[R] What to do with this data?

[mika03]

Hello,

This is not necessarily a question about R, but more about how we should
display our data in general. (Will we then use R to do that, once we know
what to do ;-) I received good replies about such things in the past on this
mailing list so I give it a go.

Here's what we did:
We showed a fairly large number of subjects search engine queries and
different possible search engine responses. We assumed that users would like
some our responses better than others and wanted to check this. Subjects
could rate a query/response pair on a scale from 0 (very bad response) to 10
(very good response).

Here are all the judgments we received for one particular class of response
to queries which we thought users would like:

Predicted-Good-0, 4 
Predicted-Good-1, 1 
Predicted-Good-2, 11 
Predicted-Good-3, 8 
Predicted-Good-4, 25 
Predicted-Good-5, 12 
Predicted-Good-6, 21 
Predicted-Good-7, 25 
Predicted-Good-8, 30
Predicted-Good-9, 52 
Predicted-Good-10, 189

And here are all the judgments we received for one particular class of
response to queries which we thought users would NOT like:

Predicted-Bad-0, 34 
Predicted-Bad-1, 23 
Predicted-Bad-2, 45 
Predicted-Bad-3, 60 
Predicted-Bad-4, 42 
Predicted-Bad-5, 50
Predicted-Bad-6, 21
Predicted-Bad-7, 20 
Predicted-Bad-8, 25 
Predicted-Bad-9, 19 
Predicted-Bad-10, 39 

Here's a small table listing number of observations, mean, standard
deviation and standard error:

Type, N, Mean, StDev, StErr
Predicted-Good, 378, 8.21693121693122, 2.47110906286224, 0.12710013550711
Predicted-Bad, 378, 4.5978835978836, 3.02059872953413, 0.155362834286119

The question we have are:

a) It doesn't seem like our data follows a standard distribution. Therefore
is it okay to calculate mean, standard deviation and standard error at all?

b) We initially created a figure plotting the mean and a bar around it
indicating standard deviation. Then somebody who knows more about statistics
told us we should display the mean and error bars around it "to depict a 95%
Confidence Interval, mean +/- 1.96*SE". But if we are doing this, aren't we
forgetting to mention vital parts of our data, that is that we indeed get
better means for "Good" responses, but that the individual data points are
all over the place (especially for "Predicted-Bad")? We would capture this
by showing standard deviation. 

c) And finally: What would be the best way to present this data anyway?


Thanks a lot!



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