I've run into a simple problem - but no idea how to access it correctly.
I've 85 people asked concerning their social network; first example: how many friends do you have. Second, what gender is each of this friend. Then I do a table which displays the average number of female friends and the average number of male frieds of each interviewed person: separated for the male and female interviews and for all together. I got the following table:
$$ \begin{array} {rrrrr}
&&\text{avg no} &&\text{answers}& & \text{Sdev in}& \\
&&\text{of friends}& & & &\text{no of friends}& \\
& & m &f& m& f& m& f \\
\text{Sex of Interviewed}& M &5.57 &4.61& 54& 54& 3.543& 2.609 \\
& F &4.84 &6.42& 31& 31& 2.734& 3.264 \\
& All& 5.31& 5.27& 85& 85 &3.273& 2.978
\end{array} $$
and I see, that for the male interviewed ("M") the avg number of male friends is higher than the avg number of female friends, and for the female interviewed ("F") it is oppositely. Now what test for significane of the difference were correct here?
I could t-test for the means-difference in the M and F-group separately, but this seems a loss of infomation to me. Or the table suggests something like a chi-square; but how should I apply it here?
[update]
Another approach is to determine the percent of male friends for each respondents, and then determine the average of this percentages for male and female respondents separately:
$$ \begin{array} {cccc}
&&\text{avg "% of }&N&\text{sdev of} & \\
&&\text{friends are male"}& &\text{"%..."} & \\
\text{sex of respondent}&M&52.746&54&21.087& \\
&W&40.868&31&17.235& \\
&all&48.414&85&20.487& \\
&&&&& \\
&f=7.101&&&& \\
&sig=0.009&&&& \\
\end{array} $$
The comparision of that means is significant due to the f-test - but is this a better sensical approach?
[update 2]
This another idea to use the chisquare-rationale. I (re-)expand the averages to the sums: "sum of male/female contacts per respondent" and compute the chisqare based on the indifference-table.
$ \qquad \small \begin{array} {c | cc |c} \text{Sum} &\text{m} &\text{f} &\text{all} & \\ \hline \text{M} &301&249&550& \\ \text{F} &150&199&349& \\ \hline \text{all} &451&448&899& \\ \\ \\ \text{Indifference} &\text{m} &\text{f} & \\ \text{M} &275.92&274.08& \\ \text{F} &175.08&173.92& \\ \\ \\ \text{Residual} &\text{m} &\text{f} & \\ \text{M} &25.08&-25.08& \\ \text{F} &-25.08&25.08& \\ \\ \\ \text{Chisq} &\text{m} &\text{f} & \\ \text{M} &2.28&2.3& \\ \text{F} &3.59&3.62& \\ \end{array} $
$ \qquad \chi^2 =11.79$
On the other hand, here -I feel- is the chisquare "inflated" because we have such a big N (which is actually an overall sum). Then the significance should be considered critically. Then gaian - what is the most sensical one?
[update 3]
Here I show a table using an "homophily"-index: 0 means completely heterophil, 1 means completely homophil (in terms of same sex between respondent and his reported friends - requires at least one response/one friend per respondent)
$ \qquad
\begin{array} {c|cc|c}
&&\text{avg of hom} &\text{sdev} &\text{semean} &\text{N} & \\
\hline
\text{sex of respondent} &\text{M} &0.53&0.21&0.03&54& \\
&\text{F} &0.58&0.16&0.03&30& \\
\hline
&\text{All} &0.55&0.19&0.02&84& \\
&&&&&& \\
&\text{f=1.297} &&&&& \\
&\text{sig=0.258} &&&&& \\
\end{array}
$
I've got another test-value f and another significance level; well here I ask, whether male and female respondents are differently homo/heterophil which is another question than before. However, it is more precisely focused to an interesting indicator. The semean shows, that (only) female respondents seem to deviate significantly (5%-level) from indifference (which means hom=0.5)
It might, anyway, have a little drawback in that the index for each respondent is based on another number of responses and thus has a more or less reliable value for each of that respondents. But this seems to be a too sophisticated problem here, so I think, I'll stay with that type of measuring.
Thanks so far to all respondents here!