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My problem is how to measure the effect of a user's participation in forums. I calculate the user's participation as the number of discussions that user posted. My hypothesis that a users' participations are not independent of each other and that the users' participations depends on the group, that is a user's behaviour changes based on the group.

For example my data will be like this:

| users | Forum 1 | Forum 2 | Forum 3 |
| u1    | 10      | 5       | NA      |
| u2    | 6       | NA      | 4       |
| u3    | 5       | 2       | 3       |

I want to be able to prove that u1 behaviour is different in forum 1 than in other forums and the particular thing about Forum 1 is that users in Forum 1 tend to have a higher value of the participation.

Does that make sense? What are the statistical techniques that I can use for verifying my hypothesis?

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    $\begingroup$ For some thoughts on a closely related matter, see the thread at stats.stackexchange.com/questions/13858/…. (BTW, I haven't a clue what your example data mean.) $\endgroup$ – whuber Oct 9 '11 at 17:52
  • $\begingroup$ sorry for the example data ... I've edited the post and I hope it's clearer now $\endgroup$ – Gawesh Oct 9 '11 at 20:55
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I would utilize rank the absolute number of postings in each forum. By this you remove the difference in the participation levels (for example Forum 1 has generally a lower participation than Forum 2). Your example becomes

| users | Rank Forum 1 | Rank Forum 2 | Rank Forum 3 | 
| u1    | 3            | 2            | NA           | 
| u2    | 2            | NA           | 2            |
| u3    | 1            | 1            | 1            |

So for example user u3 has the lowest participation rank in both Forum 1,2 and 3 while user u1 has the highest in Forum 1.

Before ranking you have to do two things:

  • Impute the NAs (By mean, by median or just set it to 0 etc. )
  • Formulate your Hypothesis. An example would be $ H_0=\{\text{mean Rank Forum 1} = \text{mean Rank Forum 2}$) which tests if a user that generally is among the highest or lowest posting participants in Forum 1 also participates often or rarely in Forum 2.
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