Rejection of Abnormal Data

In our discussions so far, we have only considered the uncertainty in the experimental data due to the randomness of radioactive decay. But there may also be 

What about the question of whether a detector or counting system is working properly For example, the data in Table 18.2 do not exactly match a Poisson or normal distribution. Was the counting system malfunctioning One parameter that we can calculate that will help us answer such questions is x (chi squared). Formally, 

2 Setting Upper Limits When No Counts are Observed 

Suppose your experiment failed to detect a type of decay you were seeking What can you say about its occurrence The simplest answer is what is termed the one-event upper limit. You assume that you had detected one event, and calculate the resulting decay rate, cross section, and the like, taking into account detection efficiencies, solid angles, and so forth. 

A more sophisticated answer can be obtained by using the properties of a Poisson distribution. The probability of observing n events if the mean value is p is given as  

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