# Quantifying the statistical error in a counting experiment

• JoePhysicsNut
In summary, to find the statistical error in a counting experiment with two decay options, the branching ratio BR_a can be calculated by dividing the number of decays in option A by the total number of decays. If the experiment is conducted multiple times, the results for BR_a will follow a binomial distribution. If there is a fixed number of decays, N_a and N_b can be treated as independent Poisson processes, while if there is a fixed denominator, N_a will come from a binomial distribution. The standard statistical error can be calculated as N_A+ - sqrt{N_A}.
JoePhysicsNut
I need to find the statistical error in a counting experiment. Specifically, a decay can proceed via option A or option B and I need to find the branching ratio BR_a=(N_a)/(N_a+N_b). If I were to do this counting experiment multiple times my results for BR_a would follow the binomial distribution since there are two decay channels.

How do I quantify the statistical error in my result given that I conduct the experiment only once?

Do you have a fixed number of decays ("I take data until I have 100 decays in those two channels")?
No => you can treat N_a and N_b as the result of independent Poisson processes.
Yes => the denominator is fixed, and N_a comes from a binomial distribution.

The usual statistical error gives N_A+ - sqrt{N_A}.

## 1. What is a counting experiment?

A counting experiment is a type of scientific experiment where data is collected by counting the number of occurrences of a specific event. This can include counting particles, cells, or any other measurable quantity.

## 2. Why is it important to quantify the statistical error in a counting experiment?

Quantifying the statistical error in a counting experiment allows researchers to determine the accuracy and reliability of their data. It also helps to identify any potential sources of error and improve the overall quality of the experiment.

## 3. How is the statistical error in a counting experiment calculated?

The statistical error in a counting experiment is typically calculated using statistical methods such as standard deviation, confidence intervals, or hypothesis testing. These methods take into account the sample size, variability of the data, and the level of confidence desired.

## 4. What factors can affect the statistical error in a counting experiment?

Several factors can affect the statistical error in a counting experiment, including the accuracy of the counting method, the sample size, and the variability of the data. Other factors such as experimental design, human error, and equipment limitations can also contribute to the statistical error.

## 5. How can the statistical error in a counting experiment be reduced?

The statistical error in a counting experiment can be reduced by increasing the sample size, using more precise counting methods, and minimizing sources of variability. Proper experimental design and careful data collection can also help to reduce the statistical error.

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