## Quantiles of the F-distribution [General Statistics]

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

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.

Example in R speak with df1=12, df2=12, alpha/2=0.05:

gives F1 = 2.686637. This is the same as

gives F2 = 0.3722125.

SAS:

gives also F1 = 2.686637, F2 = 0.3722125.

Hope this helps.

» 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}=R_{1}-R_{2}

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`_{ij}T = T_{1} - T_{2}

, 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*(Emphasis be me. Similar text for F_{α/2,ν1,ν2}is the value of the F-distribution with ν_{1}(numerator) and ν_{2}(denominator) degrees of freedom that has probability of α/2 to its right."_{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

Regards,

Detlew

### Complete thread:

- SAS and R (?) for variability comparison (FDA NTID Guidance) Shuanghe 2015-09-25 18:48
- 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

- 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

- OT: LaTeX, MathML, PNGs Shuanghe 2015-09-28 17:32
- 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

- Suggestion Shuanghe 2015-09-29 18:44
- 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

- Suggestion Helmut 2015-09-29 02:22
- 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

- SAS and R (?) for variability comparison (FDA NTID Guidance) jag009 2015-09-25 22:42