Joker, a fictional character, from the dark knight movie released in 2008 had a very thorough knowledge about human behavior but if he knew statistics then the climax could have been different.
Let’s pick a scenario where knowledge of Statistics would have helped Joker.
The Joker’s final act as criminal mastermind involves two ferries filled with people. The first ferry is filled with normal, law abiding citizens while the second ferry is filled with the population of Gotham Prison. The Joker, doing so without prior knowledge of the passengers and city officials, wired the ships with powerful explosives such that their explosion would destroy the entire ship and everyone on it. No single individual is allowed to escape. Each ship is given a detonator for the other ferry. The use of the detonator saves the ship while killing everyone on the opposing ship. Thus, if any member of Ship A pushes the detonator, then Ship B is destroyed and all of Ship A is saved. Additionally, if either ship fails to use the detonator to destroy its opponent, then both ships will be destroyed by the Joker. In the end, no one on either ship activated the detonator.
There are few statistics concepts that can be learned from the above scenario.
Joker started with a hypothesis that we all are Homo Economicus when a situation forces us to be. Homo Economicus concept believes that humans are consistently rational and narrowly self-interested agents who usually pursue their subjectively-defined ends optimally. Batman. on the other side, believed that we are not Homo Economicus.
Let’s put them in the terms which statisticians understand.
Null Hypothesis(Ho): Human Beings are Homo Economicus (Joker’s view)
Alternative Hypothesis(Ha): Human beings are not Homo Economicus (Batman’s view)
Null hypothesis Ho is a tentative assumption about a population parameter such as a population mean or a population proportion. The alternative hypothesis. Ha is a statement that is the opposite of what is stated in the null hypothesis.
To test the hypothesis, Joker filled the two ferries with the type of people he wanted. The type of sampling done by Joker was Judgment sampling. In this approach, the person most knowledgeable on the subject of the study selects elements of the population that he or she feels are most representative of the population.
Now the Joker put the sample to test. It turns out his hypothesis was rejected. Batman was right. Now as a statistician there are few things which could have gone wrong with the test.
-What if the people selected in ferries doesn’t represent the views of the population? Sampling error. Sampling error is the error arising when the sample is unrepresentative of the population.
-What if we are Homo Economics but ships didn’t explode? This is Type I error. Ho is true but our data rejects the null hypothesis. Joker would be really angry if this was true.
-What if we are not Homo Economicus but ships exploded. This is Type II error. Ho is false but our data fail to reject null hypothesis. This time Batman would be disappointed.
Could Joker have done something different? Yes, only if his hypothesis was correct. To actually prove his claim, he could have taken a good random sample and large sample size. By this he would have avoided type I and type II error. Even with this there could have been sampling error. Sampling errors keep statisticians awake at night, so Joker is no different. So, Joker with his domain knowledge and good sampling could have proved his claims are right assuming he was right about the population.