yckim ☆ 20080527 15:04 Posting: # 1874 Views: 6,364 

Dear all, I found the difference of mean calculation method between equivtest 1.0 and 2.0. Equivtest 1.0 calculates (mean_seq1+mean_seq2)/2 instead of {(mean_seq1*n1)+(mean_seq2*n2)}/(n1+n2). The company confirmed Equivtest 2.0 is right. Which is the right one in your opinion? Is the other method absolutely wrong? I would also like to know the theoretical basis. I look forward to your reply. Best regards, Yu Chul Kim Korea, Republic of 
Helmut ★★★ Vienna, Austria, 20080527 15:41 (edited by HS on 20080527 19:47) @ yckim Posting: # 1875 Views: 5,745 

Dear Yu! » I found the difference of mean calculation method between equivtest 1.0 and 2.0. Fascinating! I have both versions on my machine and will check it sometime... » Equivtest 1.0 calculates (mean_seq1+mean_seq2)/2 instead of {(mean_seq1*n1)+(mean_seq2*n2)}/(n1+n2). The company confirmed Equivtest 2.0 is right. Which is the right one in your opinion? In the case of an unbalanced study (n_{1} # n_{2}) only the latter. » Is the other method absolutely wrong? If the design is balanced (n_{1} = n_{2}), the second formula reduces to the first one. In technical terms, the second one is wrong for unbalanced studies; the bias will depend on both the overall size of the study (n_{1}+n_{2}) and the degree of unbalance (ratio of n_{1}/n_{2}). » I would also like to know the theoretical basis. There are some examples in Chow & Liu (2001).  Edit: Sorry, I don't have version 1 any more. Both EquivTest02.00 (2001) and EquivTest/PK (2006) use the correct formula  which is also given in the manuals (look for TOST). — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
yckim ☆ 20080528 01:39 @ Helmut Posting: # 1876 Views: 5,574 

Dear HS Thank you very much for your reply! However, I am a little confused about followings. » In the case of an unbalanced study (n1 # n2) only the latter. » In technical terms, the second one is wrong for unbalanced studies; the bias will depend on both the overall size of the study (n1+n2) and the degree of unbalance (ratio of n1/n2). You said the method of equivtest 2.0 is right in the former while it is wrong in the latter. Please clarify it. Thank you. Best regards, Yu Chul Kim Edit: Standard quotes restored. [Helmut] 
Helmut ★★★ Vienna, Austria, 20080528 11:55 @ yckim Posting: # 1878 Views: 5,534 

Dear Yu! » You said the method of equivtest 2.0 is right in the former while it is wrong in the latter. Please clarify it. You are right, I did not express myself clearly. EquivTest v2 and /PK are using the correct formula in all situations (n_{1}=n_{2} and n_{1}#n_{2}), whereas the formula of v1 is only correct for n_{1}=n_{2}. The formula of v1 is wrong for unbalanced studies (n_{1}#n_{2}). BTW, the correct method is the 'weighted mean'; an example: x_{1} of n_{1} numbers [1,2,3] is (1+2+3)/3 = 2,x_{2} of n_{2} numbers [4,5] is (4+5)/2 = 4.5.The weighted mean x_{w} for two groups is defined with (x_{1}n_{1}+x_{2}n_{2})/(n_{1}+n_{2}) , giving (2×3+4.5×2)/(3+2) = 3.The 'mean of the means' (x_{1}+x_{2})/2 irrespective of the size of groups (EquivTest 1) leads to (2+4.5)/2 = 3.25.The bias (in our case +0.25) can be positive or negative, but always drags the overallmean towards the mean of the smaller group. — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
d_labes ★★★ Berlin, Germany, 20080528 16:35 @ Helmut Posting: # 1879 Views: 5,552 

Dear HS, dear Yu, I think it is necessary to have the concise context of the formulas before discussing in depth. I do not own Equivtest. But a bet a big coin that because sequence means are mentioned and equivalence studies are mostly done with crossover designs, that we are talking about the evaluation of such crossover studies. The formula (x_{1}+x_{2})/2 then looks to me as that what is called a 'Least square mean'. Helmuts simple data give with
Proc GLM; If the numbers are treatment differences in one subject, then the above code is for evaluation of the overall treatment difference in Senn's basic estimator approach. Stephen Senn Crossover trials in clinical research Wiley, 2002, chapter 3. — Regards, Detlew 
yckim ☆ 20080603 07:46 @ d_labes Posting: # 1899 Views: 5,573 

Dear HS and d_labes There seems to be opinions that 'mean of the means' (least square mean?) is right in crossover study. Even Equiv 2.0 use the term of 'least square mean'. In addition, many texts on statistics use the 'mean of the means' formula. Please help me clearly understand which method is right and the rationale. Best regards, YCKim 
JPL ☆ Vienna, 20080603 09:10 @ yckim Posting: # 1900 Views: 5,729 

Dear Yu, in fact Least Square Means (LSMeans) are not an issue of Xover studies only but of unbalanced data. For the balanced case LSMeans and Means agree, for the unbalanced case, LSMeans account for the size of the group the LSMeans is determined of. Find a basic example here: http://www.uidaho.edu/ag/statprog/sas/workshops/glm/lsmeans.htm Regards, JPL 
vish14184 ★ India, 20080604 06:54 @ JPL Posting: # 1905 Views: 5,420 

Dear all, In SAS geometric mean calculated by using exp(lnLSM) that value differ from the geometric mean calculated using excel. i want to know that why this values are differ? Regards Vishal Nakrani 
JPL ☆ Vienna, 20080604 08:44 @ vish14184 Posting: # 1907 Views: 5,641 

Dear Vishal, the main difference ist that you use a LSMean in the first case, whereas Excel really does not calculate LSMeans and therefore does not produce geometric LSMeans. By the way: Don't youse Excel for statistics: http://www.burnsstat.com/pages/Tutor/spreadsheet_addiction.html Regards, JPL 