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Questions tagged [sample]

a sequence of objects or individuals collected from a larger (possibly infinite) population or process.

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Power analysis for the Cox proportional hazards model

I'm trying to work out the sample size needed for an RCT based on a small study looking at reoperation following index surgery. In this small study, there were 1000 patients, group 1 had 700 versus ...
MFA's user avatar
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cloglog.sample.size function (Binomial distribution)

I was wondering if cloglog.sample.size function from binom package in R can be used to calculate the sample size for the following model (Binomial dis with cloglog) which can be used for discrete ...
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Standard deviation on result of calculation

I'm calculating a value based on experimental data. The calculation is $$ k = \frac{a - b}{c} \cdot \frac{1}{T}, $$ and $a$, $b$ and $c$ are all measured experimentally, multiple times, with some ...
Tor's user avatar
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Calculating the value of Cox-Snell Rsquared

I want to calculate the minimum sample size for a prospective longitudinal study (using cox regression - the aim of the project is prediction). The following function pmsampsize from the pmsampsize ...
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Sample size for Survival Analysis (Cox regression) with discrete time

I have a study where the patients come to the hospital every two months for check-ups. T0 ( one week before surgery), T1 (two months after surgery), T2 (4 months after surgery) up to T9 (18 months ...
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Sample size for REPEATED MEASURES ANOVA

I am calculating a required sample size for the Repeated Measures ANOVA (within subject). I came across two different packages and the results are different. Using "WebPower" package and the ...
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Sample size for survey

My interest is to perform a statistically significant survey on a population of 1700 people, that can be described in different categories, so each person belongs to only one category. I have two ...
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Random sample and its underlying sample space [duplicate]

A random sample of size $n$ is a random vector $X=(X_1, ..., X_n)$, where all $X_i$ are i.i.d., and are measurable functions on some sample space $\Omega$. Let's say, $\Omega = \{H,T\}$, i.e., heads ...
jose89's user avatar
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Calculating sample size for comparing pretest and post-test scores

I am trying to evaluate a new curriculum. I intend to do it by giving students a test at the beginning of the academic year (pretest) and one at the end of the year (post test). There are roughly 50,...
Poulo's user avatar
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What is the meaning of confidence intervals when NOT using sample data and instead have data on the whole population? [duplicate]

I'm trying to understand why you would need confidence intervals or compute statistical tests (for comparing proportions) when your data is NOT from a sample and you have data on the whole population. ...
Jam.Wil's user avatar
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Robust estimation of standard deviation using relatively small sample taken from a Gaussian distribution

I'm sure this question was asked before, but I don't seem to be able to find a convincing answer. If there is a relatively small set (say 3<n<20) of observations of a quantity that is assumed to ...
Maciej Tomczak's user avatar
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Clarifying between sample date and input data

I'm reading section 2.6.3 from the book "The Elements of Statistical Learning" of "Trevor Hastie", "Robert Tibshirani" and "Jerome Friedman" and I have a few ...
alksdhalksjdb's user avatar
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ARIMA model underestimates

What steps should we take if my ARIMAX model consistently underestimates? Furthermore, should this underestimation be a significant concern in my analysis? Edit: I am doing an ARIMAX forecast where I ...
BarneGeniet's user avatar
6 votes
1 answer
166 views

Terminology clarification about sample moments

According to MathWorld (link): "The sample raw moments are unbiased estimators of the population raw moments". While in Wikipedia (link) it is said: ...the $k$-th raw moment of a population ...
user1420303's user avatar
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Is Federer Formula of sample size in experimentation study (t-1)(n-1) ≥ 15 legit?

I've seen this formula for sample size determination in experimental studies, which was claimed by Walter Federer, is well-known among Indonesian bio researchers. The formula is: $$ (t-1)(n-1) \geq 15$...
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Should chi-squared be used to find a probability for the sample variance? [closed]

"A random sample, of size 9, from a normally distributed population, with variance 9, yielded as sample mean of 7 and a sample variance of 7. I. What is the probability of a random sample of size ...
raffaello.sanzio's user avatar
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When calculating the sample variance, why do we divide by "n-1" and not "n-2" or "n-0.5"? [duplicate]

When calculating the sample variance we divide by $n-1$ instead of $n$ to correct the bias that results in from using the sample mean instead of the population mean. My question is why do we only ...
Sandra Sukarieh's user avatar
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2 answers
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Meaning of subscript $n$ in sample mean variable

I am reading Wasserman's All of Statistics. In Chapter 13: Linear and Logistic Regression, when deriving the least square estimates for simple linear regression, we have the data $(Y_1, X_1), \dots,(...
Ouroboroski's user avatar
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How to estimate the sample needed to train the binary classification model?

