2376 intergenerational mobility: methods of analysis

a farmers background, whereas only 33.5 per
cent of the people in class I II are recruited
from that class. However, when we look at Table
3a, we see that 29.0 percent of the people with a
farmers background become farmers them
selves, but that 61.3 percent of the people with
an origin in class I II end up in that same
class. An explanation for this can be derived
from the column and row totals in Tables 3a
and 3b, respectively: Class I II expanded from
15.5 percent in the origin distribution to 28.4
percent in the destination distribution, while the
relative size of the farmer class declined from
19.0 to 6.3 percent. This brings us to the dis
similarity index.

Dissimilarity Index

If we look upon the class distribution of desti
nations as an opportunity structure, we can say
that economic and demographic changes in
society contribute to the dissimilarity between
the contemporary opportunity structure, i.e.,
the destinations, and the class origins of current
workers. Looking at Table 1, it is evident that
the decline in agricultural jobs is balanced by an
increase in non manual positions. A summary
measure of these countervailing changes is the
index of dissimilarity between the distribution
of origins and the distribution of destinations:


i 1

In Table 4 this basic set is presented for the
data from Table 1.
Goldthorpe (1980: 77) described odds ratios
as indicating how unequal the outcomes are of
competitions between persons of different ori
gins to achieve or avoid certain jobs. For exam
ple, in Table 1, 95 men with origin I II go to
class I II and 14 go to class III. The odds of
going to class I II instead of class III from
origin I II is 95/14 6.79. For people from
class III background, this figure is 26/9 2.89.
Although men from both origins are more
likely to end up in class I II instead of class
III, the odds are 2.35 (6.79/2.89) times greater
for men from origin I II than for men from
origin III. Were the odds for both origins
equal, the odds ratio would have equaled one.
If all the odds ratios in the table are equal to
one, we can speak of perfect mobility, i.e.,
destinations do not depend on origins. It is
clear from the pattern in Table 4 that the odds
ratios in the diagonal cells are much higher
than the other ones, indicating that the propen
sity for men to stay in their own class is much
higher than moving to another class.
An important feature of the odds ratio is that
it is not dependent on the marginals: when
all frequencies in a certain row or column are

j fi fij

is a measure of net change. It does not
take into account the actual gross flows in the
mobility table, only the net outcome of all
flows. can be interpreted as the minimal pro
portion of people who have to be reclassified to
make the origin and destination distributions
identical (for Table 1 this is 0.182). Above we
saw that the gross change (mobility rate) was
0.660. A high mobility rate results if the desti
nation distribution differs substantially from
the origin distribution or if origins and destina
tions are statistically independent, that is, if the
conditional distributions of destinations are the
same for all origins. A low mobility rate results
if there is a similarity of origin and destination
distribution and if the association between
origin and destination is strong. In the analysis
of mobility, these two elements have to be
separated: mobility due to dissimilar marginal
distributions of origins and destinations (known
as structural mobility) and mobility due to
association between origins and destinations.

Mobility can also be described in terms of odds
ratios. It is possible to compute many odds
ratios from an I J table, but the association
in the complete table can be fully described
by the odds ratios of a basic set of subtables:
the 2 2 subtables formed from adjacent
rows and adjacent columns. There are (I 1)
( J 1) basic subtables. The formula for the
(adjacent) odds ratios is: