Random Combinations?

[Sarah van Mastrigt]

Hi All-

I am stuck! I need to create and test an intrinsic (rather than theoretical)
null distribution for some of my variables. I understand that I should use
a randomization/permutation test to do this, but am not sure how to proceed
as this is new territory for me, and think it might require specialised
syntax in SPSS...

Some background: I am looking at the composition of groups (based on the
combination of ages, genders, etc of group members). Groups vary in size
from 2-20 members. In my data file, each case represents an act committed
by the group, and several categorical variables represent attributes of the
indivdiuals involved i.e., in an group with 3 members, sex1, sex2, sex3.
Using these, I have computed group-level, nominal composition variables for
all events involving 2 or more individuals as follows:

With regard to gender (1=male, 2=female), I have coded groups into three
categories based on the observed combination of the group members'
attributes (1=all male, 2=all female, 3=mixed sex).

With regard to age (1=child, 2=youth, 3=adult) composition, I have coded
groups into seven categories based on the observed combinations of members'
attributes(1=all child, 2=all youth, 3=all adult, 4=child+youth,
5=child+adult, 6=youth+adult, 7=child+youth+adult).

The observed frequency of these compositions suggests that homogeneous
groups are more common than mixed groups (for groups of all sizes), but of
course, I need to know whether this represents an actual preference for
group members similar to oneself, or whether this result would be expected
based on the proportions of attributes in the data, and the size of the
group.

For the gender calculations I computed the expected frequencies (seperately
for groups of size 2-6) by hand using the binomial distribution, and the
overall proportion of males and females in the data (p male=.784). I had
then planned to do a chi-square goodness of fit test to compare O and E,
but I have several expected frequencies for the all-female groups of less
than 1, which obviously causes problems for the test (not to mention the
fact that these hand calculations are taking forever)! I haven't yet
attempted the age calculations.

So- what I am hoping is that, instead, there is a way that I can get SPSS
to create an intrinsic null distribution for these composition variables,
by performing many repetitions of random combinations of the attribute
variables for groups of size n, which I could then compare to my observed
distribution? i.e., 10,000 random combination of males/females or
children/youths/adults for groups of size 2, 3, 4, 5....etc?

Any suggestions would be greatly appreciated, as I am WAY out of my depth
here!

With thanks!

Sarah


 --
Sarah van Mastrigt
Doctoral Researcher
Institute of Criminology
University of Cambridge