16 questions linked to/from Debunking wrong CLT statement
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### Non-normal data, non-parametric tests for normality, and determination of statistical parameters

I have a database with more than 50000 observations. For the determination of normality by means of statistical contrasts, since the Shapiro-Wilk test cannot be used due to the large number of ...
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### Non-normal data, non-parametric tests for normality, and determination of statistical parameters

I have a database with more than 50000 observations. I have applied non-parametric tests to determine the normality of the data but in any case p<0.05, rejecting the null hypothesis of normality (...
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### paired data large samples

When comparing the means of matched data and large samples are taken, the differences must be Normally distributed in the population. True/False The answer that was given in class was that it was ...
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### Does a Binomial converge to Poisson or Normal?

I have read the answer here. Here the distinction is that If $n\to\infty$ and $p\to0$ while $np$ approaches some positive number $\lambda,$ then the binomial distribution approaches a Poisson ...
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### Central Limit Theorem: Sample Size or Number of Samples?

The central limit theorem states that if we take a take a large enough sum of random variables, the sum will approach a normal distribution. I am confused about why we focus only on the sample size ...
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### Why a sample of skewed normal distribution is not normal?

I was under the impression that if I randomly sample from a skewed normal distribution, the distribution of my sample would be normal based on central limit theorem, but the graph clearly shows that ...
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### why do we need the other continuous distributions if everything is just converging to normal distributions

today my teacher asked why do we need the other continuous distributions if everything is just converging to normal distributions when n is greater or equal to 30. I may partly understand the question ...
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### What statistical test to use for ordinal independent variable

I think this is a rather basic question, but it has been a rabbit hole for the last couple hours and I still haven't found an obvious answer. I'm trying to perform a statistical analysis for an ...
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### Central Limit Theorem and Skewed Distribution

I'm looking for a simple answer to this question relating the central limit theorem and Gaussian and skewed distributions, if one exists. I used the binomial function to generate calculations of the ...
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### What are the assumptions for the Empirical Rule(69, 95, and 99.7)?

I am a little confused about what assumptions are needed to meet the Empirical Rule in statistics. Does the population need to follow the normal distribution or the sample need to follow the normal ...
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### Can we ALWAYS assume normal distribution if n >30?

I'm in a debate with a coworker and I'm starting to wonder if I'm wrong but the internet is confusing me more. We have continuous data [0,infinity) that is retrospectively selected on individuals. The ...
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### Central limit theorem - num random variables vs. sample size?

Does the Central Limit Theorem require the number of random variables to increase to a sufficiently large number or the number of samples of each random variable to increase to a sufficiently large ...
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### What are the worst (commonly adopted) ideas/principles in statistics?

In my statistical teaching, I encounter some stubborn ideas/principles relating to statistics that have become popularised, yet seem to me to be misleading, or in some cases utterly without merit. I ...