Statisticians like me say CORRELATION ISN'T CAUSATION but that's not the whole story.
There are at least FOUR different scenarios!
A thread. 🧵
1. CORRELATED BY CHANCE. There's always a possibility that variables will correlate by chance. If you have a lot of data, you're almost certain to get a few high correlations. You will know you're in this situation if the same variables are much less correlated in new data.
2. CORRELATED DUE TO STRUCTURE. Clocks are correlated with each other but there's nothing about Clock A that can be changed in order to cause a change in Clock B or vice versa. There is no third thing you can change that will cause both clocks to change. There is no causation.
You might be tempted to say that the clocks have the common cause of being created by humans. Imagine two random stars that have a cyclical change in brightness every 24 hours. They will be correlated as well. It's not about who created them. It's about their similar structure.
3. MURKY CAUSATION. In the simplest case, if A and B are correlated and there is some causation then this could mean that A causes B, B causes A or some third thing C causes both A and B. In the most complex case, there could be complicated feedback loops between A and B.
In these cases, when we say "correlation isn't causation", what we mean is that we can't identify exactly what kind of causation there is but there is some.
4. EVEN MURKIER CAUSATION. A and B might not be related at all in the real world but something about your data collection may have caused data about A to be related to data about B. Technically, you could say you or your data collection are the cause of the correlation.
However, in the context of the original variables themselves and the real world, A is not causally related to B.
Hope this was educational! 🧵
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If you think about how statistics works it’s extremely obvious why a model built on purely statistical patterns would “hallucinate”. Explanation in next tweet.
Very simply, statistics is about taking two points you know exist and drawing a line between them, basically completing patterns.
Sometimes that middle point is something that exists in the physical world, sometimes it’s something that could potentially exist, but doesn’t.
Imagine an algorithm that could predict what a couple’s kids might look like. How’s the algorithm supposed to know if one of those kids it predicted actually exists or not?
The child’s existence has no logical relationship to the genomics data the algorithm has available.
These grants aren't charity. They're highly competitive contracts where the US government determines Harvard is the best institution for conducting specific research, and then pays Harvard for services rendered to US taxpayers.
Each grant represents a fair contract that a group at Harvard won after being in competition with hundreds or even thousands of other groups. These are not handouts.
The US government pays Harvard and other universities to provide answers to questions that aren't directly profitable in themselves, but which provide a foundation for private sector innovation, and help maintain American dominance over geopolitical rivals like China.
As a someone who translates ideas into math for a living, I noticed something weird about the tariff formula that I haven't seen anybody else talk about. 🧵
The formula defines the tariff rate as exactly the percent you need to charge on imports to make up for the trade deficit. Basically,
trade deficit = tariff rate x imports
It's constructed as if tariffs are a kind of compensation for trade deficits but this raises a question.
If tariffs are something foreign countries owe to the American people for having a trade deficit, then forcing US businesses to make up for the difference, by paying extra money to the US government, is kind of a weird solution.
Whenever I see students with good grades but lots of college rejections, my first thought is a bad personal essay. As predicted, this guy's essay was kind of a disaster.
Since I did get into Harvard, I'll give my two cents on the essay:
In honor of international women's day, let's take a moment to remember the most famous statistician in history.
You've definitely heard of her, but you probably have no idea she was a statistician.
It's Florence Nightingale.
Nightingale was first female member of the Royal Statistical Society and a pioneer in using statistical analysis to guide medical decisions and public health policy.
Florence Nightingale's most famous statistical analysis was her investigation into the mortality rates of soldiers during the Crimean War. She demonstrated that the majority of deaths among soldiers were due to preventable diseases rather than battlefield injuries!
Took one for the team and made a histogram of the Elon social security data. Not sure why his data scientists are just giving him raw tables like that.
It’s also weird that they keep tweeting out these extremely strong claims without taking a few days to do some basic follow up work.
It doesn’t come off like they even:
- plotted the data
- talked to any of the data collectors
- considered any alternative explanations