How can I find the strength of relationships between rows and columns in a non-mutually-exclusive contingency table? I'm an English teacher doing some research, and need help finding the right statistical tool. Here's the basics:
I have transcribed hours of student conversation from audio recordings as they played a game. Then I went through the transcripts and looked for patterns/themes of conversation that often emerged. I ended up with 9 conversational "topics" I'll call them for simplicity. Those 9 topics are the rows in my table.
I then went though the transcripts a second time, and for each time a student spoke (we call these "speaker turns") I tagged it with a keyword known as a "speech act" (which is basically the "function" or "goal" of the utterance, such as "apologize", "request", "acknowledge", "greet" etc.) So there are 39 speech acts that make up the top of the columns of my table.
So each "subject" in my sample isn't a person, but an utterance. Each utterance falls within one exclusive conversation theme, but may have more than one Speech Act or purpose behind it, which is where the overlap can happen.
For example, if a student says, "No thanks, I have that already," within a conversation about "game items" (one of the 9 possible themes mentioned above) they are both "declining" an offer and "explaining" why, so two speech acts are attached to this one utterance/subject. This kind of multiple-meaning utterance happens quite often, especially in cases of sarcasm, jokes, or compound sentences.
My goal is to try and determine the relationship between the speech acts and the topics, (if one exists or not, and if possible the significance of that relationship)
The problem I'm having is getting over the non-exclusive part, as it seems Chi-square tests are no good, and even Fisher's Exact can't handle it.  I'm no statistician, and I'm at my wits end here trying to find a way to provide statistical evidence to my findings.

This is not an anwer, but the comment box is too small ...
You should not present your data as a contingency table, but start with the data in a format like
          9 topic columns      39 speech acts columns

utterance 1
utterance 2
utterance 3
...
The columns will be indicators, that is 0's and 1's. Then there are many possibilities for an analysis, maybe starting with some form of correspondence analysis. I don't have the time at the moment, but maybe you could augment your question with information like how many utterances in your data (corresponding to number of rows in above table)
