Hi:
Given a method as the reference golden method, how do we statistically show that a new method is better than the reference one?
One way I could think of is to define a statistical variable, I, and then conduct a hypothesis test to see if avg( I_new-I_ref ) >0, which means that in average the difference of the performance of the new method and of the reference one is greaterthan zero.
But how do we define one such statistical variable? Also, I heard that sometimes people would conduct hypothesis for multiple variables. In that case, how do we know that the new method is better than the reference one or not?
Let's consider testing the effects of different types of fertilizer to increase a given type of crop. We want to know which type of fertilizer would make a given area of land product the maximum amounts of crop.
Suppose we have 4 types of fertilizer. Does it mean that we need to conduct C(5,2) times paired student t-tests to determine the best fertilizer?
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