## Observations in a linear model [General Statistics]

Hi,

I still do not quite know what it is you are trying to convince yourself about.

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.

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

Pass or fail!

ElMaestro

### Complete thread:

- Observations in a linear model Helmut 2022-11-15 10:55 [General Statistics]
- Observations in a linear model ElMaestro 2022-11-16 08:44
- Observations in a linear model Helmut 2022-11-16 09:49
- Observations in a linear modelElMaestro 2022-11-16 20:50
- And the Oscar goes to: Replicates! Helmut 2022-11-17 10:19
- It's all in the df's ElMaestro 2022-11-18 17:28

- And the Oscar goes to: Replicates! Helmut 2022-11-17 10:19

- Observations in a linear modelElMaestro 2022-11-16 20:50

- Observations in a linear model Helmut 2022-11-16 09:49

- Observations in a linear model ElMaestro 2022-11-16 08:44