In: Statistics and Probability
Can you prove things 100% with Statistics? Just because you are able to reject a hypothesis does that mean you found Causation?
No, whatever we conclude using statistics is true on average provided assumptions are satisfied.
For example if average depth of a river is 1.2 m and your height is 1.5 m then it doesnot mean that you can walk through the river withough getting your head wet, as towards banks depth would be less and in the middle depth would be higher.
Also observe mean of numbers {10,20,150} is 60, and mean of numbers {50,60,70} is 60.
In testing of hypothesis assumption of randomness of data and underlying distribution are very important. If these assumptions are satisfied larger departure from critical value gives stronger evidence. That is, if critical value is 10 and rejection is made for larger values than value of statistic 15 gives stronger evidence than 12.