#small numbers

[keebwee]

"what is your dream" to see an ivory billed woodpecker obviously

[transroboteeveegirl]

OwO Doing numbers on catgirl tumblr.

[mybeautifulchristianjourney]

"Small numbers make no difference to God. There is nothing small if God is in it."

Dwight L. Moody

[continuations]

Uncertainty Wednesday: Fooled by Small Numbers

The last couple of Uncertainty Wednesdays examined fallacies based on statistical phenomena such as imperfect correlation and the base rate. Another one of these has to do with small numbers. A famous example of this fallacy occurred when a study showed that among the best performing schools in the country there was a high percentage of small schools. This resulted in a push for making schools smaller.

A lot of money and effort was expended on this push for smaller schools. That is, until someone decided to also study the worst performing schools. And again, it turned out that there was a high percentage of small schools among them. Ouch! So apparently being a small school either gives you really good or really bad performance.

In reality much of this is simply was the result of small numbers. When you have a small number of students, you have an even smaller number of teachers. And so it is much easier to wind up either with really bad teachers or with really good teachers. As a school gets larger, it is much more likely to have some good and some bad teachers. Hence it is much more likely to be of average performance.

This small numbers effect is, like the previous fallacies, incredibly widespread. In companies think about the performance of departments (small ones versus large ones). For governments consider small cities or countries compared to large ones. And so on.

[fastesttalker]

"Small numbers"

“Small numbers”

#covid-19 #coronavirus #stayhomesavelives

This is no way any form of scientific research, just my own observations over the years, people have a really small attention span and a “if I can’t see it then it doesn’t mean me” mentality. This can best be observed on Motorways when the speed limit is temporarily reduced because of an issue ahead, people won’t reduce their speeds, they keep going…

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[continuations]

Uncertainty Wednesday: When Small Numbers Matter (Aircraft Safety)

Last week's Uncertainty Wednesday was titled “Fooled by Small Numbers” and discussed why drawing conclusions from small samples is dangerous. A reader asked how that relates to grounding the Boeing 737 Max 8 airplane after two crashes? Isn’t that also drawing a conclusion from a small sample? No. Because here we are actually looking not at a sample but at the population of all flights.

Globally there are nearly 40 million commercial flights annually. That is over 100,000 flights every day! Each and everyone one of those flights is tracked. And in an amazing accomplishment of engineering, process and public safety regulations we have had years with zero  crashes. When people complain that we are going backwards on commercial flight because we used to have supersonic flight with the Concorde, what they are ignoring is that the real demand was not for speed but for safety.

With such a large number of successful flights, a crash is a strong indicator that something went wrong. At a high level there are two possible explanations: equipment failure or operator error (of course the two can interact with each other and compound). On any single crash it would be hard to have two much of a view as to which one caused it and one might rightly suggest that grounding a whole fleet of planes is an overreaction. But two crashes with the same type of equipment point strongly at the aircraft itself.

That argument is of course further strengthened when there is significant additional evidence pointing at the plane, such as complaints by pilots along with known changes to the plane. In summary then: when something normally goes right more than 100,000 times a day every day, and then goes wrong twice in a row with the same equipment, that’s a very strong signal.

[moppabear]

70 FOLLOWERS! *throws confetti* 

[h---n]