Date:         Mon, 26 Oct 1998 09:50:19 +0100
Reply-To:     Rolf Kjoeller <rolf.kjoeller@GET2NET.DK>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From:         Rolf Kjoeller <rolf.kjoeller@GET2NET.DK>
Subject:      Re: Is my selection procedure random ?
Content-Type: text/plain; charset="iso-8859-1"

Hi SPSS-X
 
- Paul Newton and I have been corresponding a bit offlist about his samplingquestion. I think what we have come up with is in line with the suggestions given by David F. Greenberg and Dale Pietrzak:
 
- since the sampling is done with replacement, you can see the selection of one particular word as a binomialexperiment with n=2468 and pii=1/4724. The following are the probabilities of selecting one particular word 0 to 10 times in such an experiment. cpx are cummulated probabilities, p(x<=X), while px is p(x=X). Judging from this, selecting one particular word 10 times is rather unlikely:
 
x    cpx    px
0 ,5930 ,5930
1 ,9029 ,3099
2 ,9839 ,0809
3 ,9980 ,0141
4 ,9998 ,0018
5 1,0000 ,0002
6 1,0000 ,0000
7 1,0000 ,0000
8 1,0000 ,0000
9 1,0000 ,0000
10 1,0000 ,0000 
 
Paul has suggested, and I tend to agree, that you can use these probabilities to build a table with expected numbers of  words drawn x times, and actual numbers of  words drawn x times, and then do a chisquaretest:
 
x        sample   expected
0        n11        n12
1        n21        n22
2        n31        n32
3        n41        n42
...        ...         ...
10+    n101      n102
 
Does this make sense to you?
 
Rolf Kjoeller
 
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