Bioequivalence and Bioavailability Forum

Quantiles of the F-distribution [General Statistics]

posted by d_labes – Berlin, Germany, 2015-09-28 11:45 (3132 d 10:17 ago) – Posting: # 15475
Views: 25,813

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 s_WR (from D_ij=R₁-R₂ then running with PROC MIXED, output CovParms, and calculate s_WR = SQRT(estimate/2)), is it correct to assume that we need to modify the code to have something like D_ijT = T₁ - T₂, then run the same procedure as for s_WR to calculate s_WT?

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.
"... F_α/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 F_{1-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:

SAS and R (?) for variability comparison (FDA NTID Guidance) Shuanghe 2015-09-25 18:48 [General Statistics]
- SAS and R (?) for variability comparison (FDA NTID Guidance) jag009 2015-09-25 22:42
  - SAS and R (?) for variability comparison (FDA NTID Guidance) Shuanghe 2015-09-28 17:05
    - Missings d_labes 2015-09-30 10:52
      - Missings Shuanghe 2015-09-30 15:34
- LaTeX, MathML, PNGs Helmut 2015-09-27 14:23
  - OT: LaTeX, MathML, PNGs Shuanghe 2015-09-28 17:32
    - OT: LaTeX, MathML, PNGs Helmut 2015-09-28 17:46
- Quantiles of the F-distributiond_labes 2015-09-28 09:45
  - Quantiles of the F-distribution Shuanghe 2015-09-28 17:39
- What's wrong with this picture? Shuanghe 2015-09-28 18:57
  - Suggestion Helmut 2015-09-29 02:22
    - Suggestion Shuanghe 2015-09-29 18:44
      - OT: The Hadleyverse d_labes 2015-09-30 08:44
  - Another suggestion for a R-solution d_labes 2015-09-29 14:26
    - Wow – another gem from the master! Helmut 2015-09-29 16:31
    - Another suggestion for a R-solution Shuanghe 2015-09-29 18:37
      - Another R-solution d_labes 2015-09-29 21:55
    - @Shuanghe: Outdated URL gvk 2019-05-21 11:36
- SAS and R (?) for variability comparison (FDA NTID Guidance) M.tareq 2017-04-14 15:04
  - SAS and R (?) for variability comparison (FDA NTID Guidance) M.tareq 2017-04-15 01:01

Quantiles of the F-distribution [General Sta­tis­tics]

Complete thread:

Quantiles of the F-distribution [General Statistics]