Statistical anisotropy calculation

[kop442000]

Hi guys, this is not homework, but just something my supervisor asked me to think about, but I'm not sure how to start.

Homework Statement

How many events are needed to get an anisotropy of 9% at 9 sigma. (We were talking specifically in the context of Cosmic Rays).

I just want a pointer on how to start to think about it really. For a start, I'm not entirely sure what is mean by a % anisotropy. How is this quantified?

Any pointers would be gratefully received...

 

[NateD]

Anisotropy is a measure of the degree of non-uniformity of the distribution of an attribute in space. In this case, it refers to the degree of non-uniformity of the distribution of cosmic rays in space. The anisotropy of a given set of cosmic rays can be quantified by calculating the ratio of the number of events in a certain direction compared to the total number of events. For example, if there are 10 events in a certain direction and 100 total events, then the anisotropy would be 10%. In order to get an anisotropy of 9%, you need to have a ratio of 9/100 or 0.09. This means that for every 100 events, there must be 9 events in the desired direction. To determine how many events are needed to achieve this ratio, you simply need to solve for the total number of events. Doing some basic algebra, we can see that if x is the total number of events, then 0.09x = 9, so x = 90. Therefore, you would need at least 90 events to achieve an anisotropy of 9%. The 9 sigma refers to the level of confidence you have in the anisotropy result. A 9 sigma result means that you are 99.9999% sure that the result is true. This does not affect the number of events needed to achieve the desired anisotropy, but it does affect the accuracy of the result.