Let's say the population is 100 thousand, the share of the target variable is 1%. I found calculators that, based on the normal distribution, find to confirm a share of 1% and give an estimate of the ...
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Do I have to use the exact same variables in each step, if I have a two-step propensity score match followed by a regression?

I am using the propensity score match to grow my sample based on a smaller dataset of existing units that received the treatment. The match will find more likely units from its large population that ...
LifelongLearner2's user avatar
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How does a Random Sample relate to Random Processes and Random Variables?

What is the difference between a Random Sample, Random Variable (RV) and Random Process (RP)? As far as I know, a RV is a mapping from an experimental space to the real numbers and a RP is a mapping ...
Ahsan Yousaf's user avatar
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Statistical significance of a small sample binary test

I work at a hospital in a coastal area that is prone to flooding. The hospital has a long list of tasks that are performed in the event of an emergency, and a large (over 1,000) set of organizational ...
jerH's user avatar
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Multivariate sample covariance

I have a set of $X_1,...,X_n$ samples with covariance $\Sigma_1,...,\Sigma_n$. The multivariate sample mean is then $$ \left(\sum_{i=1}^n \Sigma_i^{-1} \right)^{-1} \left(\sum_{i=1}^n \Sigma_i^{-1} ...
ThibautOphelia's user avatar
7 votes
4 answers
870 views

Sample notation: When to use capital $N$ vs lowercase $n$?

In statistics and psychological research, what is denoted by capital $N$ vs lowercase $n$? I work in psychological research and I've seen them used in two ways: Capital $N$ represents the entirety of ...
Cameron's user avatar
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Sample Size Calculation-Theory

thanks for all the knowledge, have learned a lot. I am preparing for the sample size calculation block in my master program and I have a question regarding the theory of it all. As a medical doctor I ...
isagonas's user avatar
3 votes
1 answer
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Expected value of ith sample versus expected value of a random variable

Consider a random variable $X$. When we talk about the expected value of the random variable $X$, we use the notation $\mathbb{E}\left(X\right)$. However, I found that, in introductory statistics ...
MinChul Park's user avatar
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Using sample at lower hierarchical level (products) to draw inferences about a higher hierarchical level (companies)

I have a conceptual question about whether we can use a random sample of products to draw inferences about companies. More generally, I think this would extend to sampling hierarchical data, where we ...
jdcrossval's user avatar
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50 views

The point estimate and the large sample size [closed]

My colleagues and I argued about the point estimate's accuracy. They said that "The point estimate will tend to be accurate if the sample size exceeds 30." While I am saying no, "The ...
Dr. Statistics's user avatar
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Confusion forming prior beliefs

Let's say, for the sake of ease, I have a sample of data that I believe comes from the binomial distribution. Let's say I have 100 observations in my sample. Previous to this experiment, I have ...
Ewan McGregor's user avatar
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Why are Random Variables used instead of Sample Spaces? [duplicate]

Background This is related to the following question: Is an experiment's Sample Space always useful? I have been reading about Sample Spaces, and I understand they represent all possible outcomes ...
Connor's user avatar
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Is an experiment's Sample Space always useful?

Background I'm working through the Harvard Stat 110 probability course. One of the first topics discussed is the sample space of an experiment. I understand that the sample space represents all the ...
Connor's user avatar
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1 answer
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Normality assumption n=48 [closed]

Regarding normality assumptions for model evaluation I have been told by my supervisor that it is not needed in the case of analyzing but is needed in forecasting only. i am looking for an explanation....
Am Ahmed's user avatar
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1 answer
116 views

How to find the correct sample size for a non parametric hypotheis test

I have two independent population data with each having 500 K rows. The goal is to perform a hypothesis test and test the claim that the new machine takes less time than the old machine. This 500 K ...
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Sample size calculator for Ordinal Data

For my experiment, I am comparing the results of melanoma grades( ordinal data, such as Stage 1, 2, 3, 4) as obtained from my proposed noninvasive imaging modality to that obtained from the gold ...
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2 votes
0 answers
120 views

Variance of Fourth Sample Central Moment [closed]

I am trying to derive a formula for the variance of the fourth sample central moment $m_4=\frac{1}{n}\sum_{i=1}^n (X_i-\bar{X})^4$ (where $X_i$ is the $i$th realization of a random variable, $\bar{X}$ ...
Hiro's user avatar
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Range of Subset of Population based on a Sample

