown below: ...
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### Sampling 100000 times from normal distribution in R : strange distribution of samples' standard deviation

I generated, in R, one hundred thousand random samples of ten values from the normal distribution with mean zero and unit standard deviation, and registered each mean and standard deviation, in hope ...
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### Population vs. Sample [duplicate]

Can you use population to refer to a particular population? For example the population of women in Maths Class, from which we can take a sample to measure the height in order to make a judgement of ...
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### What is the difference between standard error and margin of error and when to use which?

Will someone please explain what the difference is between standard error and margin of error and when to use which? I have not had luck finding a simple explanation on the differences anywhere on the ...
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### Distribution of the sample mean of a Rayleigh random variable

Let $\{X_1,X_2,X_3\ldots,X_n\}$ be a random sample from a Rayleigh distribution with shape parameter $b$. Let $\bar{X}=(1/n)\sum_{i=1}^nX_i$ denote the sample mean. QUESTION 1: What is the ...
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### The sample size of a study is reduced. Is it still representative?

If the size of representative sample is lowered due to some genuine causes (e.g time, budget), then what are the possible ways to make it a representative sample within the decreased size.
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### Help me inform multiple regression coefficients with additional dataset

I have a data set with 24 year on year observations. That is for a single company. I have around 500 companies with incomplete datasets (i.e. with missing values). I am trying to predict a Y ...
Suppose there is a simple linear model $y=\beta_0+\beta_1x+u$. Can we state that $\bar y=\beta_0+\beta_1 \bar x + \bar u$? I have this question because I come up with $Var(\bar u)$ when doing some ...