Dear STN

I think your question is not really about octave but about mathematics,

so I guess you'll find more useful answers at mathoverflow.net or a

similar site/forum/group. Nevertheless below I give some tips that may

help you get a better answer.

> It seems that statistical tests always revolve around distributions

> and parameters. They are very well suited to prove that two samples

> are different. But they only give hints as to whether samples are equal.

A previous list member tried to explain the difference between

frequentist and Bayesian statistics. The asymmetry that you find is

specific to frequentist methods.

> I put some independent data into a simulation-model and calculate a

> result. My input-data is not arbitrary, it has been observed, for

> example in a physical experiment. Also the results of the experiment

> have been observed.

>

Tell us about the actual problem that you wish to address. The way you

formulate it is too vague for anyone (or at least for me) to understand.

Is your problem one of experimental errors? If so you may want to read

this paper:

Weise and Woger (1993) A Bayesian theory of measurement uncertainty.

Measurement Science and Technology, 4 (1).

> The usual statistical tests will only check if two samples are from

> the same target population, never if the same objects have been chosen

> for both samples.

To be frank, it seems to me that you still don't have your basic

concepts right. Here you're talking about a sampling problem

(population, samples and objects), whereas before you talked about an

experiment. The techniques to handle such problems are completely

different.

In a sampling problem there is heterogeneity between objects and the

(methodological) question being asked is how to find a sampling method

that will yield relevant information about the population (and so to

disentangle properties from the population and properties of the

sampling method).

Consider that you are a psychologists and want to do research on

people's behaviour but you only use as experimental subjects undergrad

students. Is your sample representative? Of course not. (But students

are cheap Guinea pigs, that's why they are used so often.)

Your "equality test", in the sense that I gathered from your words, is

to check if you are always using the same students (objects) in the

experiment (sample)?

Instead, if you are talking about a real-world design, there is no

sampling problem but there is measurement uncertainty. If you grow

bacteria in different Petri dishes you'll end up with a series of

cultures that develop at different rates, either due to environmental

factors (some are closer to the lab window and are a bit cooler, for

example, or the concentration of the food source differed) or because

the strains have different specific growth rates.

Here there are no populations (in the statistical sense) nor samples.

Here you have experimental data points (with measurement error) and

correlations between them.

Is your "equality test" here the question of whether the different

bacteria belong to the same strain? You could answer this question by

assessing the uncertainty of the environmental variables, positing a

model for the growth rate and then check whether the variance of the

environmental variables explains the growth rate variance (in which case

they all belong to the same strain).

I could go on with possible solutions to your problem, but it would be

easier if I knew what the actual problem was.

All the best

j

_______________________________________________

Help-octave mailing list

[hidden email]
https://mailman.cae.wisc.edu/listinfo/help-octave