Quantiles of the F-distribution [General Sta­tis­tics]

posted by d_labes  – Berlin, Germany, 2015-09-28 09:45  – Posting: # 15475
Views: 18,980

Dear Shuanghe,

» However, there's no sas code for the variability comparison ...

Wow! Seems correct. Was not aware of this fact.

At moment I don't have answers to all of your other questions but only to your points 1., 2. and 4.

Lets start with 2. and 4, the simpler ones:

» 2. From the sas code for sWR (from Dij=R1-R2 then running with PROC MIXED, output CovParms, and calculate sWR = SQRT(estimate/2)), is it correct to assume that we need to modify the code to have something like DijT = T1 - T2, then run the same procedure as for sWR to calculate sWT?

Correct.

» 4. Since FDA request that only subject who complete all 4 periods should be included in the analysis, for obtaining F-distribution value, it seems the degree of freedom vT and vR will always be equal, which is always Ntotal - 2 for full replicate. Right?

Correct for full replicate 4-periods with 2 sequences with mentioned precondition.

Now to the mysterious lower/upper (upper/lower?) CI of the variabilities (your point 1.):
The answer lies hidden in the text of the Warfarin guidance.
"... Fα/2,ν1,ν2 is the value of the F-distribution with ν1 (numerator) and ν2 (denominator) degrees of freedom that has probability of α/2 to its right." (Emphasis be me. Similar text for F1-α/2,ν1,ν2).

Example in R speak with df1=12, df2=12, alpha/2=0.05:
F1 <- qf(0.05, df1=12, df2=12, lower.tail=FALSE)
gives F1 = 2.686637. This is the same as
F1 <- qf(1-0.05, df1=12, df2=12, lower.tail=TRUE)

Usually (and in SAS) the probability to the left is given back (integral over F-density from 0 to F).
# lower.tail=TRUE is default
F2 <- qf(0.05, df1=12, df2=12)

gives F2 = 0.3722125.
SAS:
Data Finv;
  df1=12; df2=12; alpha=0.05;
  F1=Finv(1-alpha, df1, df2);
  F2=Finv(alpha, df1, df2);
run;

gives also F1 = 2.686637, F2 = 0.3722125.

Hope this helps.

Regards,

Detlew

Complete thread:

Activity
 Admin contact
20,346 posts in 4,274 threads, 1,404 registered users;
online 15 (1 registered, 14 guests [including 6 identified bots]).
Forum time (Europe/Vienna): 10:10 CET

The belief that there is only one truth and
that oneself is in possession of it,
seems to me the deepest root of all
that is evil in the world.    Max Born

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz
HTML5