I have a small population of N=137 and a (presumably representative) sample of n=81. The corresponding Finite Population Correction (FPC) factor is FPC=SQRT {(N-n)/(N-1)}= 0.64. Can I apply this correction factor to the estimated standard error of the mean regression slope as follows: (1) SEcor = SE * FPC , (2) tcor= t / FPC (because t = B/SE), resulting in a corrected p-value (using the t-distribution).
In my specific example the mean slope B and its standard error SE of one of my independent variables is B= 0.40 and SE=0.16 resulting in t= B/SE = 2.5 and in a one sided p = 0.015 (df =63) (B, SE, t, p and df are taken from the standard regression output in SPSS). With finite population correction as suggested above B = 0.40, SEcor = 0.103, resulting in tcor=B/SEcor =3.9, and in one sided pcor=0.001(df=63).
Is this the correct way for correcting for a finite population in multiple regression analysis?