Questions tagged [sample]

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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159 views

How to make sure that the random sample is representative for the whole sample?

I have 14k tweets and I want to code these tweets (categorize them based on their topics), but since it is difficult to do the coding for the whole dataset, I decided to take a sample from it. What I ...
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86 views

Time series: sample vs. population, population vs. realizations of random process

Suppose we have 120 monthly observations (Jan 2000 - Dec 2009) of unemployment rate and suppose we would like to use these in order understand the unknown underlying stochastic process that generated ...
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226 views

Why don't we use the n-1 correction for standard error of sample proportion?

From my understanding, when we construct a confidence interval for a sample mean with a sample size of n, we try to estimate the standard deviation of the sampling distribution $$σ_{\overline{x}} = \...
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136 views

Compute (bootstrap?) expected difference between two samples

What would be the correct (most statistically sound) way to tackle the following problem: Given are two samples (or empirical distributions) from two unknown distributions $X$ and $Y$, with $N_x$ and ...
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400 views

Samples size with sample proportion close to 0 or 1

For a future monitoring program on small water bodies we want to calculate the sample size. The bodies of water are so small that their number easily exceeds 100.000 in the monitoring area and ...
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139 views

Does this sampling without replacement have a name?

There can be many ways and ad hoc variants to perform sampling without replacement from a limited population. Consider we have $k$ categories (types of objects) and the k-length vector of their ...
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1answer
229 views

Population, sample and model

Background: In Statisical Methods by Pfaffenberger and Patterson, they say that "A parameter is a numerical measure of a population characteristic." (p. 306) "A statistic is a numerical measure ...
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181 views

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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899 views

Measure of similarity between two multivariate samples

I have two samples from a multivariate distribution. One is approximate and the other is exact. My aim is to measure the similarity between the approximate sample and the exact sample. In particular, ...
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0answers
921 views

Weighted sample covariance

I have read the Wikipedia article, and know that the unbiased weighted sample covariance matrix for the row vector $\mathbf{x}_i$ is $$\Sigma=\frac{1}{\sum_{i=1}^{N}w_i - 1}\sum_{i=1}^N w_i \left(\...
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64 views

Difference between sample and sequence in Law of Large Numbers

I'm comparing the Chebychev (Weak) Law of Large Numbers (LLN) to the Kolmogorov (Strong) LLN in an econometric textbook and both definitions start off differently. The Chebychev LLN begins with If $...
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0answers
260 views

“Unselected sample” vs “random sample”

I've just encountered the term "unselected sample" for the first time, which seems to be fairly commonly used in medicine. Example usages: Climacteric symptoms in an unselected sample of Swedish ...
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28 views

Increase the number of samples when the PDF is invariant

Background: $$\frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}$$ is given by Fick's second law, in which $D$ is the diffusion coefficient. The solution to this equation (given the ...
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63 views

Can we sample from a set of biased samples to get unbiased samples?

This is a follow-up question to How to uniformly sample vertices from a large graph with given distance from a fixed vertex?. Suppose I took a set $B$ of $n$ samples from a large but finite universe $...
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0answers
41 views

Does sampling fraction matter for McNemar's Test?

For McNemar's Test, does the sample need to be less than 1/20 of the population if the sample is without replacement? If so, can I correct for a sample that is larger than 1/20 of the population by ...
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54 views

What are good ways to compare how “representative” a smaller sample is compared to a larger sample from which it was taken?

So basically, we have a sample of known data taken from a larger sample of known data. Is there a good way to measure how "representative" that data is, especially in distributional terms, compared to ...
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141 views

bound on expectation of a two-variable function under an independent distribution

Consider a probability distribution $P(x)$, a set observed samples $S = \{x_1,\cdots, x_n\}$ where $x_i \stackrel{iid}{\sim} P(x)$ for $i \leq n$, and a symmetric function $h(x,y)$. How can one ...
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171 views

How to evaluate similarity of datasets based on summary data?

I have summary data that I want to compare to my own data. For the summary data I do not have access to the underlying data, however, I know the percentiles as shown below (A). I also calculated ...
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68 views

Estimating the mean from knowing the first n largest values

There is a sample of n values that are the first n largest values of a population. Is there a way of getting any statistic such as mean or dispersion from such piece of information provided that the ...
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692 views

Combining covariances

Imagine we have one sample (n=40) from a population on 2 variables, for which we estimate the covariance (say, 0.1). If we would have another sample (n=10) from the same population, and we estimate ...
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305 views

How to calculate the 'loss' in information when decreasing sample size?

I have a questionnaire with ~40 questions where the respondent answers on a scale 1-7 on each question. At the moment we have a sample size of say 10,000 people. The question is how I calculate the ...
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19 views

Average of geometric mean across subsamples

I am looking for a simple closed-form expression simplifying the sum (or average, if you prefer) of the geometric means of all subsamples $A\subset X$ of cardinality $|A|=k$ from a grand set $X$, \...
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1answer
67 views

Why is importance-weighted empirical risk minimization finite-sample biased?

