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Re: Statistical test for equality ?


From: João Rodrigues
Subject: Re: Statistical test for equality ?
Date: Fri, 03 Jan 2014 10:42:39 +0000
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:24.0) Gecko/20100101 Thunderbird/24.2.0


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


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