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I have a question on how to compare two distributions. I'm currently a 2nd year biology grad student, and I'm trying to compare a parameter that evaluates the efficacy of a cell type. The math problem is this:

Let [itex]X[/itex] and [itex]Y[/itex] each be an average of three variables divided by an average of another three variables, e.g. [itex]X = \frac{x_1 + x_2 + x_3}{x_4 + x_5 + x_6}[/itex]. Assume that each [itex]x_i[/itex] are normally distributed.

How can I compare [itex]X[/itex] and [itex]Y[/itex] in terms of statistical significance? I am not sure if [itex]X[/itex] and [itex]Y[/itex] are normal distributions themselves. My guess is that they are not, since the product of two normal distributions results in a non-normal distribution?

edit: I just did some google searching and the term that describes X and Y are "ratio distributions". Is there a standard way to test for significance in this case?

Any help or suggestions would be much appreciated. Thanks!

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# Comparing normal distribution divided by normal distribution

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