I keep seeing this when studying economics but it feels like it cant be true
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The idea that a few situations will have an extreme high or low result, but most results will fall within a more typical range with high and low ends in that range, is pretty ubiquitous. We see it in nature, in social structures, in systems of all types in the world. A few people have no money, a few people have tons of money, most people have somewhere in between. A few people are really tall, a few people are really short, most people fall somewhere in between. A few people get straight A’s, a few people get straight F’s, most people fall somewhere in between. A few people eat no hamburgers, a few people eat lots of hamburgers, most people fall somewhere in between. A few people drive real real slow, a few people drive super fast, most people drive somewhere in between.
This is the idea of a normal distribution. It’s not necessarily the only model out there.
I hope this helps.
The idea that a few situations will have an extreme high or low result, but most results will fall within a more typical range with high and low ends in that range, is pretty ubiquitous. We see it in nature, in social structures, in systems of all types in the world. A few people have no money, a few people have tons of money, most people have somewhere in between. A few people are really tall, a few people are really short, most people fall somewhere in between. A few people get straight A’s, a few people get straight F’s, most people fall somewhere in between. A few people eat no hamburgers, a few people eat lots of hamburgers, most people fall somewhere in between. A few people drive real real slow, a few people drive super fast, most people drive somewhere in between.
This is the idea of a normal distribution. It’s not necessarily the only model out there.
I hope this helps.
It’s usually not a good idea to *assume* a normal distribution. When you hear someone say “this statistical method assumes the data is normally distributed”, what they actually mean is that the statistical method is only valid and reliable when used on normally distributed data.
so “assume” basically means “We’re assuming you’re not dumb enough to use this method on non-normal data”
So when you use those kinds of statistical methods, you should always start by determining if your data is normally distributed, or not. That way you aren’t *assuming* that it’s normally distributed.
Sometimes it’s a practical thing, if you don’t know the underlying distribution, Normal shows up often enough to be a good first guess.
BUT, there’s also the Central Limit Theorem.
If you have multiple sample sets, the distribution of the mean of the sample sets becomes normal!
In other words, if you study a distribution of distributions it becomes normal.
For example, individual income is likely not normal, but rather lognormal.
You might do a meta-analysis of 200 studies where each study looks at 1000 individually sampled people. The meta-analysis of averaged 1000 sampled incomes WILL be normally distributed.
It’s usually not a good idea to *assume* a normal distribution. When you hear someone say “this statistical method assumes the data is normally distributed”, what they actually mean is that the statistical method is only valid and reliable when used on normally distributed data.
so “assume” basically means “We’re assuming you’re not dumb enough to use this method on non-normal data”
So when you use those kinds of statistical methods, you should always start by determining if your data is normally distributed, or not. That way you aren’t *assuming* that it’s normally distributed.
Sometimes it’s a practical thing, if you don’t know the underlying distribution, Normal shows up often enough to be a good first guess.
BUT, there’s also the Central Limit Theorem.
If you have multiple sample sets, the distribution of the mean of the sample sets becomes normal!
In other words, if you study a distribution of distributions it becomes normal.
For example, individual income is likely not normal, but rather lognormal.
You might do a meta-analysis of 200 studies where each study looks at 1000 individually sampled people. The meta-analysis of averaged 1000 sampled incomes WILL be normally distributed.
The normal distribution is one common way that natural data can shake out, and one that CAN be a fair assumption IF AND ONLY IF you don’t have reason to believe it will be otherwise. Consider some alternatives:
* How is height distributed? Well, for adult males it’s normal, and for adult females it’s normal, but for all adults it’s bimodal (two-humped) because the average man is taller than the average woman. Add in children and you’ll have a skewed distribution.
* How is wealth distributed? Some nations will have a strong concentration of wealth in the hands of a few, showing strong skewing. Others will have a more even distribution. Regardless, there’s no guarantee that the middle class will be large enough to ensure a nice symmetric normal distribution, or that there will be as many rich people as poor people. Of course, unless we count debt as negative wealth, you can’t have less than zero dollars, but you can have as many billions as you can make, so it will also have a long tail.
The normal distribution is one common way that natural data can shake out, and one that CAN be a fair assumption IF AND ONLY IF you don’t have reason to believe it will be otherwise. Consider some alternatives:
* How is height distributed? Well, for adult males it’s normal, and for adult females it’s normal, but for all adults it’s bimodal (two-humped) because the average man is taller than the average woman. Add in children and you’ll have a skewed distribution.
* How is wealth distributed? Some nations will have a strong concentration of wealth in the hands of a few, showing strong skewing. Others will have a more even distribution. Regardless, there’s no guarantee that the middle class will be large enough to ensure a nice symmetric normal distribution, or that there will be as many rich people as poor people. Of course, unless we count debt as negative wealth, you can’t have less than zero dollars, but you can have as many billions as you can make, so it will also have a long tail.
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