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yckim ☆ 2008-05-27 17:04 (6186 d 20:38 ago) Posting: # 1874 Views: 10,356 |
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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 |
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Helmut ★★★   Vienna, Austria, 2008-05-27 17:41 (6186 d 20:01 ago) (edited on 2008-05-27 19:47) @ yckim Posting: # 1875 Views: 8,917 |
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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 (n1 # n2) only the latter. ❝ Is the other method absolutely wrong? If the design is balanced (n1 = n2), 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 (n1+n2) and the degree of unbalance (ratio of n1/n2). ❝ 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). — Dif-tor heh smusma 🖖🏼 Довге життя Україна! ![[image]](https://static.bebac.at/pics/Blue_and_yellow_ribbon_UA.png) Helmut Schütz ![[image]](https://static.bebac.at/img/CC by.png) The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes |
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yckim ☆ 2008-05-28 03:39 (6186 d 10:03 ago) @ Helmut Posting: # 1876 Views: 8,794 |
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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] |
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Helmut ★★★ Vienna, Austria, 2008-05-28 13:55 (6185 d 23:47 ago) @ yckim Posting: # 1878 Views: 8,555 |
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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 (n1=n2 and n1#n2), whereas the formula of v1 is only correct for n1=n2. The formula of v1 is wrong for unbalanced studies (n1#n2). BTW, the correct method is the 'weighted mean'; an example: x1 of n1 numbers [1,2,3] is (1+2+3)/3 = 2,x2 of n2 numbers [4,5] is (4+5)/2 = 4.5.The weighted mean xw for two groups is defined with (x1n1+x2n2)/(n1+n2), giving (2×3+4.5×2)/(3+2) = 3.The 'mean of the means' (x1+x2)/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 overall-mean towards the mean of the smaller group. — Dif-tor heh smusma 🖖🏼 Довге життя Україна! Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes |
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d_labes ★★★ Berlin, Germany, 2008-05-28 18:35 (6185 d 19:08 ago) @ Helmut Posting: # 1879 Views: 8,593 |
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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 cross-over designs, that we are talking about the evaluation of such cross-over studies. The formula (x1+x2)/2then 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 Cross-over trials in clinical research Wiley, 2002, chapter 3. — Regards, Detlew |
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yckim ☆ 2008-06-03 09:46 (6180 d 03:56 ago) @ d_labes Posting: # 1899 Views: 8,573 |
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Dear HS and d_labes There seems to be opinions that 'mean of the means' (least square mean?) is right in cross-over 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 |
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JPL ☆ Vienna, 2008-06-03 11:10 (6180 d 02:32 ago) @ yckim Posting: # 1900 Views: 8,738 |
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Dear Yu, in fact Least Square Means (LSMeans) are not an issue of X-over 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 |
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vish14184 ★ India, 2008-06-04 08:54 (6179 d 04:48 ago) @ JPL Posting: # 1905 Views: 8,416 |
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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 |
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JPL ☆ Vienna, 2008-06-04 10:44 (6179 d 02:59 ago) @ vish14184 Posting: # 1907 Views: 8,670 |
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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.burns-stat.com/pages/Tutor/spreadsheet_addiction.html Regards, JPL |
Ing. Helmut Schütz