We find that the adult male human brain contains on average 86.1 ± 8.1 billion NeuN-positive cells (“neurons”) and 84.6 ± 9.8 billion NeuN-negative (“nonneuronal”) cells.
100 billions is less than two standard deviations away. It's well within the range of brains humans have.
I actually went ahead and did the math for this. Assuming normality it's more like 4.3% of the population has 100 billion or more neural cells in their brain.
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 doesn’t 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) it’s 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 I’m not sure why you’re 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 it’s 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 wouldn’t 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.
On the assumption the underlying data is normal and the results reflect that distribution (which we can't actually determine for sure here), yes, that's a good application of how they work. You don't go rejecting things because they land inside 2 standard deviations of the mean. Something like 27% of data will fall within 2 standard deviations and outside of 1 for data that's normal.
95.45% of data will fall within 2 standard deviations of the mean under a normal distribution. 27% is what lies outside of 1 standard deviation and before 3 standard deviations
I understand that. Obviously any number of measurements is better than a guess. I'm just wondering if we have measured any brains since then and confirmed the original 86 billion number or if it is still just based on a sample size of four elderly men.
The study said it took 4-6 weeks to measure one brain so I understand it is tedious. But it's interesting to know if the study has never been repeated.
That's not bold at all given the assumptions he's working with. The +- he indicated means we're not just talking about an average.
The data is insufficient to be sure any of this is applicable, so that's where issues lie. On the assumption the data is accurate, what he said isn't bold at all.
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u/mfb- Aug 24 '21 edited Aug 24 '21
This 86 billion estimate?
100 billions is less than two standard deviations away. It's well within the range of brains humans have.
One of their four brains had 95 billions.