Helmut ★★★ Vienna, Austria, 2022-11-15 11:55 (728 d 09:24 ago) Posting: # 23367 Views: 3,985 |
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Dear all, off-list I was asked whether it makes a difference if we have single observations or replicates. When you look at the standard equations, clearly the answer is no. If you don’t believe that, an -script for the simulation example at the end.
— 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 |
ElMaestro ★★★ Denmark, 2022-11-16 09:44 (727 d 11:34 ago) @ Helmut Posting: # 23368 Views: 3,265 |
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Hi Helmut I have no idea what is it is you were trying to test. If it makes a difference to have more replicates, or something along such lines, please put more word to it. It is way too vague for me. Please at least define "it" and "difference" in your own context with ample words. — Pass or fail! ElMaestro |
Helmut ★★★ Vienna, Austria, 2022-11-16 10:49 (727 d 10:30 ago) @ ElMaestro Posting: # 23369 Views: 3,311 |
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Hi ElMaestro, ❝ If it makes a difference to have more replicates, or something along such lines, please put more word to it. It is way too vague for me. ❝ ❝ Please at least define "it" and "difference" in your own context with ample words. I try. Two examples:
— 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 |
ElMaestro ★★★ Denmark, 2022-11-16 21:50 (726 d 23:29 ago) @ Helmut Posting: # 23370 Views: 3,253 |
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Hi, I still do not quite know what it is you are trying to convince yourself about. ❝ I try. Two examples: ❝ – Two calibration curves spanning the same range with either n single measurements or n/2 duplicates. ❝ – A 2×2×2 crossover with n subject vs a 4-period full replicate design with n/2 subjects. ❝ The question was whether the estimates of the models (obtained by single observations or replicates) are different. The estimates are unbiased estimators of the effects you are extracting. That's how it works, so there is no surprise here. Now try and consider the quality of the estimates, for example if you want to know how well is a mean (or slope or intercept or ...) estimated. Look for example at the SE of the estimates, easily extractable from an lm via e.g. summary(M)$coeff[,2] More replicates, better estimates. Or, expressed in clear BE terms, higher sample size gives narrower confidence intervals, but the expected value of the point estimate is unchanged. — Pass or fail! ElMaestro |
Helmut ★★★ Vienna, Austria, 2022-11-17 11:19 (726 d 10:00 ago) @ ElMaestro Posting: # 23371 Views: 3,218 |
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Hi ElMaestro, ❝ The estimates are unbiased estimators of the effects you are extracting. That's how it works, so there is no surprise here. Now try and consider the quality of the estimates, for example if you want to know how well is a mean (or slope or intercept or ...) estimated. Look for example at the SE of the estimates, easily extractable from an lm via e.g. ❝ Your wish is my command.
❝ More replicates, better estimates. You are right! I always preferred calibration curves with duplicates. ❝ Or, expressed in clear BE terms, higher sample size gives narrower confidence intervals, but the expected value of the point estimate is unchanged. Not only that. Power depends roughly on the total number of treatments. Even more, in replicate designs we have more degrees of freedom than in a 2×2×2 crossover.
— 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 |
ElMaestro ★★★ Denmark, 2022-11-18 18:28 (725 d 02:51 ago) @ Helmut Posting: # 23372 Views: 3,204 |
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Hi again, stating the entire thread in fewer terms and no code: more df's = better (more precise) estimates. You can increase the df's in two ways:
Amen. — Pass or fail! ElMaestro |