It’s informative about what what’s causing death at the moment of death.
But, what I’d really like to see is a chart of how many days of premature death each disease causes.
For example, tuberculosis took people of all ages a century ago. But the critical thing is that tuberculosis prevented people from getting cancer: cancer is a disease of the old, and you have to get through all the others to have a chance at it. Not recognizing that is a form of innumeracy.
Here’s a site that plots spurious correlations* between variables. The description indicates that these correlations are found by a data mining program rather than a person.
The above is a true spurious correlation: even though the data is measured across time, it’s hard to see that time is intimately involved in the data generation. Per capita cheese consumption is just not something I can see trending off to infinity.
I do wish there was a section that isolated spurious correlations between trending times series though. In this one, we could reasonably expect both variables to go to infinity if given enough time.
For my part, I think pairs like the second one are more critical to recognize, because there isn’t a sense in which this is ever going to go away if we get more data. In contrast, the correlation in the upper plot will probably go away if we keep plotting it year after year, as eventually per capita cheese consumption levels off or starts to decline.
* A correlation is spurious if it occurs by chance, and has nothing to do with an identifiable cause and effect.
In statistics, when you test hypotheses, you can make two kinds of mistakes.
But those mistakes are based on your null hypothesis. What’s that? Students and practitioners are often very confused about this. They think the null hypothesis has to have some deep significance to the data they’re looking at. Not so (although it might be useful if it did). What is most important about the null hypothesis is that you can describe how the data is going to behave if it is true. You don’t need to know if the null is true or not to be able to do that, and in fact you may never know if it really is true.
In the images, the null hypothesis is that you’re not pregnant. We never know (before the test, and sometimes even after) whether that’s true or not. But if it were true, the data would behave in a certain way: mustaches might be observed, or maybe presenting a swollen abdomen would not be observed, and a host of other more important details that might show up in urine or blood.
A Type I error is what you get when a true null hypothesis is rejected in favor of the alternative. Again, you never know for sure, but it’s plausible that if you’re null is that someone isn’t pregnant, and they have mustaches, and you conclude that they’re pregnant, you’ve probably made a mistake.
A Type II error is what you get when a false null hypothesis is not rejected. Again, you never know for sure, but it’s plausible that if you’re null is that someone isn’t pregnant, and they present with a swollen abdomen, and you conclude that they’re not pregnant, you’ve probably made a mistake.
I’ve been making this point to my dean (deaf-eared on this issue) for years: that if you choose speakers for your group because they are successful, you are avoiding huge slices of useful information.
Business Insider agrees:
… There's a very good statistical reason why you should probably take a healthy serving of salt with whatever you hear, and it's called survivor bias.
Survivor bias is a type of selection bias, where a study focuses on people that survived some process, overlooking those who didn't survive, which skews the results.
An example helps:
… Let's say you looked at 100 commencement speeches, 90% of which encouraged you to do as the speaker did and follow your dreams.
You might conclude then that following your dreams is a surefire way to succeed …
… You don't know several things, like the failure rate of all people who followed their dreams.
It's just worthwhile to remember that the skills that these people recommend aren't guarantees of success, and because being highly successful is by definition exceptional, they're probably the exception rather than the rule.
I am going through this with a co-author right now. His vision was to use raw data put out by the NHL. My reality was that this data was over 1,000 observations on over 1,200 games. I went with the script:
Now that it’s done (thanks to Trevor MacDonald) I know I am way out on the right of this chart.
The conceptual basis of classical hypothesis testing is useful in a wide variety of areas.* Pity most students get too caught up in following the recipes for constructing test statistics to realize this.
A Type I error is foreclosing against a good borrower. A Type II error is letting a bad borrower avoid foreclosure. I will readily grant that a Type I error is worse than a Type II error, so we should tolerate some of the latter in order to avoid the former. However, I contend that we have let this bias get completely out of hand, resulting in a huge pileup of Type II errors with catastrophic effects on the housing market.
This is in regard to a Maryland family that has gamed the system and not made a payment on the house they continue to live in for over 5 years.
* A Type I error is when you make the mistake of rejecting something that is true. A Type II error is when you make the mistake of not rejecting something that is false. For example, a Type I error is convicting someone who is innocent, while a Type II error is letting someone go who is guilty.
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