18 questions linked to/from Debunking wrong CLT statement
3k views

### 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 ...
40k views

### 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 ...
902 views

### 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 ...
686 views

### 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 ...
294 views

### 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 ...
1k views

### 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 ...
138 views

### Is there such a thing as having too large a sample when it comes to trying to estimate the population distribution?

The relevant statement is as follows: "the larger the sample size, the more the sample mean reaches that of a normal distribution EVEN if the population distribution is inherently skewed/biased. In ...
164 views

### How can the CLT fix OLS regression residuals that are not normally distributed?

I often hear that when the residuals depart from normality, the central limit theorem can be used to fix things. I do not quite understand how this works, since the central limit theorem is a ...
342 views

### 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 ...
300 views

### 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 ...
152 views

### 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 ...
242 views

### 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 ...
86 views

### 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 ...