Africa Foreign Investor Survey 2005 - unido

Annex 2.4
Sample size requirements
The required degree of confidence is 95 per cent. This means, that with a confidence of 95 per cent, the observed
percentages are either plus or minus 5 per cent away from the unknown population parameter. The formula that
can be used to determine the minimum required sample size in order to fulfill these requirements is the following
(Cochran, 1963):
n z2 1–/2(p(1 – p))
For z=1.96, p=0.05, d=0.05 we get a minimum required sample size of n 384, regardless of the unknown size of
the whole target population. Another formula that includes the size of the whole target population is available but
it would only produce results for the minimum required sample size of less than 384 responses. 2 Given the chosen
parameters, the solution for n is thus the safest.
d 2
As depicted in table 2.1, the sample size of 1,216 exceeds the minimum required sample size by far. Even when opting
for more rigid criteria, e.g. by reducing the acceptable sampling error to 4 per cent or even 3 per cent, we would still
get minimum required sample sizes (600 or 1,067 respectively) smaller than the actual sample size. By the same token,
the confidence could be reduced to 99 per cent, which would require a minimum sample size of 664 respondents for
an acceptable sampling error of 5 per cent or 1,037 for a sample error of 4 per cent.
1
1 n is minimum sample size; z is the z-value of the normal distribution (equals 1.96 for 95 per cent required confidence); p is the estimated
proportion of answers for a dichotomous variable (“Yes” or “No”), the worse case is a prediction of 50 per cent i.e. the sample size needs to
be higher; d is the acceptable sampling error.
2
n
n corrected =
1 + (n–1)
N
The nature of the formula is as such that n corrected cannot be greater than n, with N going towards infinite. The formula yields meaningful results
when the total population N is “small”.
Annex
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