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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Sampling bias using addresses as frame

A selected address in the sample has no residents. Will this cause bias in the results of a survey where house addresses are used as the frame? I think it wouldn't, because an address with no ...
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12 views

How to test statistical significance to prove that a particular technique estimates a variable better than another technique?

Suppose the following is the scenario: I am estimating the measure of a construct. I have Subject Matter Experts (SME) who have manually (through observation) estimated the measures. Suppose I have ...
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6 views

3-arm RCT with black vs white comparisons

I am trying to design a 3-arm randomized controlled trial - intervention A for group 1, intervention A+ B for group 2 and control group for group 3. I would also like to look for black vs white impact ...
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28 views

Sampling rate and regression

I am interested in developing a regression model. The data (about 1000 observations) that I have are not really random (i.e., spatially, the closest ones are correlated to some degree), so I drew a ...
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1answer
28 views

Check population randomness in an A/B test?

I am fairly new to A/B testing and I don't really understand some points that my colleagues make. On our website users are randomly assigned to A or B when their session start (by randomly assigned, ...
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2answers
60 views

Sample mean and variance independence in the case of correlated observations

Are the sample mean and sample variance of correlated normal observations independent? The classic theory relies on the independence of observations, but this is not the case. So as an example I ...
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34 views

Understanding Chebyshev rule

http://www.stt.msu.edu/users/makagon/2.5-7.pdf For any data set, the proportion (or percentage) of values that fall within $k$ standard deviations from mean (that is, in the interval $\bar{x} - ...
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35 views

SD probability problem involving chi-square distribution

Preparing for an exam in statistics, I have been pondering the following problem: Given that in country X 14 % of people hold a university degree, find the probability that for random sample of size ...
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2answers
27 views

Is a pairwise Cox regression approach valid for small samples?

Firstly, some background on the dataset: I am performing survival analysis on a 28-event dataset. We found a genetic marker that predicts survival on a drug. Examining the data, the proportional ...
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12 views

How to calculate the standard deviation for distribution estimates in classification problems?

Suppose I have a sample of 1000 measurements that are classified as A or B. A : 640 B : 360 Hence, the estimator for the percentage in the underlying population ...
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38 views

Bayesian A/B testing - Sample Size

I've been reading up on Bayesian A/B testing - in particular, the Math behind VWO's Smart Stats. I understand that the way they compute and decide which test is better is by comparing the threshold of ...
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10 views

How to undersample in percentage terms majority class using knime?

I'd like to undersample the majority class and then use SMOTE to improve accuracy (or maybe recall with cost to precision?). Do you know how to do that with KNIME?
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20 views

Pooling data from n groups with different means and variances; finding the standard deviation

I want to pool data from different samples, each with a different mean, standard deviation and n. I don't have the original data, only these three parameters.I'm sure they can be pooled because they ...
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1answer
13 views

Understanding sample and population (real life scenario)

A real life case: a firm desing, produces and sells 52 vehicles. I collect failure data of the components of the vehicles. after a time, -for example- for the oil filter I have 52 data. Some of them ...
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1answer
218 views

Consequences of exceeding sample size after determination of sample in power analysis

Challenge In our office, I have been involved in a discussion about sample size and its influence on effect size - can you help me out and explain further? Base When conducting a power analysis, ...
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28 views

How can I estimate the approximation quality of the odds ratio based on a sample or how can I ignore infrequent items?

I am analyzing URLs found in tweets of the Twitter stream. I have two samples of tweets from that stream: a random sample of tweets all tweets of a subset of users I want to find URLs which are ...
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1answer
49 views

How should I estimate the variance using a sample (not knowing the mean)?

The unadjusted sample variance is biased, yet it has a smaller mean squared error. Also, if we assume the sample comes from a normal distribution, the maximum likelihood estimator for the variance is ...
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22 views

comparing ranks for a multinomial distribution between sample and population

I have a known multinomial distribution of a population due to a census. I want to compare a sample with this population. I want to know the probability that the same ranking of the classes of the ...
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13 views

Graphing statistical significance in R for an A/B test

I've never graphed anything in R relating to statistical significance. These are the results of an A/B test. Here are the specs: Sample 1 (Successes/Trials): 20/1224 = 0.91% Confidence Interval ...
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1answer
139 views

Exercise on Chebyshev inequality compared to the Central Limit Theorem

Problem Take this (easy) problem as an example: An astronomer is interested in measuring the distance, in light-years, from his observatory to a distant star. Although the astronomer has a measuring ...
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1answer
20 views

Computing the expected value for a sample

Assume that we have a dataset $D$ having $N$ instances: $X_1,\cdots,X_N$. We select $n$ items $(Y_1,\cdots,Y_n)$ using sampling without replacement. We use $\bar{Y}$ as an estimate for $\bar{X}$, and ...
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1answer
22 views

Why standard normal samples multiplied by sd are samples from a normal dist with that sd

This answer notes that if a programming language/libraries provide a procedure that returns random samples from a standard normal distribution, we can generate samples from another normal distribution ...
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1answer
33 views

Confused about the sample size in large sample confidential interval and population proportion intertal

My professor said when sample size is large, it will has the following formula, but how big is the sample can be considered to be a large sample and use the following formula? I did some questions ...
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26 views

Chi-squared and sample variance

Each member of a random sample of 20 business economists was asked to predict the rate of inflation for the coming year. Assume that the predictions for the whole population of business economists ...
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1answer
29 views

Population vs sample

When we think of linear regression, the implicit assumption is that we only observe a small fraction of a possibly infinite large population. Thinking of simple averages, imagine a fair die. The ...
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1answer
30 views

