Design of Experiments: D-Optimal Designs

[D.Weiland]

Hello,

 

Assuming I design an experiment containing N separate measurements to measure something (different samples, different factors etc).

Each of these measurements has the same standard deviation of SD.

How would I calculate the standard error of the final result after fitting the data to a model?

 

I assume this will be better than the standard deviation SD.

 

I know when repeating the exact same measurement N times, the standard error of the result is: SD /sqrt(N).

 

But how is this for a DoE with N experiments?

 

In particular I'm looking into a D-Optimal design, and the question is how many experiments do I have to do in order to achieve a certain accuracy (standard error) of the results.

 

 

Thanks very much for your help,

 

Dom

[Math Team]

The scetch of how to deal with this problem is the following:

 

 

1. Set the desired accuracy [\math] \epsilon [math] and the confidence level P.

 

2. Calculate the SD of Your estimator after N experiments.

 

3. Then You should find such N(the number of experiments) that the following inequality is satisfied:

 

P(|real value - estimated value in N exp.|>eps) < P

 

For this You should either use the information about the law of distribution or use some general estimates(like Chebyshevs theorem).

 

If this scetch was unclear, fill free to write me PM.

[lucaspa]

Hello,

 

Assuming I design an experiment containing N separate measurements to measure something (different samples, different factors etc).

Each of these measurements has the same standard deviation of SD.

 

Measurements do not have a SD. SD applies to ALL the measurements within that particular group.

 

How would I calculate the standard error of the final result after fitting the data to a model?

 

I assume this will be better than the standard deviation SD.

 

Not "better", but different. With a mean and SD you can describe any normal distribution. SEM gives you a rough and ready means to compare 2 groups and make an eyeball estimate whether they are statistically significantly different. If the difference of the means > the sum of the SEM of both groups, then they are probably statistically different at p <0.05.

 

What you are trying to do, it sounds like, is do several repetitions of an experiment and then getting a SD of the experimments.

 

This is meta-analysis, which does compare results of independent experiments. Places to start reading are:

http://allpsych.com/stats/unit5/21.html

http://userpage.fu-berlin.de/~health/meta_e.htm

http://www.statistics.com/ourcourses/meta/