What happens statistically, if you create more observations by measuring more aspects of the same observational unit Let's say that I want to measure the effect of a treatment on the performance of a firm. However my sample is very small. Let's say 10 firms. It is not possible to observe more firms. All these firms currently have one performance indicator.
Now, what happens if I start measuring 5 performance indicators per firm instead of the one?
One could argue that measuring 5 separate performance indicators, would give more certainty on the performance of the firm and therefore improve the amount of observations to n=50.
The counter argument would be that you are still measuring the same 10 firms.
Maybe the truth is somewhere in between?
I guess it also relates to clustering, for which I added an interesting article (which argues that researchers "over-cluster"):
When Should You Adjust Standard Errors for Clustering?
EDIT:
From the comments to the answer by Dave:
The argument would for example be that profit is a more short term indicator of performance and number of new hires is a more long term indicator. Together they would then give a better indication of the performance of a firm (there is more information).
Now I am wondering if this is perhaps a similar mechanism as measurement error: One measure is not a good measure of true performance (so there is measurement error), but multiple measures could solve this error.

I would argue that you still have $n=10$.
When you measure one indicator per firm, you have ten univariate observations. When you measure five indicators per firm, you have ten multivariate observations.
Either way, $n=10$.