Sample Error vs. True Error

I'm reading Mitchell's Machine Learning and am on Chapter 5, evaluating hypotheses. In it, he defines sample error and true error: The sample error, denoted $error_s(h)$ of hypothesis h with respect ...
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1answer
45 views

Sampling and design problem

Suppose there are quite many (hundreds/thousands) variables, $X_1$,...,$X_m$, in a computer model, following some multivariate distribution. How can we get a sample of these variables that has good ...
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11 views

Effect of sample size on generalizing to a broader population

What effect will sample size have on your ability to infer your sample findings to a broader population?
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1answer
42 views

Gaussian distribution sample norm versus mean norm

Consider a Gaussian distribution with mean $\boldsymbol\mu$ and covariance matrix $\mathbf{Q}$, and suppose I take a sample from this distribution and compare its norm with the mean norm. My goal is ...
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1answer
33 views

What can be inferred from Simple Random Sampling?

Suppose I have access to a population data set. I then perform Simple Random Sampling on this data set to pull a sample. I perform some tests to see if the population data set and the sample data set ...
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1answer
15 views

Sample size for entire population to determine sub population?

Let's say a bus company has 500 markets with an average of 10000 passengers each day but some markets as large as 100000 and some as small as 300. How would I determine the simple random sample size ...
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14 views

Minimum Sample Size for A/B Test with Subgroups

I'm conducting an A/B test for my new website. I have reviewed some A/B and polling sample size calculators but they don't seem to account for measuring based on metrics other than conversation rate. ...
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19 views

Approximation variance of sample correlation, for independent gaussian variables

I would like to have method to approximate the variance of the sample correlation estimator $$r = r_{xy} =\frac{\sum ^n _{i=1}(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum ^n _{i=1}(x_i - \bar{x})^2} ...
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1answer
29 views

Probability question about sample proportion

This question goes, "According to a study, 4% of a population in a region have lung disease. Of those people without lung disease, 13% are smokers. Of those people with lung disease, 92% are ...
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32 views

Non-response in organization survey

I am a research analyst and recently conducted an employee satisfaction survey at the organization I work for. Ideally, I should have received completed questionnaires from all 380 employees (making ...
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1answer
44 views

Simulate mixture of betas

Suppose that we have $X_1, ..., X_n$ iid such that $X_i| \theta \sim Ber(\theta)$ and $\theta \sim g(\theta)$ such that $$g(\theta) = 0.6 Beta(2,1) + 0.4 Beta(1,1) = 1.2 \theta + 0.4$$ Doing the ...
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32 views

Linear regression with sample duplicated

In a linear regression, how will the statistics (beta, r-squared, t-stat, etc) change if I duplicate my sample?
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1answer
20 views

Expected sample proportion given known population proportion?

Taking all accounts on a website, 66% of users have uploaded a photo. I sample 21 users, what can I expect to find in the sample? I'm looking for an answer like "usually, between 10 and 18 users (in ...
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14 views

Narrow distribution and Hasting-Metropolis

I would like to sample from a density $\tilde{\pi}=C(\pi)\pi$ whose support is $[0,1]$. The normalization constant $C(\pi)$ of the function $\pi$ is unknown and $\pi$ is very narrow. To see how narrow ...
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58 views

Two-sample Kolmogorov-Smirnov test with errors on data points

Short version I want to test if two samples, which follow a skewed distribution, can be distinguished from each other. A Kolmogorov-Smirnov statistic for two samples would be sufficient if there was ...
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16 views

about degree of precision and how to select randomly a sample by using minitab or spss

I have a data set which contains dependent variable Y,and independent variable X. and Population size is N = 270 I want to choose sample from this data set with simple random sampling. What should I ...
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64 views

Why is multicollinearity a sample phenomenon?

We say that multicollinearity is a sample phenomenon. That means we postulate the PRF such that each independent variable is bound to have an independent effect on the dependent variable but due to ...
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26 views

What is it? sampling variance OR sampling variance of the mean

I got confused about some terms! I have group of studies that measure a parameter X in certain group of subjects. Each study used certain number of subjects N and ...
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38 views

Ratio estimator in sampling

Let the population $U=(1,2,3)$. We want to estimate $R=\frac{\mu_y}{\mu_x}$.Consider the estimators $$\hat{R_1}=\frac{\overline{y}}{\overline{x}},\hat{R_2}=\frac{\overline{y}}{\mu_x}$$ where ...
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1answer
22 views

Is this considered a random/probability sample?

a company that conducts face to face surveys have described their sampling procedure as follows: We use a unique and rigorous sampling method - a form of random location sampling, using a ...
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23 views

On fitting a Poisson distribution to make sense of data

Hi guys I am working with a regular network which has the shape of a square grid and contains 100x100=10000 nodes. The edges (links) between these nodes simply ...
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22 views

Comparing variances across multiple samples in two groups

I have a data set looking at the mass of cells over time. There are two conditions, one of which is a "control" condition. In both conditions, I have measure the mass of about 40 cells, over 180 ...
3
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2answers
56 views

Estimate of population total

I am going through the book Sampling Techniques by Cochran. I'm requesting for assistance with the following question: A simple random sample of 30 households was drawn from a city area containing ...
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3answers
98 views

Sample size in a population of 300

I have to conduct a survey in the discipline of International relations. I have a list of 300 diplomats to interview for close ended, open ended questionnaire. I want to select randomly every fifth ...
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If y=f(x̄), in which x̄ is the mean of xi, how can I calculate the minimum number of x samples to obtain y with 95% confidence and 10% error? [duplicate]

I am able to calculate the minimum number of samples of x based on the standard deviation of x and the assumption of normal distribution using the standard equation. However, I need to know what that ...