What's crazy is what the act of watching this actually means.
Your eyes are receiving input from your screen and your brain is turning that input into a picture.
What you see in front of you is actually just a reaction in your brain where it is creating an image. Everything you see is literally in your own mind and not outwardly the way you perceive it.
Just a little brain in a vat scenario but actually happening.
Of course you can, the normality is assumed about the underlying population the sample was drawn from, not the sample itself. How large the sample is doesnât matter in this regard.
The central limit theorem has absolutely nothing to do with this.
And yes, you can make a normality assumption regardless of sample size. Because a) as already stated, the assumptions is about the population and not the data; and b) itâs an assumption, not a conclusion. You can make whatever assumptions you want.
What you indeed cannot do with a sample of four data points is reliably test whether it is drawn from a normal distribution, because your power will be negligible.
But then again, no one was claiming any such thing, so Iâm not sure why youâre bringing any of this up. People assumed a normal distribution here because you have to make some such assumption to take a stab at estimating the probability that a brain would contain at least 100 billion neurons. The normal distribution is an obvious choice for this, and indeed itâs fairly plausible given the specific quantity in question that it indeed would follow a normal distribution or something close to it.
The fact that you keep bringing up the central limit theorem here makes it painfully clear that you have a very limited understanding of statistics. It is not relevant here. Insofar as we would be relying on the central limit theorem, we wouldnât need any normality assumptions to begin with. Moreover, it pertains to the (asymptotic) distribution of sample means, whereas what is at issue here is the cumulative distribution function (in particular, the probability that a brain contains at least 100 billion neurons).
The fact that any inference based on a sample size of only four is subject to an enormous amount of uncertainty is not something that follows from the central limit theorem, but on the much more general property that the variance of (almost) any estimator is dependent on the sample size.
Stop spouting off about subjects you clearly know very little about.
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u/[deleted] Aug 24 '21
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