## Al Gore Rhythms [🇷 for BE/BA]

Dear D Labes!

❝ Hope you have already waited for me.

Yesss!

❝ Here are the results of the SAS Proc Power.

❝ Seems the power is calculated in this case totally wrong!

Fascinating.

❝ My own rolled code (relying on Owens Q-functions, undocumented but available in SAS) gives:

That’s the more interesting part (homebrew)!

                        n  % power    n  % power ------------------------------------------------ #1 Diletti et al.       4 >70         6 >90 #2 PASS                 4  72.90 #3 D Labes' SAS code    4  72.9014    6  98.6992 #4 nQuery Advisor 7     4  71.559     6  97.943 #5 R-code               4  66.674     6  98.697 #6 FARTSSIE 1.6         4  66.674     6  98.697 #7 StudySize 2.0.1      4  15.9 (!)   6  93.201

n=4 takes the lead by 4:3! Observations:
#5 (based on Algorithm AS 243) and #6 give identical results. This is not surprising, because the VBA-routine within FARTSSIE was written by Russell V. Lenth, the author of AS 243. #2/3 agree; for n=6 power is comparable with #5/6. #4 calculates lower power than #1-3, but still would suggest n=4. The difference between #1-3 and #5/6 might be due to different algorithms for estimating the noncentral t-distribution (#1/3: ?, #2: AS 243?, #4: AS 184, #5/6: AS 243). #7 uses approximations (Ref. 2 in this post); however, yields conservative results.

Maybe I should contact Dieter Hauschke to join the party…

Edit: Many, many years later.

library(PowerTOST) res <- data.frame(method = c("exact", "mvt", "nct", "central"),                   n = NA_integer_, power = NA_real_) for (j in 1:nrow(res)) {   res[j, 2:3] <- sampleN.TOST(CV = 0.075, theta0 = 1,                               targetpower = 0.7,                               method = res\$method[j],                               print = FALSE)[7:8] } print(res, row.names = FALSE)   method n     power    exact 4 0.7290143      mvt 4 0.7290142      nct 6 0.9869738  central 6 0.9611687

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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