Note: Statistical test
Keisuke Kawata
Hiroshima University
Econometrics 1
Review: Statistical test
Econometrics 2
Purpose: We would like to argue that the population (true) mean is not equal to a
value ��,0.
⇒We a argue so if it is a rare e e t that e o ser e our urre t sa ple under the null hypothesis; the population mean is equal to ��,0.
⇒It’s easure e t is the pro a ilit that e o ser e sa ples hi h ha e ore e tre e ea s tha our urre t sa ple. ⇒Called as p-value.
⇒If p- alue is lo , our data is rare a d e a reje t the ull h pothesis.
Review: How to calculate the p-value
Econometrics 3
• The p-value depends on the probability distribution of our sample means.
⇒
Sample mean
��,0.
Sample mean of current data
E tre e ea s E tre e ea s
Fro the e tral li it theore , it’s distri utio a e appro i ated the normal distribution,
Review: Procedure of statistical test
Econometrics 4
4. We decide whether reject the null hypothesis or not reject. 3. To do so, we calculate the p-value under the null hypothesis.
2. To do so, we estimate the probability distribution by using the central limit theorem, the estimated variance of sample mean, and the null hypothesis. 1. To do so, we estimate the variance of sample mean.
