# Combining separate upper & lower limits into a total?

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• Anchovy
In summary, when trying to determine the overall upper limit at the same confidence level for two separate experiments, it is not valid to simply sum the individual upper limits. This would result in a weaker limit with more data. Additionally, there may be correlations and systematics that need to be taken into account. If it is one Monte Carlo simulation instead of two separate experiments, the analysis becomes even more complex due to correlations between the two values.
Anchovy
If the results of two separate experiments to measure the same quantity are stated in terms of upper and lower limits at the same confidence level, is it valid to say that the overall upper limit (at the same C.L.) is just the sum of the two individual upper limits? Or is something more complicated necessary here?

Anchovy said:
is it valid to say that the overall upper limit (at the same C.L.) is just the sum of the two individual upper limits?
No, definitely not. That would be a weaker limit with more data!

In general, there might also be correlations and systematics that are the same in both experiments. You need to have more information to do a proper analysis.

Orodruin said:
No, definitely not. That would be a weaker limit with more data!

In general, there might also be correlations and systematics that are the same in both experiments. You need to have more information to do a proper analysis.

Ah, I see. Do things become much simpler if it's not actually two different experiments, but rather it's one Monte Carlo simulation, counting the same thing happening two different ways?

You would still need to know a lot more about the actual simulation in order to make a statement. In particular about the systematic errors going in.

Orodruin said:
You would still need to know a lot more about the actual simulation in order to make a statement. In particular about the systematic errors going in.

OK, thanks.

I think just addining them will result to taking them 100% correlated, in contrast to adding them in quadrature... but as already pointed out, without knowing information on systematics, it will not give you the right result...

Anchovy said:
Ah, I see. Do things become much simpler if it's not actually two different experiments, but rather it's one Monte Carlo simulation, counting the same thing happening two different ways?
That probably makes it more complicated, as the two values are now certainly correlated.

## What is the purpose of combining separate upper and lower limits into a total?

The purpose of combining separate upper and lower limits into a total is to get a more accurate and precise estimate of a quantity or value. By considering both the upper and lower limits, you can reduce the margin of error and have a more reliable result.

## How do you combine separate upper and lower limits into a total?

To combine separate upper and lower limits into a total, you need to add the upper limit and lower limit together and divide the sum by two. This will give you the average or mean value, which is the total.

## What are the potential sources of error when combining separate upper and lower limits into a total?

The potential sources of error when combining separate upper and lower limits into a total include measurement error, sampling error, and human error. It is important to minimize these errors as much as possible to get an accurate result.

## Can you combine more than two separate upper and lower limits into a total?

Yes, you can combine more than two separate upper and lower limits into a total. The process is the same - add all the upper limits and all the lower limits, then divide the sums by the number of limits to get the average or mean value.

## Why is it important to combine separate upper and lower limits into a total in scientific research?

Combining separate upper and lower limits into a total is important in scientific research because it allows for a more comprehensive and accurate analysis of data. It also helps to reduce the potential for bias and error, making the results more reliable and valid.

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