Suppose I have a population with a known mean, range, and variance of a characteristic $v$. I am producing sets from this population that are of negligible size compared to the size of the population. ...
Mark McDermott's user avatar
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Lower bounding weighted sample variance

Let us assume that we draw a sample $\{X_i\}_{i=1}^N$ from a random variable $X$ and we have a discrete probability distribution $q_{ij}$, i.e. $0 \leq q_{ij}\leq 1$ and $\sum_{ij} q_{ij} =1$ (the $...
raskolnikov's user avatar
2 votes
2 answers
76 views

Is the average of N linear regression coefficients equivalent to the regression coefficients for the entire dataset?

There have been some questions that are a bit similar to this one. However, I do not feel like the answers given truly answer the following question. Suppose I have a large dataset of $nN$ points. I ...
hhh3's user avatar
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1 vote
1 answer
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Large sample distributions

Suppose we have observations $x_1, x_2, \ldots, x_n$ where $n$ is very large. Now we standardize the observations as $$y_i=\frac{x_i-\bar{x}}{\frac{s}{\sqrt{n}}},$$ where $s=\frac{\sum\limits_{i=1}^n(...
user671269's user avatar
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0 answers
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Sample Size Question - Population- Multiple Regression?

I am doing a research project for class. Our research questions are as follows: Has news exposure impacted parental decision-making in preparation for the new school year? Has Media exposure to ...
Alyssa Leeanne's user avatar
1 vote
1 answer
32 views

What are the individual elements within the outcome of a sample space called?

What is each entry in an outcome of a sample space called? For example, say our outcome is ${HHT}$, describing two heads and one tail. What is each head ($H$) and tail ($T$) member of the outcome ...
Estimate the estimators's user avatar
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79 views

Closed form formula for distance of multinomial sample from underlying distribution

Suppose that I have a probability vector $p$ e.g. of size 10, and that I draw a multinomial sample of size $n$ from $p$. Does there exist a closed form formula to compute the expected total variation ...
Caldym's user avatar
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1 vote
1 answer
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How can we use average total time if a job to determine time of components?

Imagine a scenario where there are tasks (called jobs) made of many smaller tasks (called assemblies). Each assembly has an average time to completion, and the job time to completion is a sum of the ...
Jackson Dunn's user avatar
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How to test that a sample of a discrete random variable is representative?

I am given a discrete random variable and several large samples from it. The methods how the samples are obtained are not truly random samples but are reasonable approximations to a random sample. An ...
quarague's user avatar
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4 votes
1 answer
140 views

Do I need a hypothesis test to compare two populations of complete annual count data?

I would like to compare the total number of public M&A transactions observed in two separate years (e.g. 2021 vs 2022). Given the data set for each year is complete (i.e. a population), can I ...
Kerry's user avatar
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3 votes
1 answer
341 views

Question about Analogy to Statistics

If anyone could help me verify if my analogy is correct, thanks so much! Here is an analogy: A population is like a pot of soup. We stir the pot of soup with the ladle because naturally the contents ...
YamotoLight's user avatar
1 vote
0 answers
44 views

Bayesian inference on model parameters from summary statistics alone

Consider quantities $y_1,y_2,\dots,y_p$, for the $j$th of which we have $n_j$ measurements $y_{1j},y_{2j},\dots,y_{n_jj}$. Unfortunately, I do not have access to the raw data $y_{ij}$ -- only to the ...
SoupyTwist's user avatar
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58 views

What is the distribution of the sample (empirical) KL divergence and can we use bootstrapping to approximate it?

Let $p, q$ be two distributions, and suppose one can evaluate them pointwise. Let $\{x_i \}_{i = 1}^n$ be an IID sample from $p$, and let $KL_n = \frac{1}{n}\sum_i \log\left[ \frac{p(x_i)}{q(x_i)} \...
travelingbones's user avatar
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Bridging the gap from theory to implementation in "Conditional Distance Correlation" by Wang et al. 2015?

In an attempt to implement a form of conditional distance correlation for random variables represented as vectors of observations, I came upon this paper that nicely extends the notion of distance ...
QMath's user avatar
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2 votes
0 answers
81 views

How to prove that if the bootstrapped sample means are approximately normal, then the sample mean is approximately normal?

I'm considering the scenario described in this question, namely: we have IID $X_i, i = 1, ..., n$ sampled from a population with mean $\mu$, variance $\sigma^2$ unknown the goal is to put a ...
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