Insecurity of Inductive Reasoning
I have not encountered this in any math book, but I guess this is where to ask.
A generalisation (more accurately, an inductive generalisation) proceeds from a premise about a sample to a conclusion about the population.
The proportion Q of the sample has attribute A.
The proportion Q of the population has attribute A.
How great the support which the premises provide for the conclusion is dependent on (a) the number of individuals in the sample group compared to the number in the population; and (b) the randomness of the sample.
If we know the proportion , the sample/population ratio and the randomness (where R=0 means 0% randomness and R=1 means 100% randomness), would it be possible to calculate/find a formula for the insecurity of the inductive reasoning above, if we measure the insecurity in the interval [0,1], where I=0 means 100% secure and I=1 means 0% secure?
The formula for would most likely have an overall factor , I think.
I just realized that Q and P are the same. That means that the forumula will most likely be , right?