Dear forumers,
In advance, thank you for reading this post and helping me solving this.
The problem is the following :
I have a population (say, a bag) from which i take 3 samples.
Each sample gets analysed once by a laboratory in order to know their concentration of a product.
The result from the laboratory for each sample "i" is in the form : the real value of the concentration is somewhere (i.e. normally distributed) around µ_i with the variance sigma²_i.
sigma²_i depends on the time of measurement t_i, : the longer the measurement, the more accurate the result is, which means that µ_i gets closer to the real value of concentration of the samplie "i". The relation between sigma_i and t_i is known.
So far, so good.
Now the question is simply :
To me, the problem seems a bit similar to an ANOVA analysis, except that, for ANOVA, u have multiple values for each sample while here, u have only one value with a known uncertainty. I don't know, I'm lost...
Would be amazing if u guys can give me some help on this !
In advance, thank you for reading this post and helping me solving this.
The problem is the following :
I have a population (say, a bag) from which i take 3 samples.
Each sample gets analysed once by a laboratory in order to know their concentration of a product.
The result from the laboratory for each sample "i" is in the form : the real value of the concentration is somewhere (i.e. normally distributed) around µ_i with the variance sigma²_i.
sigma²_i depends on the time of measurement t_i, : the longer the measurement, the more accurate the result is, which means that µ_i gets closer to the real value of concentration of the samplie "i". The relation between sigma_i and t_i is known.
So far, so good.
Now the question is simply :
- What do i know about the concentration of my whole bag ? With which uncertainty (expressed as a variance sigma) ?
- If i take a 4th sample, what can I expect from it ? If I measure it during a time t_4, what will be the associated uncertainty (using all the information I have) ?
- What do i know about the heterogeneity of my bag ? (i.e. how can i split sigma between a relation with all the sigma_i and another "heterogeneity" term representing the variance of the 3 means µ1, µ2 and µ3).
To me, the problem seems a bit similar to an ANOVA analysis, except that, for ANOVA, u have multiple values for each sample while here, u have only one value with a known uncertainty. I don't know, I'm lost...
Would be amazing if u guys can give me some help on this !