Muslim Life in Germany - Deutsche Islam Konferenz

How many Muslims live in Germany? 55
background living in the households are extrapolated on the
basis of the data from the Ausländerzentralregister (AZR, Central
Register of Foreigners). This extrapolation is carried out using
the standard procedure for calculating confidence intervals
in the social sciences (Kühnel/Krebs 2001: 237 ff.). This interval
covers the number range in which the targeted population value
can be expected to lie with a specified probability. While the
interval estimation procedure does not yield an exact figure - in
this case the exact number of Muslims - it is still more reliable
due to the fact that it is far more likely that an interval will contain
the desired population value than that an estimated value
will be exactly correct. 25 The width of the confidence interval
depends in part on the level of significance α which is chosen.
In keeping with the standards of the social sciences, the level
of significance has been set at α = 5 per cent for the purposes of
this study; i.e. the probability that the desired value lies within
the calculated interval is 95 per cent. 26 The width of this interval
also depends on the sample size that is being targeted. A higher
number of cases also results in a higher level of accuracy.
25 Confidence intervals are generally calculated on the basis of a simple random
sample in accordance with statistical assumptions. This criterion is not strictly
fulfilled by the data used here due to the fact that the information on household
members has been drawn from a randomly selected interviewee. As a result of
the cluster effect which this entails, it is therefore possible that the calculations
made here have resulted in confidence intervals which are too small. Taking
into account the information on all household members when making extrapolations
is standard practice in the social sciences for other studies as well, e.g. the
microcensus (see Federal Statistical Office 2008a: 4).
26 The formula for calculating a 95% confidence interval for the share is:
p+ p(
1 p)
p1,96
−
± 1,
9 6
n
(cf. Fahrmeir et al 2003: 390 f.; Kühnel/Krebs 2001: 248; Schumann 2000: 193).