# Experimental Design - Purely Experimental Variance

I am new to Experimental Design. I would greatly appreciate if you could help.

Suppose one is interested in estimating a regression model with three explanatory variables (two of which are categorical) within the framework of experimental design. I need to come up with a way to study the purely experimental variance. How should go about it?

My initial idea was to replicate the experiment at any one combination of the centre of the continuous explanatory variable with levels of the two categorical variables and calculate the empirical corrected variance of the replicated responses but I am unsure whether this is the way to go. Shouldn't I rather take into account the various combined categories in some clever (and not too costly) way?

EDIT: For some perspective, suppose the categorical variables are called "education" (four levels, say) and "language" (two levels) for example, and that the continuous explanatory variable is called "salary".

My problem with my initial approach is that various selected combinations of levels may lead to drastically different values for the purely experimental variance.

Now, if we make $$n_1, ..., n_8$$ repetitions (respectively) at each combination of levels, how is one to estimate the purely experimental variance?

• Have you considered a mixed effects model with random intercepts for the experiment ID ? The variance of the random intercepts will then be a measure of the intra-experiment variation, which, if I understand your question correctly, is what you want to measure.. – Robert Long Apr 13 at 19:07
• @RobertLong I haven't encountered mixed effects models yet but I'm sure I do not need to deal with any notion other than the ones mentioned in my question. Is it sensible to follow my initial hunch? – Mickybo Yakari Apr 14 at 10:53
• It is not clear to me what your hunch is. How, exactly, will you "calculate the empirical corrected variance of the replicated responses" ?? – Robert Long Apr 14 at 10:56
• Assuming that one planned and executed a series of experiments with $n$ repetitions at one point in the factor space only, the purely experimental variance is estimated based on those repeated experiments by taking the (corrected) empirical variance of the response at the chosen point in the factor space. – Mickybo Yakari Apr 15 at 14:31