Statistics：How to prove that one variable's change is influenced by another variable,that is to say ,they are related? I major in Bioinformatics. Now,I am in a problem: we all know that temperature changes during a year , I find that a disease incidence is really high when temperature is relatively high , while it becomes really low when the temperature is relatively low , that is to say ,they are related. So ,I want to find out a way to prove that they are related ,not just intuitively feel that they are related. So, any suggestions?
 A: If you are trying to prove that higher temperatures cause the disease incidence to increase (vs merely being associated with it) and vice versa, then even a correlation of 1 will not show that, merely that they co-occurr. 
To show causation, you have to rule out the possibility that other variables are responsible for increase in disease incidence. For example, perhaps air conditioner use tends to increase the probability of lung infection. Air conditioners are used almost exclusively in the summer, hence you would expect infection rates to be positively correlated with temperature, perhaps to a very high degree, even though heat, per se, does not increase infection rates.
The gold standard for causation is the double-blind randomzied trial. Absent that, you need to show that other plausible causes admit of counterexamples where a cause is present but the effect is absent. Most epidemiology texts will discuss options for observational studies, but hard evidence of causation requires controlled trials.
