New statistics problem

At least one good thing can be said about my data analysis: I’ve now specified the actual question which needs to be tested. But I’m still not entirely certain how I should test it. Suggestions much appreciated.

I’ve done a study of what players talk about when playing different types of video games.
An example: One group played three games and each spoken statement was coded YES/NO on a number of variables. For instance, a statement could be: “Critique of other player” YES or NO.

One group made 481 statements playing Game 1, 670 statements playing Game 2, and 328 statements playing Game 3.
In this case “Critique of other player” occured 0 times in Game 1, 0 times in Game 2, and 7 times in Game 3 (i.e. 0%, 0% and 2,1%).

The hypothesis is that game type affects (verbal) behaviour. Thus, the null hypothesis is: The percentages are the same for all three game types.

How do I test this?

(I have various resource persons working on this and will post any solution that they come up with).

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