Question

Dr. Phil conducts a study to find out whether or not a specific PTSD therapy is effective. At the end of the study he would like to provide evidence that the treated individuals are different than before. What statistics does he need to do this?

Answer 1

To conduct the particular study, Dr Phil should use the statistical procedure of Testing the value of the difference between two population means for paired data. Here he has to check that whether the PTSD therapy is effective. So he should collect the corresponding data for participants before and after receiving the PTSD treatment.

Null hypothesis H_o : U_B = U_A i.e. mean parameter before and after the PTSD treatment is same.

v/s

Alternative hypothesis H₁ : U_A > U_Bi.e. mean parameter after the PTSD treatment is more than before.

The data would be of the form:

(X11,X21), (X12,X22 ), (X13,X23 ),...,(X1n ,X2n )

This is called paired data. Essentially having paired or matched data means that there is one sample:

Paired data are analysed using the differences Di = X1i - X2i and estimation of mean_D = mean₁ - mean₂ is considered. A z result or a t result can be used but the latter willcbe more common as it is unlikely that the variances of the differences will be known. Assuming normality of the population of such differences (but not necessarily the normality of the X1 and X2 populations), the pivotal quantity for the t result is

(D_mean - 0) / (Standard Deviation of D) / (n)^0.5 ~ t_n-1