Insurance company A sample size 200
Insurance company B sample size 200
A $300 per year for 100 people, B $400 per year for those same 100 people
A $400 per year for 100 people, B $300 per year for those same 100 people
If some person does a two tailed t test based on the sample results above to try to figure out if one company is cheaper than the other one on average they will find neither one is statistically significantly different
Insurance company A and Insurance company B have the same mean, sample size and standard deviation
People allowed to make individual choices switched companies if it saved them money and did not switch if it did not save them money
People who switched from A to B saved $100 per year on average
People who switched from B to A also saved $100 per year on average
It does not make sense to use a group average to make your decision as a individual
It makes more sense to look at your own individual results than the average results of other people when making life decisions
A statistical t test would be useless to make such a decision in this case
People wear shoe type A and shoe type B for one month each, each person trying both types of shoes
Shoe type A results in 70% of the people slipping on a workplace floor within a month
Shoe type B results in only 30% of people slipping on a workplace floor within a month
The 30% that slipped wearing type B did not slip wearing type A and the the 70% that slipped wearing type A did not slip wearing type B.
There was no overlap in which someone did not slip wearing either type of shoe and no overlap in which someone slipped wearing both types of shoes
Statistically having a corporate or government policy of forcing everyone to wear shoe type B will result in which slipping incidents then forcing everyone to wear shoe type A
But it might make more sense to let the people decide on their own. Those who did not slip with their individual results wearing type A shoes might choose to wear type A shoes and those that did not slip with their individual results wearing type B shoes might choose to wear type B shoes. This might result in lower rates of slips and falls when they knew their individual results and could make choices than forcing those people to all wear the same shoe type based on whatever results had the least falls for the group even in cases in which it resulted in more falls for them as an individual.
Often in real life people who use group average results for other people make a mistake when they can access individual results for themself to make a decision
Since statistics provides no mechanism to explain results it is poor practice to enforce the best statistical results for a group of other people upon a single individual if one has a goal of the best good for a community in addition to being an violation of individual autonomy
Good practice is to find the mechanism that explains which people will have better results and which people will have worse results for making one choice instead of another choice and then to explain that mechanism to people and let them make their own choices
Good scientific practice is based on finding non probabilistic functions by which you can predict output for one set of variables by controlling the input of another set of variables not statistical probability tests which can not predict output as a function of input
Copyright Carl Janssen 2022 June 12
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