Sample size, confounding, bias

[#1]

I have doubts. I use data on electricity consumption per capita (per year) from 1960-2014. The sample size in this case is N = 55 for the whole world, as well as for individual regions and countries. However, the annual per capita consumption of electricity for the world covers approximately 7,000,000,000 people, and for Norway, for example, about 5 million, but in both cases for the period from 1960 to 2014, N = 55. Is there a way to statistically evaluate the fact that in the first case the population of 7 billion people is included, and in the second much less, in terms of reduction of confounding and bias?

[#2]

Maybe the question is not clear. I will try to clarify. This is about the statistical analysis of time series. The period from 1960 to 2014 covers 55 years. Thus, the sample size is N = 55 for all countries and regions. Population size (number of people) is not reflected in sample size in time series (number of years). When calculating the p value in this case, it does not matter whether the research covers 1000 people, or a million, or a billion, the width of the sample is always 55. It is illogical to me, but mathematically it is so.

[#3]

Hi,
I looks like nobody has been able to tackle your issue. It might be due, in part, to the limited information provided about your specific case. Would it be possible to provide an example of the data structure (mock data if the information is sensitive) and the exact hypothesis you would like to test in this data.
Also, it looks like you are trying to estimate the error in the measurements based on aggregate ratios (electricity consumption per capita). To the best of my knowledge, I don't think that there is any valid method to retrospectively derive such information.
Hopefully, with the additional information you may provide, experts in this board (I'm not really one of them) will be able to provide an answer.
Best,
TS