37 questions linked to/from Debunking wrong CLT statement
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### Given the Central Limit Theorem, can sampling ever tell us whether or not the underlying distribution is normal or not? [duplicate]

According to CLT, randomly selecting values from a distribution will result in a convergence towards a normal distribution. Does this mean that we can never figure out whether or not the underlying ...
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### Central Limit Theorem and Normal Distribution Approximation [duplicate]

The central limit theorem states that: for identically distributed independent samples, the standardized sample mean tends towards the standard normal distribution even if the original variables ...
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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 ...
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### What intuitive explanation is there for the central limit theorem?

In several different contexts we invoke the central limit theorem to justify whatever statistical method we want to adopt (e.g., approximate the binomial distribution by a normal distribution). I ...
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### What are the myths associated with linear regression, data transformations?

I have been encountering many assumptions associated with linear regression (especially ordinary least squares regression) which are untrue or unnecessary. For example: independent variables must ...
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### Is Central Limit Theorem about multiple samples or just one?

I've studied CLT and my understanding is that multiple samples will generate a normal distribution centered in the mean of the population. However, today, one post in Linkedin was saying that "...
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### How is CLT related to the condition of data (normality assumption)?

I apply statistical methods in sociological researches and now I feel a bit confused as I found out more about CLT. For instance, if I have sample of 1000 observations, do I even need to check it for ...
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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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### Central Limit Theorem - Rule of thumb for repeated sampling

My question was inspired by this post which concerns some of the myths and misunderstandings surrounding the Central Limit Theorem. I was asked a question by a colleague once and I couldn't offer an ...
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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 $[0, \infty)$ that is retrospectively selected on individuals. ...
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### Central limit theorem and strong law of large numbers

I had a question in my mind , if a i.i.d distribution function follows central limit theorem , does that mean it will follow Strong law of large numbers also ?? Since in both cases sample means tends ...
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### What is the reasoning behind expecting residuals in OLS regression to be normally distributed?

There are a lot of similar questions here but I have not found an answer to this specific question. Source: for example in https://peopleanalytics-regression-book.org/linear-reg-ols.html#norm-dist-...
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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? [duplicate]

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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