Educational Research - the Ethics and Aesthetics of Statistics

100 E. Hemelsoet
a very informative schematic overview, see Appendixes 1 and 2). Three examples
are given though, as they are paradigmatic for the problems related to estimating
irregular migrants.
Multiplier methods calculate the size of the unknown total from the size of a
known subtotal by use of an appropriately estimated multiplier. The use of multipliers
to derive the size of a hidden population from the size of a known subtotal
of that population is probably the most common way of estimating an unknown
population. The problem of giving adequate estimations is then translated in finding
the right multiplier (Vogel, 2002). An example of using the multiplier method
for estimating irregular migrant numbers is provided by a recent study in Belgium
by Van Meeteren, Van San, and Engbergsen (2007). In this study, police data on
arrested criminal foreigners is combined with data from in-depth interviews with
120 irregular migrants. The police data on criminal offences committed by foreigners
without legal residence is compared with the ‘crime rate’ among the migrants
that were interviewed. Three assumptions are internal to this method, assumptions
that modify the quality of the outcomes. First, there is the expectation that the crime
rate derived from the interview sample is a good indicator for the actual crime rate
among the target population. Second, the estimate is based on the assumption that
the reported crime figures are a good indicator for total crime figures. Thirdly, the
sampling group is expected to be representative of the total population of irregular
migrants. Concerning the first assumption, it can be argued that long in-depth
interviews lead to sufficient trust between the interviewer and the respondent so as
to retrieve realistic answers. As regards the second assumption, things get slightly
more complicated. It is not clear to what extent police data on arrests cover the
total amount of criminal offences that are actually committed. It is very likely that
the police do not detect all cases of crime and the resulting estimate is therefore
unreliable (Kraler & Vogel, 2008). The third assumption implies problems concerning
generalisation, as the sampling group is rather small and it is impossible
to retrieve a randomised sample if the composition of the total group is largely
unknown.
Similar problems arise with the capture-recapture method. This method is used
in biology to estimate animal populations in the wild. The basic idea is to develop a
multiplier through repeated sampling of the same population. Estimating a fish population
goes as follows: first, capture 1,000 fish and mark them before releasing them
again. Capture another 1,000 fish and look how many are marked. If for example 100
are marked, the 1,000 fish will statistically make up approximately 10% of the total,
i.e. 10,000 fish. In the Netherlands Van der Leun, Engbersen, and van der Heijden
(1998) have used this principle to estimate numbers of irregular migrants. Their
‘repeated capture method’ is based on a dataset that tries to apprehend numbers of
illegal immigrants in Amsterdam, Rotterdam, The Hague and Utrecht, (the four big
Dutch cities) during 1995. Using the number of persons captured and arrested again,
it is argued that the number of people who will show up again follows a probabilistic
distribution called the Poisson distribution (λ). On the basis of the available data,
the crucial parameter determining the Poisson distribution can be estimated. This