The problem I am working on can be formulated as follows:
$S$ is the set of events $X_i$'s where each $X_i$ has occured different number of times. Also, if you think this process in turns; in each occurance of $X_i$, it is followed with one of the events $Y_{i,j}$'s. What I want to investigate is whether one -or any numbers- of $Y_{i,j}$ is occuring significantly more often than others.
I first thought of calculating the mean and variance of the number of times that $Y_{i,j}$'s occur, seperately for each $X_i$. After that, I could perform a t-test where $t={( {mean}_i -Y_{i,j} )}/ {stddev}_i $. And if any $Y_{i,j}$ was significantly more then this mean with an alpha of 0.05, then I would conclude that the proportion of occurance of this $Y_{i^* , j^*}$ is significantly more often than others.
Then I noticed that it might be required to divide stddev with root of $n$, where $n$ is the number of occurance of any given $X_i$.
After that, I again doubted this conclusion, thinking that a hypothesis tests based on proportion formulas might be better representative of the problem at hand.
Since I am not a statistician, I thought of asking for advice on this issue. What approach do you think, would be appropriate for this problem?
Xprecedes the particularYas the last sentence in your second paragraph suggests this is not important. But if differentYs are correlated with differentXs, then whichXoccurred becomes very important. – Michelle Mar 15 '12 at 6:50Yis associated with whichXprecedes it, or the number of times a certainXoccurs, then theXs need to be taken into account. Can you provide more detail in your problem, if possible could you tell us what theXs andYs are? – Michelle Mar 15 '12 at 16:13