Which is the correct hypothesis test formulation for this problem?

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?

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Hi there. Does it matter which X precedes the particular Y as the last sentence in your second paragraph suggests this is not important. But if different Ys are correlated with different Xs, then which X occurred becomes very important. –  Michelle Mar 15 '12 at 6:50
Sorry for using the answer field, as the account that I used to open this thread was unregistered and I no longer have access to it. I also cannot answer below @Michelle 's post for the same reason. It is particularly important for this problem that $Y_{i,j}$'s are preceded by $X_i$. This is also how $Y_{i,j}$'s are being defined. So, as they are not occuring at the same time with the $X_i$, I cannot calculate correlations. –  DSCilek Mar 15 '12 at 10:33
I merged your two accounts: you should have access to this question again. –  whuber Mar 15 '12 at 15:35
If the probability of a certain Y is associated with which X precedes it, or the number of times a certain X occurs, then the Xs need to be taken into account. Can you provide more detail in your problem, if possible could you tell us what the Xs and Ys are? –  Michelle Mar 15 '12 at 16:13
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