Observations in a linear model [General Sta­tis­tics]

posted by ElMaestro  – Denmark, 2022-11-16 21:50 (574 d 14:29 ago) – Posting: # 23370
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I still do not quite know what it is you are trying to convince yourself about. :-D

❝ 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.

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!

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