Linked Questions

62
votes
32answers
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 ...
183
votes
8answers
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 ...
12
votes
2answers
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 ...
3
votes
2answers
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 ...
6
votes
2answers
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 ...
3
votes
1answer
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 ...
2
votes
3answers
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 ...
3
votes
1answer
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 ...
3
votes
1answer
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 ...
0
votes
2answers
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 ...
1
vote
2answers
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 ...
2
votes
2answers
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 ...
4
votes
2answers
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 ...
3
votes
1answer
56 views

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 ...
1
vote
0answers
69 views

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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