## Nitpicker! [Two-Stage / GS Designs]

Hi ElMaestro,

» I imagine I was not able to explain what I meant??

No, you were. I’m currently busy with other stuff.

» I looked at the code available here.

Better to have a look at the current version of sampsiz2.R. There you find in lines 42–46:
  # degrees of freedom as expression   # n-2 for 2x2 crossover and 2-group parallel design   dfe <- parse(text="n-2", srcfile=NULL)   # or should that read n-3? see Kieser/Rauch   #dfe <- parse(text="n-3", srcfile=NULL)

You have a point. IMHO, this question should be answered: yes! n1+n2−3 degrees of freedom mentioned already by Mdm. Povin.
Forget my last code. Should be: n2 <- n + n %% 2 - n1

n1 = 12; stage 2 sample sizes (n2), method = exact    CV sampleN.TOST pwr.TOST sampleN2.TOST pwr.sampleN2.TOST  0.10           NA  0.97308            NA           0.97308  0.15            2  0.81765             2           0.82711  0.20           12  0.83603            12           0.83875  0.25           22  0.81272            22           0.81411  0.30           36  0.81708            36           0.81775  0.35           50  0.80576            50           0.80616  0.40           68  0.81051            68           0.81075  0.45           86  0.80654            86           0.80670  0.50          106  0.80584           106           0.80595  0.55          126  0.80158           126           0.80165  0.60          148  0.80090           148           0.80096  0.65          172  0.80292           172           0.80297  0.70          196  0.80299           196           0.80303  0.75          220  0.80198           220           0.80201  0.80          244  0.80040           244           0.80042
Good news: Equal sample sizes (so we can use sampleN.TOST() till we have code specific for the 2nd stage; for studies proceeding to the 2nd stage power wrong in the 3rd decimal or less). Now one of the riddles of Potvin’s paper is resolved. Could never figure out the reported power of the examples.
1. n1 12, s²1 0.020977 ⇒ N 14, reported power 83.1%.
CV <- mse2CV(0.020977) print(round(sampleN.TOST(alpha=0.0294, CV=CV, method="shifted",                          details=FALSE, print=FALSE)[7:8], 3),       row.names=FALSE) Sample size Achieved power          14          0.837 print(round(sampleN2.TOST(alpha=0.0294, CV=CV, n1=12,                           method="shifted")[8:9], 3),       row.names=FALSE) Sample size Achieved power           2          0.831

2. n1 12, s²1 0.032634 ⇒ N 20, reported power 82.4%.
CV <- mse2CV(0.032634) print(round(sampleN.TOST(alpha=0.0294, CV=CV, method="shifted",                          details=FALSE, print=FALSE)[7:8], 3),       row.names=FALSE) Sample size Achieved power          20          0.826 print(round(sampleN2.TOST(alpha=0.0294, CV=CV, n1=12,                           method="shifted")[8:9], 3),       row.names=FALSE) Sample size Achieved power           8          0.824

Dif-tor heh smusma 🖖
Helmut Schütz

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