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A probability provides a quantitative description of the likely occurrence of a particular event.

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Compare the difference of two probabilities or a ratio of probabilities?

I would like to compare the probability of getting a particular length range in two different conditions. e.g. $P1=P(0.1<L<0.2, {\rm fertilizer\ A})$, $P2=P(0.1<L<0.2, {\rm fertilizer\ B})$. … differences for various L and if possible to use a statistical test which tests the significance of probability differences for just one range and not overall (what a t-test does). …
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