Quote from abattia:
Sorry, your serious point deserves a serious answer...
I would assume the same criticism might be applied to testing two groups of patients for the effectiveness of a new treatment (apparently that is, or at least has been, a field of application of the two sample K-S test). After all, you could say that the two groups of patients will also be different in so many other ways (i.e. not just in whether that get the new treatment or just the placebo) that you won't be able to isolate the difference you are looking to focus on? No?
Intuitively, I think the response is that if your two groups of patients (or samples of price) are large enough, then you get to the point that both samples contain examples of "all" the things that could be different, and (if you have a big enough sample), the only difference that you end up with is the thing you know about (because you set it up that way). No?
I suggest you put this joker on ignore. As you see he did not even try to answer your question. He instead tried to raise controvesy for the purpose of instigating ad hominen attacks later and turning threads into insults.
He should know that when a police radar catches someone speeding the ticket is the same, regardless of whether the driver is on a vacation trip, going to work, living near by, or travelling with his daughter and son. He belongs to the population of those that exceed the speed limit and that is all that counts. It does not matter whether he started the trip an hour ago or 10 minutes ago.
So basically, whether two samples belong to the same population depends on the measurement objectives and not on their specific properties that may be irrelevant to those objectives.
"The word big is small". It is sampled from the set of small words. You don't care what it says, you only care how many characters it contains.
In other words, we do not look at the river but at things caused by the river which we can measure. A 'river" is an abstract concept. Rivers are not measured dynamically, except geometrically. It is the motion of particles in the river that can be measured. These particles obey the same laws. Their motion is governed by Navier-Stocks equations. If the boundary conditions are the same, the motions will be on the average the same resulting in the same pressure, temperature, etc.
Relating the the markets, there are periods when the same conditions prevail. If we know that after a given set of conditions something happend, let us say a correction, next time we measure the same conditions we can have some confidence interval that a correction will happen.
Matching distributions is essentially another way of pattern recognition. It is like matching signatures in signal processing.
