Independence of Observations

[Alfred Dubois]

I need to calculate volume-weighted means of wholesale prices and then compare them to determine whether there are statistically significant differences. I'm concerned about the independence of the observations. I know this isn't a Stata issue per se, but a statistics related question.

So from one store there may be an order for 30 cartons (12 in a carton) of a particular item and 20 cartons (144 in a carton) of a similar item from another manufacturer. There are a few dozen stores and 3-10 manufacturers of the item and the carton sizes are all different. I need to get the volume-weighted mean for the item and then calculate whether there is a statistically significant difference in price between manufacturers.

What should be the observation? Should each unit be an observation? it seems that works for the mean, especially since the mean price is supposed to be volume weighted. But I wonder about the standard deviation and standard error. It seems that the 12 (or 144) units in a carton aren't independent observations. How should the weighting be done so a test of difference of means is correct?

[Carlo Lazzaro]

Alfred:
your concern can be addressed via -regress- with clustered standard errors (-vce(cluster clusterid)).

[Alfred Dubois]

Hi Carlo,

I also need to compare the prices to price lists from other manufacturers. I believe I need to calculate the SE of the mean so this can be done. Will the method you suggest allow me to do this?

Thanks,
Alfred

[Carlo Lazzaro]

Alfred:
I'm not clear with what you're after but you may want to see -mean-.

[Phil Bromiley]

You may want to think more about the model or problem you're solving. Why you would want to combine price and volume is not clear.

Price and volume are almost certainly not independent - there is lots of history on how to estimate such models.

Do all stores face the same wholesale price? If you are trying to understand retail pricing decisions, then it probably doesn't matter how much a given store sells - if the store only has one price, it only has one pricing decision. If you're trying to explain retail value in some way, I'm not sure why you'd care about volume - I'd think you'd want to look at product characteristics versus price. So, why you want a volume weighted pricing decision is not clear.

You need to be careful that you get the unit of analysis right. If there is one wholesale price, then there is probably only one wholesale pricing decision (i.e., one observation), but there may be many purchase decisions by retailers.