[R] What to do with this data?

Lucke, Joseph F Joseph.F.Lucke at uth.tmc.edu
Thu Apr 3 21:36:33 CEST 2008

First compute side-by-side boxplots for the two data sets.  You will see
that the PG group has one (189), maybe 2 (also, 52) extreme values
whereas the PG group has none.  The PG group will have a smaller median
than the PB group.  Means, st devs, and se's are legitimate statistics
but do not have the usual (normal theory) interpretation, at least until
you can account for or eliminate the extreme values. 

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of mika03
Sent: Thursday, April 03, 2008 2:16 PM
To: r-help at r-project.org
Subject: [R] What to do with this data?


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,

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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