Classical risk minimization (RM) minimizes the expected loss over the training distribution $p_{\mathrm{train}}(x)$, $$\theta^*_{RM} = \arg \min_\theta E[\ell(x, \theta)]_{p_{\text{train}}}.$$ As the ...
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1answer
46 views

Parameter estimation of a transformation

imagine you have a sample $X_1, X_2, \ldots, X_n$ from a random variable $X$, and another sample $Y_1, Y_2, \ldots, Y_m$ from a random variable $Y$. You know that $Y = \phi(X)$. For concreteness, say $...
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1answer
33 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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1answer
138 views

How to estimate log-normal distribution parameters from a set of data?

I don't have any background in statistics, so maybe I may say things that are incorrect. I have to model the production of waste deposition at each container of a set of containers and I have access ...
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29 views

Expected standard deviation of probabilistic sample

Let's say I have a collection of $n$ individuals, each individual is associated with a single value $x_i$, with $i = 1, 2, 3, ... n$. I now gather a sample of $s$ individuals from this collection, ...
2
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1answer
41 views

Logit regression (Panel data): resample?

I have a panel data (all listed companies in the US with quarterly data) in which the dependent variable is 1 if the company was recommended on a investment recommendations website, and 0 otherwise. ...
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43 views

Unbiased Estimator of the Standard Deviation of the Sample Standard Deviation

I'm looking for an unbiased estimator of the standard deviation $\text{SD}(s)$ of the sample standard deviation $s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \overline{x})^2}$. I have found this ...
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38 views

Why is unbiased estimation from a sample only possible for certain properties?

I was thinking about finding some monotonic measure of entropy of a sample from a continuous distribution (2D, btw), but couldn't think of any such without making assumptions. Why is it that one can ...
2
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1answer
16 views

Evaluating usefulness of estimations of a parameter for different distributions

If I had a sample of size n and wished to estimate some parameter, say p for two different distributions from the produced sample what would be required to determine which was more useful? Assume the ...
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19 views

Sample size for comparing two properties of time series data

I have a dataset of observations of two properties of an object (x and y), which are distributed over time, ...
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0answers
161 views

Construction of i.i.d. sample

My task is to describe the construction of i.i.d. sample $\mathbf{X} = (X_1, \ldots, X_n)$ where random variables $X_1, \ldots, X_n$ should get the predefined univariate distribution $P$. Specifically,...
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18 views

What is the effect of more than one chance of selection when sampling?

I am designing a clustered sample. Within each cluster there are 3 groups that will be sampled from - two at a higher rate than the other. The two subgroups that will be sampled at a higher rate are ...
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0answers
1k views

Unbiased estimator of standard deviation. Simulation results

As an exercise I decided to check if unbiased estimator of standard deviation of sample is giving better results than biased estimator . So far it looks that only in aprox 55% cases. Am I doing ...
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137 views

What are the sample size confidence interval calculations for the Agresti-Coull and Wilson methods for finite populations?

There are formulations for the calculus of the sample size based on Agresti-Coull and Wilson confidence intervals for infinite population in some works (like Piegorsch - 2004). However, I didn´t find ...
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260 views

For boostrapping: stratified or cluster sampling?

I am trying to apply bootstrapping on several regression models to obtain SEs of parameters. My question is about preparing the bootstrapping samples in proper manner. The data I am working on are ...
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0answers
178 views

Confusion between definitions of random variable (especially sequence of random variables) and random sample

I am having a hard time understanding the actual definition of random variable (especially sequence of random variables) and a random sample, as well as the relation between these definitions. ...
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1answer
24 views

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 ...
2
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0answers
73 views

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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0answers
272 views

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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0answers
260 views

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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34 views

Making Inferences from a sample

I am trying to teach myself basic inferential statistics by going through online video lectures. However there are some gaps in my core concepts. I have a couple of quick questions Assume I take a ...
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38 views

Weighted measures in surveys

In sample surveys a weight is typically calculated so that the weighted population measure by certain pre-selected categories (e.g., gender, age groups, geographic areas, etc.) match national total ...
2
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1answer
264 views

Confidence intervals for percentage share of multiple response

If I have a sample of 100, who give responses to a set of multiple response variables, say for example, the brands they have purchased in the last 12 months. How can I calculate the confidence ...
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0answers
874 views

(Pretty) large sample size, unequal variance, unequal sample sizes, non-normal distribution. T-test alternative?

So, I've never had all these problems at the same time before, but I have: - Likert data, from a 9 point scale - n = 317 v 177 respectively - SD = 2.08 v. .274; 1.9 v. 2.6; 2.5 v. 2.9 etc. (you get ...
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0answers
79 views

Accuracy of approximation to sample median

Suppose we sample $n$ real numbers uniformly on $[a, b]$. We wish to find the sample median, but we will approximate it as follows: randomly choose a subset of the sample of size $k$ with uniform ...
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0answers
61 views

Why is the every data item in a sample is considered to be produced by a different random variable?

In the stats book I am studying, while explaining bias and mean, the author goes like this: "... Suppose a sample $$S=(X_1, X_2,...,X_n)$$ has been collected. ... Sample mean $\bar{X}$ estimates $\mu$...
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112 views

Need Help w/ Research Proposal

I am currently doing a master's research proposal (experiment hasn't been completed yet) and need to decide what statistical test to use. My research question is observing increases in bowling ...
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77 views

Sampling Size for a large Dataset

I am having a dataset of size upwards of 200 million rows. I have no knowledge of the distribution of this dataset. Would like to perform some analysis on this - like look at the ...

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